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 = (Π4r³)/3, in which Π 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.

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)