Unit Conversions in Science and Math

Conversions

• 1 m = 100 cm = 1000 mm
• 1 km = 1000 m
• 1 mile = 5280 feet = 1609 meters
• 1 mile/hour = 1.47 ft/second
• 1 inch = 2.54 cm
• 1 foot = 30.48 cm = 12 inches
• 1 meter = 3.2 feet
• 1 foot = 12 inches

Energy

• 1 calorie = 4.187 J = 0.003968 Btu
• 1 Btu = 252 cal = 1055 J
• 1 joule = 1 kg · m/s²

Length

• 1 micron = 0.001 mm
• 1 inch = 2.54 cm = 25.4 mm
• 1 foot = 30.48 cm = 12 inches
• 1 yard = 3 feet
• 1 mile = 5280 feet = 1609 meters
• 1 nautical mile = 0.868 US miles

Area

• 1 square inch = 6.452 square cm
• 1 square foot = 144 square inches = 0.09290 square meters
• 1 square yard = 9 square feet

Volume

• 1 cubic centimeter = 1 milliliter
• 1 cubic inch = 16.39 cubic centimeters
• 1 cubic foot = 1728 cubic inches = 0.02832 cubic meters
• 1 liter = 1.057 quarts (US)

Temperature

• To convert to absolute temperature scales: oR = oF + 460, oK = oC + 273
• Tc = Tf - 32/1.8, Tk = Tc + 273, F = 460 + R

Force

• 1 kilogram-force = 9.80665 newton [N]

Radiation

• 1 rad = 10⁻² gray, 1 rem = 10⁻² sievert, 1 curie = 3.7 × 10¹⁰ becquerel
• 1 becquerel = 1 disintegration/second

Density of Water

• 1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)

Light

• 1 candela = 1 lumen/steradian
• 1 footcandle = 10.76 lux

Physical Constants

• acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
• velocity of light = 3.0 × 10⁸ m/sec
• Planck's constant = 6.626 × 10⁻³⁴ J·sec
• Avogadro's number = 6.024 × 10²³/gram-mole

Boolean Postulates

• Area of a rectangle: Area = length × width
• Area of a square: Area = s², where s = side
• Area of a triangle: Area = (1/2) b × h, where b = base and h = height
• Area of a circle: Area = π × r², where r = radius

Volume of Shapes

• Rectangular solid: V = l × w × h
• Cube: V = a³
• Cylinder: V = πr²h
• Prism: V = B × h
• Sphere: V = (4/3)πr³
• Pyramid: V = (1/3) × B × h

Trigonometric Functions

• C² = a² + b² - 2ab cos C
• A/SinA = b/SinB = c/SinC

Energy and Work

• Kinetic energy: K.E. = ½ mv²
• Potential energy: P.E. = mgh
• Elastic potential energy: P.E. = ½ kx², where k = spring constant and x = amount of compression

Force and Friction

• A newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s²
• Tension forces are required to pull an object (opposite of compression)
• Spring force exerted by a compressed or stretched spring
• Frictional force: F = μN, where μ = coefficient of friction and N = force acting on the surface

Statistics

• Mean, median, mode, and standard deviation are measures of central tendency
• Standard deviation (S): a measure of the average distance of all observations from the mean
• Variance: Σ(X-Xav)²/N
• Standard deviation (S) = √(X-Xav)²/N
• 1 standard deviation = 68% of the data set
• 2 standard deviations = 95.45% of the data set
• 3 standard deviations = 99.73% of the data set

Hypothesis Testing

• Null hypothesis (H0): no significant difference between the population
• Alternative hypothesis (H1): significant difference between the population
• Type I error: rejecting the null hypothesis when it is true (α)
• Type II error: failing to reject the null hypothesis when it is false (β)

Unit Conversions

• 1 quart = 0.9463 L
• 1 US gallon = 3.785 L
• 1 ft³ = 28.317 L
• 1 psia = 6.895 kN/m²
• 1 atm = 760 mm Hg = 14.7 psi
• 1 bar = 14.5 psi = 0.98 atm = 105 N/m²
• 1 mm Hg = 0.01934 psia

Mass and Weight

• 16 ounces = 1 lb
• 1 g = 1000 mg
• 2.205 lb = 1 kg
• 1 ton (US) = 2000 lb
• 1 tonne (Metric ton) = 1000 kg
• 1 dram = 1771.85 mg

Heat Capacity

• 1 Btu/lb/°F = 1 cal/g/°C
• 1 cal/g/°C = 4187 J/kg·K

Force, Pressure, or Stress

• 1 pound-force = 4.45 Newtons
• 1 pound-force/square inch = 6.89 Kilopascals

Illumination

• 1 foot-candle = 10.76 lux
• 1 foot-lambert = 3.426 candela/square meter

Length

• 1 inch = 25.4 millimeters
• 1 foot = 0.305 meters
• 1 yard = 0.914 meters
• 1 mile = 1.61 kilometers

Area

• 1 square inch = 645.2 square millimeters
• 1 square foot = 0.093 square meters
• 1 square yard = 0.836 square meters
• 1 acre = 0.405 hectares
• 1 square mile = 2.59 square kilometers

