AP Calc - Necessary Formulas

Circle Circumference

Circle Circumference

C = 2πr

Circle Area

A = πr²

Arc Length

L = rθ (where θ is the angle in radians)

Area of a Sector

A = ½r² θ

Square Perimeter

P = 4s

Square Area

A = s²

Triangle Perimeter

P = a+b+c

Triangle Area

A = ½bh

Rectangle Perimeter

P = 2(l+w)

Rectangle Area

A = lw

Sphere Surface Area

SA = 4πr²

Sphere Volume

V = 4/3πr³

Cube Surface Area

SA = 6s²

Cube Volume

V = s³

Rectangular Prism Surface Area

SA = 2(lw+lh+wh)

Rectangular Prism Volume

V = lwh

Triangular Prism Surface Area

SA = bh+P_bh

Triangular Prism Volume

V = ½bhl

Square Pyramid Surface Area

SA = s² +2sl

Square Pyramid Volume

V = 1/3s² h

Cylinder Surface Area

SA = 2πr(h+r)

Cylinder Volume

V = πr² h

Cone Surface Area

SA = πr(r+l)

Cone Volume

V = 1/3πr² h

Sin(θ)

opposite/hypotenuse

cos(θ)

adjacent/hypotenuse

tan(θ)

opposite/adjacent

Pythagorean Theorem

a² +b² = c²

Law of Sines

a/sin(A) = b/sin(B) = c/sin(C)

Law of Cosines

c² = a² +b² -2abcos(C)