AP Calculus AB/BC Formulas

Related Rates & Optimization

Area of a circle

A = πr²

Circumference of a circle

C = 2πr

Surface area of a sphere

S = 4πr²

Volume of a sphere

V = 4/3πr³

Volume of a cylinder

V = πr²h

The radius of a cylinder is constant

Surface area of a cylinder

S = 2πrh+2πr²

Perimeter of a rectangle

P = 2w+2l

Surface area of a rectangular prism

S = 2lw + 2lh + 2hw

Area of a equilateral

A = s²√3/4

Area of a triangle

A = 1/2bh

Volume of a cone

V = 1/3πr²h

The radius and height are always proportional to eachother

Pythagorean theorem

a²+b²=c²

Distance formula

d = √(x₂-x₁)²+(y₂-y₁)²

Surface area of a pyramid

S = B +1/2Pl

Volume of a pyramid

V = 1/3bh