Volume

• 1 fluid ounce = 29.57 milliliters
• 1 gallon = 3.785 liters
• 1 cubic foot = 0.028 cubic meters
• 1 cubic yard = 0.765 cubic meters

Temperature

• Fahrenheit to Celsius: (°F - 32) / 9
• Celsius to Fahrenheit: (°C × 9) / 5 + 32
• Celsius to Kelvin: °C + 273
• Fahrenheit to Rankine: °F + 460

Energy

• 1 British Thermal Unit (Btu) = 1055 J
• 1 faraday = 9.65 × 10⁴ coulombs
• 1 g-cal = 4.19 J
• 1 ampere-hour = 3600 coulombs
• 1 kwh = 3.6 × 10⁶ J

Standards

• STP (physical science) = 0°C and 1 atm
• STP (ventilation) = 70°F and 1 atm
• STP (industrial hygiene) = 25°C and 1 atm
• Air density = 0.075 lb/ft³ at 70°F and 1 atm

Density of Water

• 1 g/cm³ = 1.94 slugs/ft³
• Weight density = 62.4 lb/ft³
• 1 US gallon of H₂O = 8.345 lb

Angles

• 1 radian = 180°/π

Light

• 1 candela = 1 lumen/steradian
• 1 foot-candle = 10.76 candela/m² = 10.76 lux

Magnetic Fields

• 1 tesla = 10,000 gauss

Physical Constants

• Acceleration of gravity = 32.2 ft/s² = 9.8 m/s²
• Velocity of light = 3.0 × 10⁸ m/s
• Planck’s constant = 6.626 × 10⁻³⁴ J·s
• Avogadro’s number = 6.024 × 10²³/g-mol

Radiation

• 1 rad = 10⁻² gray
• 1 rem = 10⁻² sievert
• 1 curie = 3.7 × 10¹⁰ becquerel
• 1 becquerel = 1 disintegration/s

Mechanics

• Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration, and h is the height above the earth's surface
• Elastic Potential Energy (P.E.) = ½kx², where k is the spring constant and x is the amount of compression
• Force (F) = ma, where m is the mass of the object and a is the acceleration
• Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction perpendicular to the surface

Statistics

• Histogram: a graph used to display the frequency distribution of the data
• Mean: the average value of a data set, calculated using ΣXn/n
• Median: the central number of a data set, where if there are two numbers in the middle, the median is the average of those two numbers
• Mode: the number in a data set that occurs most frequently
• Left Skewed: Mean < Median < Mode, where the majority of values are at the right of the Mean
• Right Skewed: Mode < Median < Mean, where the majority of values are at the left of the Mean
• No Skew: Mean = Median = Mode, where the distribution is symmetrical

Standard Deviation

• Standard Deviation (S) = √(Σ(X-Xav)²/N)
• Variance = Σ(X-Xav)²/N
• Coefficient of Variation (CV) = S/Xmean
• Relative Standard Deviation (RSD) = S/Xmean

Hypothesis Testing

• Null Hypothesis (H₀): no significant difference between the populations, where if any observed difference is due to sampling or experimental error
• Type I Error: rejecting the null hypothesis when it is true, where there is no actual difference between the means
• Type II Error: failing to reject the null hypothesis when it is false, where there is an actual difference between the means

Conversions

• 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm) = 1,000,000 microns
• 1 kilometer (km) = 1000 m
• 1 mile = 5280 feet = 1609 m
• 1 mile per hour = 1.47 feet per second

Length

• 1 inch = 2.54 cm
• 1 foot = 30.48 cm = 12 inches
• 1 meter = 3.2 feet

Area

• 1 square inch (sq.in.) = 6.452 square centimeters (sq.cm) = 6452 square millimeters (sq.mm)
• 1 square foot (sq.ft) = 144 sq.in. = 0.09290 square meters (sq.m)
• 1 square yard (sq.yd.) = 9 sq.ft

Volume

• 1 cubic centimeter (cm³) = 1 milliliter (mL)
• 1 cubic inch (in³) = 16.39 cm³
• 1 cubic foot (ft³) = 1728 in³ = 0.02832 cubic meters (cu.m)
• 1 liter (L) = 1.057 quarts (US)

Temperature

• To convert to absolute temperature scales: oR = oF + 460, oK = oC + 273
• Temperature conversion formulas: Tc = Tf - 32/1.8, Tk = Tc + 273, F = 460 + R

Energy

• 1 calorie = 4.186 Joules
• 1 British thermal unit (BTU) = 1055 Joules
• 1 foot-pound = 1.356 Joules
• 1 Joule = 1 kilogram· meter per second square

Radiation

• 1 rad = 10⁻² gray, 1 rem = 10⁻² sievert, 1 curie = 3.7 × 10¹⁰ becquerel
• 1 becquerel = 1 disintegration per second

Density of Water

• 1 gram per cubic centimeter (gm/cm³) = 1.94 slugs per cubic foot (weight density = 62.4 pounds per cubic foot)

Light

• 1 candela = 1 lumen per steradian
• 1 footcandle = 10.76 candela per square meter = 10.76 lux

