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