Metric System Measurements

Metric System

The metric system uses the following prefixes: Kilo, Hecto, Deka, UNIT, Deci, Centi, Milli.
The metric system is used to measure: meters (length), liters (volume), grams (mass).

Length

1 inch (in) = 2.54 centimeters (cm)
1 foot (ft) = 30.48 cm = 0.3048 meters (m)
1 yard (yd) = 91.44 cm = 0.9144 m
1 mile (mi) ≈ 1.61 kilometers (km)
1 millimeter (mm) ≈ 0.03937 in
1 centimeter (cm) ≈ 0.3937 in
1 meter (m) ≈ 1.0936 yd = 3.2808 ft
1 kilometer (km) ≈ 0.6214 mi
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 ft
1 yard (yd) = 36 in
1 mile (mi) = 5280 ft
1 mile (mi) = 1760 yd

Area

1 square foot (ft2) = 144 square inches (in2)
1 square yard (yd2) = 9 ft2 = 1296 in2
1 square mile (mi2) = 27,878,400 ft2 = 3,097,600 yd2
1 acre = 43,560 ft2
1 square mile (mi2) = 640 acres
1 square inch (in2) ≈ 6.45 cm2
1 square foot (ft2) ≈ 0.093 m2
1 square yard (yd2) ≈ 0.836 m2
1 square mile (mi2) ≈ 2.59 km2
1 acre ≈ 4,047 m2

Volume

1 pint (pt) = 16 ounces (oz)
1 quart (qt) = 2 pt
1 gallon (gal) = 4 qt
1 pint (pt) = 2 cups
1 cup = 8 oz
1 gallon (gal) = 128 oz
1 cubic foot (ft3) ≈ 7.48 gal
1 cubic yard (yd3) ≈ 201.97 gal
1 gallon (gal) ≈ 231 in3
1 cubic foot (ft3) of fresh water ≈ 62.5 lb
1 cubic foot (ft3) of salt water ≈ 64 lb
1 cubic centimeter (cm3) = 1 milliliter (mL) = 1 gram (g) = 1000 mm3
1 cubic decimeter (dm3) = 1000 cm3 = 1 liter (L) = 1 kilogram (kg)
1 cubic meter (m3) = 1000 dm3 = 1 kiloliter (kL) = 1,000 L
1 liter (L) ≈ 1.06 qt
1 gallon (gal) ≈ 3.7854 L
1 quart (qt) ≈ 0.9464 L
1 ounce (oz) ≈ 29.5735 mL
1 cubic foot (ft3) = 1728 in3
1 cubic yard (yd3) = 27 ft3
1 cubic foot (ft3) ≈ 0.02832 m3
1 cubic yard (yd3) ≈ 0.7646 m3

Weight

1 pound (lb) = 16 ounces (oz)
1 ton (T) = 2,000 lb
1 ton (T) ≈ 0.9072 metric ton (t)
1 kilogram (kg) = 1000 grams (g)
1 metric ton (t) = 1,000 kg
1 kilogram (kg) ≈ 2.2 lb
1 ounce (oz) ≈ 28 g

Time

1 minute (min) = 60 seconds (sec)
1 hour = 60 min
1 day = 24 hours
1 year = 365 days

Percentage

To find a percentage, divide the part by the whole and multiply by 100.
Percentage = Rate * Base

Math Formulas

Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏 , where 𝑚 is the slope and 𝑏 is the y-intercept.
Slope Formula: 𝑚 = (𝑦2 − 𝑦1) / (𝑥2 − 𝑥1)
Celsius to Fahrenheit Conversion: 𝐹= (9/5)𝐶 + 32
Fahrenheit to Celsius Conversion: 𝐶 = (5/9)(𝐹 − 32)
Simple Interest: 𝐼 = 𝑃𝑟𝑡 , where 𝐼 is interest, 𝑃 is principle, 𝑟 is rate and 𝑡 is time
Compound Interest: 𝐴 = 𝑃(1 + 𝑟/𝑛) 𝑛𝑡 , where 𝐴 is the final amount, 𝑃 is the principle, 𝑟 is the rate, 𝑡 is the time, and 𝑛 is the number of times compounded per year.
Future Value: 𝐴 = 𝑃 + 𝐼
Present Value: 𝑃 = 𝐴 / (1 + 𝑟/𝑛) 𝑛𝑡
Range: highest value – lowest value
Pythagorean Theorem: 𝑎2 + 𝑏 2 = 𝑐 2

Geometry Formulas

Area of a Rectangle: 𝐴 = 𝐿𝑤, where 𝐿 is length and 𝑤 is width.
Perimeter of a Rectangle: 𝑃 = 2(𝐿) + 2(𝑤)
Area of a Square: 𝐴 = 𝑠2, where 𝑠 is the side length.
Perimeter of a Square: 𝑃 = 4𝑠
Area of a Parallelogram: 𝐴= 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
Perimeter of a Parallelogram: 𝑃 = 2(𝑏) + 2(ℎ)
Area of a Triangle: 𝐴 = (1/2) 𝑏ℎ, where 𝑏 is the base and ℎ is the height.
Perimeter of a Triangle: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3, where 𝑠 represents the side lengths.
Area of a Trapezoid: 𝐴 = (1/2) ℎ(𝑎 + 𝑏), where 𝑎 and 𝑏 are the parallel sides and ℎ is the height.
Perimeter of a Trapezoid: 𝑃 = 𝑠1 + 𝑠2 + 𝑠3 + 𝑠4, where 𝑠 represents the side lengths.
Area of a Circle: 𝐴 = 𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Circumference of a Circle: 𝐶 = 𝜋𝑑, where 𝜋 is the constant (approximately 3.14) and 𝑑 is the diameter.
Circumference of a Circle: 𝐶 = 2𝜋𝑟, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Volume of a Cube: 𝑉 = 𝑠3, where 𝑠 is the side length.
Surface Area of a Cube: 𝑆𝐴 = 6𝑠 2, where 𝑠 is the side length.
Volume of a Sphere: 𝑉 = (4/3)𝜋𝑟 3, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Surface Area of a Sphere: 𝑆𝐴 = 4𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14) and 𝑟 is the radius.
Volume of a Rectangular Prism: 𝑉 = 𝐿𝑤ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
Surface Area of a Rectangular Prism: 𝑆𝐴 = 2𝐿𝑤 + 2𝑤ℎ + 2𝐿ℎ, where 𝐿 is the length, 𝑤 is the width, and ℎ is the height.
Volume of a Cylinder: 𝑉 = 𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Surface Area of a Cylinder: 𝑆𝐴 = 2𝜋𝑟ℎ + 2𝜋𝑟 2, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Volume of a Cone: 𝑉 = (1/3)𝜋𝑟 2 ℎ, where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Surface Area of a Cone: 𝑆𝐴 = 𝜋𝑟 + 𝜋𝑟√𝑟 2 + ℎ 2 , where 𝜋 is the constant (approximately 3.14), 𝑟 is the radius, and ℎ is the height.
Sum of Interior Angles of a Polygon: (𝑛 − 2) ∙ 180°, where 𝑛 is the number of sides.