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# Common Formulas

Updated February 11, 2017 | Infoplease Staff ### CIRCUMFERENCE

Circle:
C = πd, in which π is 3.1416 and d the diameter.

### AREA

Triangle:
A = (ab)/2 , in which a is the base and b the height.
Square:
A = a2, in which a is one of the sides.
Rectangle:
A = ab, in which a is the base and b the height.
Trapezoid:
A = (h(a + b))/2, in which h is the height, a the longer parallel side, and b the shorter.
Regular pentagon:
A = 1.720a2, in which a is one of the sides.
Regular hexagon:
A = 2.598a2, in which a is one of the sides.
Regular octagon:
A = 4.828a2, in which a is one of the sides.
Circle:
A = πr2, in which π is 3.1416 and r the radius.

### VOLUME

Cube:
V = a3, in which a is one of the edges.
Rectangular prism:
V = abc, in which a is the length, b is the width, and c the depth.
Pyramid:
V = (Ah)/3, in which A is the area of the base and h the height.
Cylinder:
V = πr2h, in which π is 3.1416, r the radius of the base, and h the height.
Cone:
V = (πr2h)/3, in which π is 3.1416, r theradius of the base, and h the height.
Sphere:
V = (4πr3)/3, in which π is 3.1416 and r the radius.

### TEMPERATURE SCALES

Degrees Fahrenheit to Degrees Celsius:
TC = 5/9 (TF – 32)
Degrees Celsius to Degrees Fahrenheit:
TF = 9/5 TC + 32
Degrees Celsius to Kelvins:
TK = TC + 273.15

### MISCELLANEOUS

Distance in feet traveled by falling body:
d = 16t2, in which t is the time in seconds.
Speed of sound in feet per second through any given temperature of air:
take the square root of (273 + t), in which t is the temperature Centigrade, multiply it by 1087, and divide the result by 16.52.
Cost in cents of operation of electrical device:
C = (Wtc)/1000, in which W is the number of watts,t the time in hours, and c the cost in cents per kilowatt-hour.
Conversion of matter into energy (Einstein's Theorem):
E = mc2, in which E is the energy in ergs, m the mass of the matter in grams, and c the speed of light in centimeters per second: (c2 = 9 × 1020)

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