Physical Constants

• Acceleration of gravity = 32.2 feet per second square = 9.8 meters per second square
• Velocity of light = 3.0 × 10⁸ meters per second
• Planck's constant = 6.626 × 10⁻³⁴ Joule-seconds
• Avogadro's number = 6.024 × 10²³ per gram-mole

Boolean Postulates

• No notes provided for this section

Area Formulas

• Rectangle: Area = length × width
• Square: Area = s², where s = side
• Triangle: Area = (1/2) × b × h, where b = base and h = height
• Circle: Area = π × r², where r = radius

Volume Formulas

• Rectangular solid or cuboid: V = l × w × h
• Cube: V = a³, where a = length of edge or side
• Cylinder: V = π × r² × h
• Prism: V = B × h, where B = area of base and h = height
• Sphere: V = (4/3) × π × r³
• Pyramid: V = (1/3) × B × h

Trigonometric Functions

• C² = a² + b² - 2ab × cosC
• A/SinA = b/SinB = c/SinC

Kinetic Energy

• K.E. = ½ × m × v²
• 1 Newton (N) = 1 kilogram × meter per second square
• 1 kilogram = 2.2 pounds

Force and Distance

• F₁ × D₁ = F₂ × D₂

Momentum

• ρ = m × v, where ρ = momentum, m = mass, and v = velocity

Force

• F = m × a, where F = force, m = mass, and a = acceleration
• F = 40 × 9.8 = 392 N, F = μ × N = 0.6 × 392 = 235.2 N

Work Done

• W = F × S, where W = work done, F = force, and S = distance
• W = FS, where W = work done, F = force, and S = distance

Newton's Second Law

• F = m × a, where F = force, m = mass, and a = acceleration
• F = m × a / g, where F = force, m = mass, a = acceleration, and g = acceleration due to gravity

Statistics

• Histogram: a graph used to distribute frequency of data
• Mean: the average value of a data set, found using the formula ΣXn/n
• Median: the central value of a data set
• Mode: the value that occurs most frequently in a data set
• Left skewed distribution: Mean < Median < Mode
• Right skewed distribution: Mode < Median < Mean
• No skew: Mean = Median = Mode

Standard Deviation

• Central tendency: the measure of four Mean, Median, Mode, and Standard Deviation
• Variance: the average of the squared differences from the mean, Σ(X-Xav)²/N
• Standard Deviation S = √(X-Xav)²/N
• 1 standard deviation = 68% of the data set
• 2 standard deviations = 95.45% of the data set
• 3 standard deviations = 99.73% of the data set

Statistic and Parameter

• Statistic: a numerical value that describes data taken from a sample
• Parameter: a characteristic of the population, summarizes data, and entire population
• F-test: used to measure the accuracy of a statistic

Null Hypothesis

• No significant difference between the population, if any observed difference is due to sampling or experimental error
• H0 = M1 = M2, no difference between population means

Type I and Type II Errors

• Type I error: reject the null hypothesis when it is true (α)
• Type II error: fail to reject the null hypothesis when it is false (β)

Coefficient of Variation

• Relative standard deviation RSD, measures the dispersion of a probability distribution or frequency distribution
• Coefficient of variation CV = S/Xmean = %
• Cumulative error: used to calculate the upper confidence limit and lower confidence limit for air sampling

Energy

• Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
• Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
• Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

Force

• A newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s²
• Tension forces are required to pull an object (opposite of compression)
• Spring force is exerted by a compressed or stretched spring
• Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

Force and Distance

• F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

Momentum

• ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

Velocity

• v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
• S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

Work Done

• W = FS, where W is the work done, F is the force, and S is the distance from the original position

Newton's Second Law

• F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

Statistics

• Histogram is a graph used to distribute frequency of the data
• Mean is the average value of a data set and is found using the calculation ΣXn/n
• Median is the central number of a data set
• Mode is the number in a data set that occurs most frequently

Temperature

• Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
• Tk = Tc + 273, where Tk is the temperature in Kelvin
• F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

Conversion

• 1 calorie = 4.186 Joule
• 1 BTU (British thermal unit) = 1055 Joule
• 1 foot-pound = 1.356 Joule
• 1 joule = 1 kg · m/s²

Radiation

• 1 rad = 10⁻² gray
• 1 rem = 10⁻² sievert
• 1 curie = 3.7 x 10¹⁰ becquerel
• 1 becquerel = 1 disintegration/sec

Density of Water

• 1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)

Light

• 1 candela = 1 lumen/steradian
• 1 footcandle = 10.76 candela/m² = 10.76 lux

Physical Constants

• acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
• velocity of light = 3.0 x 10⁸ m/sec
• Planck's constant = 6.626 x 10⁻³⁴ J-sec
• Avogadro's number = 6.024 x 10²³/gram-mole

Area and Volume

• Area of a rectangle = length * width
• Area of a square = s², where s is the side
• Area of a triangle = (1/2) b * h, where b is the base and h is the height
• Area of a circle = π * r², where r is the radius
• Volume of a rectangular solid = l * w * h
• Volume of a cube = a³
• Volume of a cylinder = πr²h
• Volume of a prism = B * h
• Volume of a sphere = (4/3)πr³
• Volume of a pyramid = (1/3) * B * h

