Formulas/Geometry

Geometry Formulas

Area, volume, perimeter, and surface area for all common shapes

Circle

Shape
Area = πr²
Circumference = 2πr
Diameter = 2r

Rectangle

Shape
Area = l × w
Perimeter = 2(l + w)
Diagonal = √(l² + w²)

Triangle

Shape
Area = ½ × base × height
Perimeter = a + b + c
Heron's: A = √(s(s-a)(s-b)(s-c))

Square

Shape
Area = s²
Perimeter = 4s
Diagonal = s√2

Sphere

Shape
Volume = (4/3)πr³
Surface Area = 4πr²

Cylinder

Shape
Volume = πr²h
Lateral Area = 2πrh
Total Area = 2πr(r+h)

Cone

Shape
Volume = (1/3)πr²h
Slant height = √(r²+h²)
Lateral Area = πrl

Trapezoid

Shape
Area = ½(a+b)h
Perimeter = a+b+c+d