Common Formulas

Circumference

Circle:

C = d, in which 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 = r², in which 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 = r²h, in which is 3.1416, r the radius of the base, and h the height.

Cone:

V = (r²h)/3, in which is 3.1416, r theradius of the base, and h the height.

Sphere:

V = (4r³)/3, in which is 3.1416 and r the radius.

Temperature Scales

Degrees Fahrenheit to Degrees Celsius:

T_C = ⁵/9 (T_F 32)

Degrees Celsius to Degrees Fahrenheit:

T_F = ⁹/5 T_C + 32

Degrees Celsius to Kelvin:

T_K = T_C + 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.

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)