Trigonometric Functions

• C² = a² + b² - 2ab cos 0C
• A/SinA = b/SinB = c/SinC

Energy

• Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
• Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
• Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

Force

• A newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s²
• Tension forces are required to pull an object (opposite of compression)
• Spring force is exerted by a compressed or stretched spring
• Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

Force and Distance

• F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

Momentum

• ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

Velocity

• v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
• S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

Work Done

• W = FS, where W is the work done, F is the force, and S is the distance from the original position

Newton's Second Law

• F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

Statistics

• Histogram is a graph used to distribute frequency of the data
• Mean is the average value of a data set and is found using the calculation ΣXn/n
• Median is the central number of a data set
• Mode is the number in a data set that occurs most frequently

Temperature

• Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
• Tk = Tc + 273, where Tk is the temperature in Kelvin
• F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

Conversion

• 1 calorie = 4.186 Joule
• 1 BTU (British thermal unit) = 1055 Joule
• 1 foot-pound = 1.356 Joule
• 1 joule = 1 kg · m/s²

Radiation

• 1 rad = 10⁻² gray
• 1 rem = 10⁻² sievert
• 1 curie = 3.7 x 10¹⁰ becquerel
• 1 becquerel = 1 disintegration/sec

Density of Water

• 1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)

Light

• 1 candela = 1 lumen/steradian
• 1 footcandle = 10.76 candela/m² = 10.76 lux

Physical Constants

• acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
• velocity of light = 3.0 x 10⁸ m/sec
• Planck's constant = 6.626 x 10⁻³⁴ J-sec
• Avogadro's number = 6.024 x 10²³/gram-mole

Area and Volume

• Area of a rectangle = length * width
• Area of a square = s², where s is the side
• Area of a triangle = (1/2) b * h, where b is the base and h is the height
• Area of a circle = π * r², where r is the radius
• Volume of a rectangular solid = l * w * h
• Volume of a cube = a³
• Volume of a cylinder = πr²h
• Volume of a prism = B * h
• Volume of a sphere = (4/3)πr³
• Volume of a pyramid = (1/3) * B * h

Trigonometric Functions

• C² = a² + b² - 2ab cos 0C
• A/SinA = b/SinB = c/SinC

Energy

• Kinetic Energy (K.E.) = ½ mv², where m is the mass of the object and v is the speed of the object
• Potential Energy (P.E.) = mgh, where m is the mass of the object, g is the gravitational acceleration of the earth (9.8 m/s²), and h is the height above the earth's surface
• Elastic Potential Energy (P.E. elastic) = ½ kx², where k is the spring constant and x is the amount of compression

Force

• A newton (N) is the amount of force required to give a 1-kg mass an acceleration of 1 m/s²
• Tension forces are required to pull an object (opposite of compression)
• Spring force is exerted by a compressed or stretched spring
• Frictional Force (F) = μN, where μ is the coefficient of friction and N is the force acting on the surface in a direction that is normal (perpendicular) to the surface

Force and Distance

• F₁D₁ = F₂D₂, where F₁ and F₂ are forces and D₁ and D₂ are distances

Momentum

• ρ = mv, where ρ is the momentum, m is the mass, and v is the velocity

Velocity

• v = v₀ + at, where v is the final velocity, v₀ is the original velocity, a is the acceleration, and t is the time
• S = v₀t + ½ at², where S is the distance from the original position, v₀ is the initial velocity, a is the acceleration, and t is the time

Work Done

• W = FS, where W is the work done, F is the force, and S is the distance from the original position

Newton's Second Law

• F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration of the earth (9.8 m/s²)

Statistics

• Histogram is a graph used to distribute frequency of the data
• Mean is the average value of a data set and is found using the calculation ΣXn/n
• Median is the central number of a data set
• Mode is the number in a data set that occurs most frequently

Temperature

• Tc = Tf - 32/1.8, where Tc is the temperature in Celsius and Tf is the temperature in Fahrenheit
• Tk = Tc + 273, where Tk is the temperature in Kelvin
• F = 460 + R, where F is the temperature in Fahrenheit and R is the temperature in Rankine

Conversion

• 1 calorie = 4.186 Joule
• 1 BTU (British thermal unit) = 1055 Joule
• 1 foot-pound = 1.356 Joule
• 1 joule = 1 kg · m/s²

Radiation

• 1 rad = 10⁻² gray
• 1 rem = 10⁻² sievert
• 1 curie = 3.7 x 10¹⁰ becquerel
• 1 becquerel = 1 disintegration/sec

Density of Water

• 1 gm/cm³ = 1.94 slugs/ft³ (weight density = 62.4 lb/ft³)

Light

• 1 candela = 1 lumen/steradian
• 1 footcandle = 10.76 candela/m² = 10.76 lux

Physical Constants

• acceleration of gravity = 32.2 ft/sec² = 9.8 m/sec²
• velocity of light = 3.0 x 10⁸ m/sec
• Planck's constant = 6.626 x 10⁻³⁴ J-sec
• Avogadro's number = 6.024 x 10²³/gram-mole

