Geometric Formulas
Rectangle
Perimeter \(P = 2l + 2w\)
Area \(A = lw\)
Area \(A = lw\)
Square
Perimeter \(P = 4s\)
Area \(A = s^2\)
Area \(A = s^2\)
Circle
Perimeter \(P = 2\pi r\)
Area \(A = \pi r^2\)
where \(\pi \approx 3.14\) or \(\dfrac{22}{7}\)
Area \(A = \pi r^2\)
where \(\pi \approx 3.14\) or \(\dfrac{22}{7}\)
Triangle
Perimeter \(P = a + b + c\)
Area \(A = \tfrac{1}{2}bh\)
\(m\angle A + m\angle B + m\angle C = 180°\)
Area \(A = \tfrac{1}{2}bh\)
\(m\angle A + m\angle B + m\angle C = 180°\)
Right Triangle
Pythagorean theorem
\(a^2 + b^2 = c^2\)
\(a^2 + b^2 = c^2\)
Parallelogram
Area \(A = bh\)
Trapezoid
Area \(A = \tfrac{1}{2}h(B + b)\)
Cube
Surface area \(S = 6s^2\)
Volume \(V = s^3\)
Volume \(V = s^3\)
Rectangular Solid
Surface area \(S = 2wh + 2lh + 2lw\)
Volume \(V = lwh\)
Volume \(V = lwh\)
Sphere
Surface area \(S = 4\pi r^2\)
Volume \(V = \tfrac{4}{3}\pi r^3\)
Volume \(V = \tfrac{4}{3}\pi r^3\)
Right Circular Cylinder
Surface area \(S = 2\pi r^2 + 2\pi rh\)
Volume \(V = \pi r^2 h\)
Volume \(V = \pi r^2 h\)
Right Circular Cone
Surface area \(S = \pi rl + \pi r^2\)
Volume \(V = \tfrac{1}{3}\pi r^2 h\)
Volume \(V = \tfrac{1}{3}\pi r^2 h\)
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Length
1 kilometer (km) = 1000 meters
1 hectometer (hm) = 100 meters
1 dekameter (dam) = 10 meters
1 meter (m) = 1 meter
1 decimeter (dm) = 0.1 meter
1 centimeter (cm) = 0.01 meter
1 millimeter (mm) = 0.001 meter
Weight (Mass)
1 metric ton (t) = 1,000,000 grams
1 kilogram (kg) = 1000 grams
1 hectogram (hg) = 100 grams
1 dekagram (dag) = 10 grams
1 gram (g) = 1 gram
1 decigram (dg) = 0.1 gram
1 centigram (cg) = 0.01 gram
1 milligram (mg) = 0.001 gram
Volume (Capacity)
1 kiloliter (kL) = 1000 liters
1 hectoliter (hL) = 100 liters
1 dekaliter (daL) = 10 liters
1 liter (L) = 1 liter
1 deciliter (dL) = 0.1 liter
1 centiliter (cL) = 0.01 liter
1 milliliter (mL) = 0.001 liter
Temperature: Celsius Scale
100°C = Boiling point of water
−273.15°C = Absolute zero: coldest possible temperature
0°C = Freezing point of water
37°C = Normal human body temperature
Length
1 mile (mi) = 1760 yards (yd)
1 mile (mi) = 5280 feet (ft)
1 yard (yd) = 3 feet (ft)
1 foot (ft) = 12 inches (in.)
Weight (Mass)
1 ton (T) = 2000 pounds (lb)
1 pound (lb) = 16 ounces (oz)
Volume (Capacity)
1 gallon (gal) = 4 quarts (qt)
1 quart (qt) = 2 pints (pt)
1 pint (pt) = 2 cups (c)
Temperature: Fahrenheit Scale
212° = Boiling point of water
−459.67° = Absolute zero
32° = Freezing point of water
98.6° = Normal human body temperature
| Unit type | American to Metric | Metric to American |
|---|---|---|
| Units of Length | 1 mile = 1.61 kilometers 1 yard = 0.914 meter 1 foot = 0.305 meter 1 inch = 2.54 centimeters |
1 kilometer = 0.62 mile 1 meter = 3.28 feet 1 meter = 1.09 yards 1 centimeter = 0.394 inch |
| Units of Volume (Capacity) | 1 gallon = 3.79 liters 1 quart = 0.946 liter |
1 liter = 0.264 gallon 1 liter = 1.06 quarts |
| Units of Weight (Mass) | 1 pound = 0.454 kilogram 1 ounce = 28.35 grams |
1 kilogram = 2.2 pounds 1 gram = 0.0353 ounce |
| Units of Temperature | \({}^{\circ}\text{F} = \tfrac{9}{5}C + 32\) | \({}^{\circ}\text{C} = \tfrac{5}{9}({}^{\circ}\text{F} - 32)\) |
| Notation | \(\frac{1}{10}\) | \(\frac{1}{8}\) | \(\frac{1}{6}\) | \(\frac{1}{5}\) | \(\frac{1}{4}\) | \(\frac{3}{10}\) | \(\frac{1}{3}\) | \(\frac{3}{8}\) | \(\frac{2}{5}\) | \(\frac{1}{2}\) | \(\frac{3}{5}\) | \(\frac{5}{8}\) | \(\frac{2}{3}\) | \(\frac{7}{10}\) | \(\frac{3}{4}\) | \(\frac{4}{5}\) | \(\frac{5}{6}\) | \(\frac{7}{8}\) | \(\frac{9}{10}\) | 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Decimal | 0.1 | 0.125 | 0.16 | 0.2 | 0.25 | 0.3 | 0.3 | 0.375 | 0.4 | 0.5 | 0.6 | 0.625 | 0.6 | 0.7 | 0.75 | 0.8 | 0.83 | 0.875 | 0.9 | 1 |
| Percent | 10% | 12.5% or 12½% |
16.6% or 16⅔% |
20% | 25% | 30% | 33.3% or 33⅓% |
37.5% or 37½% |
40% | 50% | 60% | 62.5% or 62½% |
66.6% or 66⅔% |
70% | 75% | 80% | 83.3% or 83⅓% |
87.5% or 87½% |
90% | 100% |
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