Area and Volume

• Area of a rectangle = length * width
• Area of a square = s², where s is the side
• Area of a triangle = (1/2) b * h, where b is the base and h is the height
• Area of a circle = π * r², where r is the radius
• Volume of a rectangular solid = l * w * h
• Volume of a cube = a³
• Volume of a cylinder = πr²h
• Volume of a prism = B * h
• Volume of a sphere = (4/3)πr³
• Volume of a pyramid = (1/3) * B * h

Trigonometric Functions

• C² = a² + b² - 2ab cos 0C
• A/SinA = b/SinB = c/SinC

Conversions

• 1 meter (m) equals 100 centimeters (cm), 1000 millimeters (mm), and 1,000,000 microns
• 1 kilometer (km) equals 1000 meters
• 1 mile equals 5280 feet, 1609 meters, and 1.47 feet per second
• 1 inch equals 2.54 cm, and 1 foot equals 30.48 cm and 12 inches
• 1 meter equals 3.2 feet
• 1 foot equals 12 inches
• 1 mile per hour equals 1.47 feet per second, 0.4470 meters per second, and 0.8618 miles per hour
• 1 foot per second equals 0.3048 meters per second, 0.5921 knots, and 0.8618 miles per hour

Length

• 2.54 cm equals 1 inch
• 25.4 mm equals 1 inch
• 12 inches equals 1 foot
• 3 feet equals 1 yard
• 5280 feet equals 1 mile
• 1760 yards equals 1 mile
• 1.6 kilometers equals 1 mile
• 0.868 nautical miles equals 1 US mile

Area

• 1 square inch (sq.in.) equals 6.452 square centimeters (sq.cm) and 6452 square millimeters (sq.mm)
• 1 square foot (sq.ft) equals 144 square inches and 0.09290 square meters
• 1 square yard (sq.yd) equals 9 square feet

Volume

• 1 cubic centimeter (cm3) equals 1 milliliter (mL)
• 1 cubic inch (in3) equals 16.39 cubic centimeters
• 1 cubic foot (ft3) equals 1728 cubic inches and 0.02832 cubic meters
• 1 liter (L) equals 1.057 quarts (US)

Temperature

• To convert to absolute temperature scales, use: oR = oF + 460, and oK = oC + 273
• Temperature conversion formulas: Tc=Tf-32/1.8, Tk=Tc+273, F=460 + R

Energy

• 1 calorie equals 4.186 Joules
• 1 British thermal unit (BTU) equals 1055 Joules
• 1 foot-pound equals 1.356 Joules
• 1 Joule equals 1 kg · m/s2

Radiation

• 1 rad equals 10^-2 gray
• 1 rem equals 10^-2 sievert
• 1 curie equals 3.7x10^10 becquerel
• 1 becquerel equals 1 disintegration/second

Density of Water

• 1 gram per cubic centimeter (gm/cm3) equals 1.94 slugs per cubic foot (weight density equals 62.4 pounds per cubic foot)

Light

• 1 candela equals 1 lumen per steradian
• 1 footcandle equals 10.76 candela per square meter equals 10.76 lux

Physical Constants

• Acceleration of gravity equals 32.2 feet per second squared equals 9.8 meters per second squared
• Velocity of light equals 3.0 x 10^8 meters per second
• Planck's constant equals 6.626 x 10^-34 J-sec
• Avogadro's number equals 6.024 x 10^23 per gram-mole

Boolean Postulates

• Not applicable

Area Formulas

• Rectangle: Area equals length times width
• Square: Area equals side squared
• Triangle: Area equals half times base times height
• Circle: Area equals pi times radius squared

Volume Formulas

• Rectangular solid or cuboid: Volume equals length times width times height
• Cube: Volume equals edge cubed
• Cylinder: Volume equals pi times radius squared times height
• Prism: Volume equals base area times height
• Sphere: Volume equals four-thirds times pi times radius cubed
• Pyramid: Volume equals one-third times base area times height

Trigonometric Functions

• C2 equals a2 plus b2 minus 2ab times cosine C
• A divided by sine A equals b divided by sine B equals c divided by sine C

Kinetic Energy

• Kinetic energy equals half times mass times velocity squared

Potential Energy

• Potential energy equals mass times gravitational acceleration times height
• Elastic potential energy equals half times spring constant times compression squared

Force

• One newton equals the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
• Tension forces are required to pull an object (opposite of compression)
• Spring force exerted by a compressed or stretched spring
• Frictional force equals coefficient of friction times normal force

Statistics

• Left-skewed distribution: Mean less than Median less than Mode
• Right-skewed distribution: Mode less than Median less than Mean
• No skew-symmetrical distribution: Mean equals Median equals Mode
• Standard deviation: average distance of all observations from the mean
• Variance equals summation of X minus X average squared divided by N
• Standard deviation S equals square root of summation of X minus X average squared divided by N
• One standard deviation equals 68% of the data set
• Two standard deviations equal 95.45% of the data set
• Three standard deviations equal 99.73% of the data set

Statistic and Parameter

• Statistic: numerical value that describes data taken from a sample
• Parameter: describes the characteristic of the population

Null Hypothesis

• No significant difference between the population
• If any observed difference is due to sampling or experimental error
• H0 equals M1 equals M2, no difference between population
• Used in conjunction with 95% confidence means that there is a 95% chance of true

Type I and Type II Errors

• Type I error: reject the null hypothesis when it is true
• Type II error: fail to reject the null hypothesis when it is false

Coefficient of Variation

• Relative standard deviation RSD, measure of the dispersion of probability distribution or frequency distribution
• Coefficient of variation CV equals standard deviation divided by mean times 100%

Cumulative Error

• Used to calculate the upper confidence limit and lower confidence limit for air sampling
• Due to common errors: calibration, lab, instrument measurement, and correction errors during sampling calculation
• As sample size increases, the result and assessment of mean enhanced

Conversions

• 1 meter (m) equals 100 centimeters (cm), 1000 millimeters (mm), and 1,000,000 microns
• 1 kilometer (km) equals 1000 meters
• 1 mile equals 5280 feet, 1609 meters, and 1.47 feet per second
• 1 inch equals 2.54 cm, and 1 foot equals 30.48 cm and 12 inches
• 1 meter equals 3.2 feet
• 1 foot equals 12 inches
• 1 mile per hour equals 1.47 feet per second, 0.4470 meters per second, and 0.8618 miles per hour
• 1 foot per second equals 0.3048 meters per second, 0.5921 knots, and 0.8618 miles per hour

Length

• 2.54 cm equals 1 inch
• 25.4 mm equals 1 inch
• 12 inches equals 1 foot
• 3 feet equals 1 yard
• 5280 feet equals 1 mile
• 1760 yards equals 1 mile
• 1.6 kilometers equals 1 mile
• 0.868 nautical miles equals 1 US mile

Area

• 1 square inch (sq.in.) equals 6.452 square centimeters (sq.cm) and 6452 square millimeters (sq.mm)
• 1 square foot (sq.ft) equals 144 square inches and 0.09290 square meters
• 1 square yard (sq.yd) equals 9 square feet

Volume

• 1 cubic centimeter (cm3) equals 1 milliliter (mL)
• 1 cubic inch (in3) equals 16.39 cubic centimeters
• 1 cubic foot (ft3) equals 1728 cubic inches and 0.02832 cubic meters
• 1 liter (L) equals 1.057 quarts (US)

Temperature

• To convert to absolute temperature scales, use: oR = oF + 460, and oK = oC + 273
• Temperature conversion formulas: Tc=Tf-32/1.8, Tk=Tc+273, F=460 + R

Energy

• 1 calorie equals 4.186 Joules
• 1 British thermal unit (BTU) equals 1055 Joules
• 1 foot-pound equals 1.356 Joules
• 1 Joule equals 1 kg · m/s2

Radiation

• 1 rad equals 10^-2 gray
• 1 rem equals 10^-2 sievert
• 1 curie equals 3.7x10^10 becquerel
• 1 becquerel equals 1 disintegration/second

Density of Water

• 1 gram per cubic centimeter (gm/cm3) equals 1.94 slugs per cubic foot (weight density equals 62.4 pounds per cubic foot)

Light

• 1 candela equals 1 lumen per steradian
• 1 footcandle equals 10.76 candela per square meter equals 10.76 lux

Physical Constants

• Acceleration of gravity equals 32.2 feet per second squared equals 9.8 meters per second squared
• Velocity of light equals 3.0 x 10^8 meters per second
• Planck's constant equals 6.626 x 10^-34 J-sec
• Avogadro's number equals 6.024 x 10^23 per gram-mole

Boolean Postulates

• Not applicable

Area Formulas

• Rectangle: Area equals length times width
• Square: Area equals side squared
• Triangle: Area equals half times base times height
• Circle: Area equals pi times radius squared

Volume Formulas

• Rectangular solid or cuboid: Volume equals length times width times height
• Cube: Volume equals edge cubed
• Cylinder: Volume equals pi times radius squared times height
• Prism: Volume equals base area times height
• Sphere: Volume equals four-thirds times pi times radius cubed
• Pyramid: Volume equals one-third times base area times height

Trigonometric Functions

• C2 equals a2 plus b2 minus 2ab times cosine C
• A divided by sine A equals b divided by sine B equals c divided by sine C

Kinetic Energy

• Kinetic energy equals half times mass times velocity squared

Potential Energy

• Potential energy equals mass times gravitational acceleration times height
• Elastic potential energy equals half times spring constant times compression squared

Force

• One newton equals the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
• Tension forces are required to pull an object (opposite of compression)
• Spring force exerted by a compressed or stretched spring
• Frictional force equals coefficient of friction times normal force

Statistics

• Left-skewed distribution: Mean less than Median less than Mode
• Right-skewed distribution: Mode less than Median less than Mean
• No skew-symmetrical distribution: Mean equals Median equals Mode
• Standard deviation: average distance of all observations from the mean
• Variance equals summation of X minus X average squared divided by N
• Standard deviation S equals square root of summation of X minus X average squared divided by N
• One standard deviation equals 68% of the data set
• Two standard deviations equal 95.45% of the data set
• Three standard deviations equal 99.73% of the data set

Statistic and Parameter

• Statistic: numerical value that describes data taken from a sample
• Parameter: describes the characteristic of the population

Null Hypothesis

• No significant difference between the population
• If any observed difference is due to sampling or experimental error
• H0 equals M1 equals M2, no difference between population
• Used in conjunction with 95% confidence means that there is a 95% chance of true

Type I and Type II Errors

• Type I error: reject the null hypothesis when it is true
• Type II error: fail to reject the null hypothesis when it is false

Coefficient of Variation

• Relative standard deviation RSD, measure of the dispersion of probability distribution or frequency distribution
• Coefficient of variation CV equals standard deviation divided by mean times 100%

Cumulative Error

• Used to calculate the upper confidence limit and lower confidence limit for air sampling
• Due to common errors: calibration, lab, instrument measurement, and correction errors during sampling calculation
• As sample size increases, the result and assessment of mean enhanced

Conversions

• 1 meter (m) = 100 centimeters (cm) = 1000 millimeters (mm) = 1,000,000 microns
• 1 kilometer (km) = 1000 meters (m)
• 1 mile = 5280 feet = 1609 meters
• 1 mile per hour = 1.47 feet per second
• 1 inch = 2.54 centimeters = 25.4 millimeters
• 1 foot = 30.48 centimeters = 12 inches
• 1 meter = 3.2 feet

Energy

• 1 calorie (cal) = 0.003968 British Thermal Units (Btu) = 4.187 Joules (J)
• 1 Btu = 252 calories
• 1 joule (J) = 0.239 calories

Velocity

• 1 foot per second (ft/s) = 0.3048 meters per second (m/s) = 0.8618 miles per hour (mi/h) = 0.5921 knots
• 1 meter per second (m/s) = 3.281 feet per second = 2.237 miles per hour
• 1 mile per hour = 0.4470 meters per second = 1.467 feet per second
• 1 knot = 0.5148 meters per second = 1.151 miles per hour = 1.689 feet per second

Area

• 1 square inch (sq.in.) = 6.452 square centimeters = 6452 square millimeters
• 1 square foot (sq.ft) = 144 square inches = 0.09290 square meters
• 1 square yard (sq.yd) = 9 square feet

Volume

• 1 cubic centimeter (cm³) = 1 milliliter (mL)
• 1 cubic inch (in³) = 16.39 cubic centimeters
• 1 cubic foot (ft³) = 1728 cubic inches = 0.02832 cubic meters
• 1 liter (L) = 1.057 quarts (US) = 0.9463 quarts (Imperial)
• 1 US gallon = 0.8327 Imperial gallons

Mass and Weight

• 1 ounce (oz) = 28.35 grams
• 1 pound (lb) = 0.454 kilograms
• 1 ton (US) = 2000 pounds = 1000 kilograms
• 1 dram = 1771.85 milligrams

Force, Pressure, or Stress

• 1 pound-force (lbf) = 4.45 Newtons
• 1 pound-force per square inch (psi) = 6.89 kilopascals

Illumination

• 1 foot-candle = 10.76 lux
• 1 foot-lambert = 3.426 candelas per square meter

Other Conversions

• 1 radian = 180°/π
• 1 candela = 1 lumen per steradian
• 1 foot-candle = 10.76 lux
• 1 tesla = 10,000 gauss

Physical Constants

• Acceleration of gravity = 32.2 feet per second squared = 9.8 meters per second squared
• Velocity of light = 3.0 × 10^8 meters per second
• Planck's constant = 6.626 × 10^−34 Joule-seconds
• Avogadro's number = 6.024 × 10^23 per gram-mole

Radiation

• 1 rad = 10^−2 gray
• 1 rem = 10^−2 sievert
• 1 curie = 3.7 × 10^10 becquerels
• 1 becquerel = 1 disintegration per second

Statistics

• Histogram: a graph used to distribute frequency of data
• Mean: the average value of a data set, calculated using ΣXn/n
• Median: the central number of a data set
• Mode: the number in a data set that occurs most frequently
• Skewed distributions: left-skewed (mean < median < mode), right-skewed (mode < median < mean), and no skew (symmetrical distribution: mean = median = mode)

Standard Deviation

• A measure of the average distance of all observations from the mean
• Variance = Σ(X-Xav)^2/N
• Standard deviation = square root of variance

Statistics and Parameters

• Statistic: a numerical value that describes data taken from a sample
• Parameter: a characteristic of the population, summarizing data from the entire population

Hypothesis Testing

• Null hypothesis: no significant difference between populations
• Type I error: rejecting the null hypothesis when it's true (false positive)
• Type II error: failing to reject the null hypothesis when it's false (false negative)
• Alpha (α): the probability of a Type I error
• Beta (β): the probability of a Type II error

Conversions

• 1 meter (m) is equal to 100 centimeters (cm) and 1000 millimeters (mm)
• 1 kilometer (km) is equal to 1000 meters (m)
• 1 mile is equal to 5280 feet and 1609 meters
• 1 mile per hour is equal to 1.47 feet per second
• 1 inch is equal to 2.54 centimeters and 25.4 millimeters
• 1 foot is equal to 30.48 centimeters and 12 inches
• 1 meter is equal to 3.2 feet

Energy

• 1 calorie (cal) is equal to 0.003968 British thermal units (Btu) and 4.187 joules (J)
• 1 Btu is equal to 252 calories
• 1 cal is equal to 4.187 J

Velocity

• 1 foot per second (ft/s) is equal to 0.3048 meters per second (m/s) and 0.8618 miles per hour (mi/h)
• 1 foot per second is equal to 0.5921 knots
• 1 meter per second is equal to 3.281 feet per second and 2.237 miles per hour
• 1 mile per hour is equal to 0.4470 meters per second and 1.467 feet per second
• 1 knot is equal to 0.5148 meters per second and 1.151 miles per hour

Area

• 1 square inch (sq in) is equal to 6.452 square centimeters (sq cm) and 6452 square millimeters (sq mm)
• 1 square foot (sq ft) is equal to 144 square inches and 0.09290 square meters
• 1 square yard (sq yd) is equal to 9 square feet

Volume

• 1 cubic centimeter (cm³) is equal to 1 milliliter (mL)
• 1 cubic inch (in³) is equal to 16.39 cubic centimeters
• 1 cubic foot (ft³) is equal to 1728 cubic inches
• 1 cubic foot is equal to 0.02832 cubic meters
• 1 liter (L) is equal to 1.057 quarts (US)

Density

• 1 pound per cubic foot (lb/cu ft) is equal to 0.01602 grams per cubic centimeter (g/cm³)
• 1 gram per cubic centimeter is equal to 62.42 pounds per cubic foot
• 1 gram per cubic centimeter is equal to 1000 kilograms per cubic meter (kg/m³)

Potential Energy

• Potential energy (PE) is equal to mgh, where m is the mass of the object, g is the gravitational acceleration, and h is the height above the earth's surface
• Elastic potential energy is equal to ½kx², where k is the spring constant and x is the amount of compression

Force

• A newton (N) is the amount of force required to give a 1-kilogram mass an acceleration of 1 meter per second squared
• Tension forces are required to pull an object, opposite of compression
• Spring force is exerted by a compressed or stretched spring
• Frictional force (F) is equal to μN, where μ is the coefficient of friction and N is the normal force

Force and Distance

• F₁D₁ = F₂D₂, where F is the force and D is the distance

Momentum

• Momentum (ρ) is equal to mv, where m is the mass and v is the velocity

Velocity

• Velocity (v) is equal to v₀ + at, where v₀ is the initial velocity, a is the acceleration, and t is the time
• v² = v₀² + 2as, where v is the final velocity, v₀ is the initial velocity, a is the acceleration, and s is the distance
• s = v₀t + ½at², where s is the distance, v₀ is the initial velocity, t is the time, and a is the acceleration

Work Done

• Work done (W) is equal to FS, where F is the force and S is the distance
• W = ∫F dl, where F is the force and dl is the infinitesimal displacement

Newton's Second Law

• F = ma/g, where F is the force, m is the mass, a is the acceleration, and g is the gravitational acceleration

Statistics

• Definition: A histogram is a graph used to distribute the frequency of the data
• Mean is the average value of a data set and is found using the calculation ΣXn/n
• Median is the central number of a data set
• Mode is the number in a data set that occurs most frequently
• Left skewed: Mean < Median < Mode
• Right skewed: Mode < Median < Mean
• No skew: Mean = Median = Mode

Standard Deviation

• Central tendency is the measure of the mean, median, mode, and standard deviation
• Standard deviation (S) is the square root of (X-X̄)²/N
• Variance is the average of the squared differences from the mean
• 1 standard deviation (1σ) is equal to 68% of the data set
• 2 standard deviations (2σ) are equal to 95.45% of the data set
• 3 standard deviations (3σ) are equal to 99.73% of the data set

Statistic and Parameter

• Statistic: A numerical value that describes data taken from a sample
• Parameter: A characteristic of the population
• F-test is used to measure the accuracy of the sample

Null Hypothesis

• H₀: M₁ = M₂, no significant difference between the populations
• Used in conjunction with 95% confidence means that there is a 95% chance of the true hypothesis

Type I and Type II Errors

• Type I error: Rejecting the null hypothesis when it is true
• Type II error: Failing to reject the null hypothesis when it is false

Coefficient of Variation

• Coefficient of variation (CV) is a measure of the dispersion of a probability distribution or frequency distribution
• CV is equal to the ratio of the standard deviation to the mean

Cumulative Error

• Cumulative error is used to calculate the upper confidence limit and lower confidence limit for air sampling
• Due to common errors: calibration, lab, instrument measurement, and correction errors during sampling calculation

Test your knowledge of unit conversions in length, energy, and more with this advanced science and math quiz. Review common conversions and practice applying them to real-world problems.