Geometry formulas cheat sheet

Area formulas are all variations of base times height. Volume formulas are all base area times height, with a factor of one third whenever the shape tapers to a point.

Practise trigonometry

Plane figures

$A = ℓ w, P = 2 (ℓ + w)$ Rectangle
$A = \frac{1}{2} bh$ Triangle
$A = \frac{1}{2} (b_{1} + b_{2}) h$ Trapezoid
$A = π r^{2}, C = 2 π r$ Circle
$A = \frac{1}{2} r^{2} θ$ Sector, θ in radians

Solids

$V = ℓ w h$
$V = π r^{2} h, S A = 2 π r^{2} + 2 π r h$ Cylinder
$V = \frac{1}{3} π r^{2} h$ Cone
$V = \frac{4}{3} π r^{3}, S A = 4 π r^{2}$ Sphere
$V = \frac{1}{3} B h$ Pyramid

Angles

$Triangle sum = 18 0^{\circ}$
$(n - 2) 18 0^{\circ}$ Polygon interior sum
$a^{2} + b^{2} = c^{2}$ Pythagorean theorem
$θ_{inscribed} = \frac{1}{2} θ_{central}$

Coordinate geometry

$d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$
$M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$
$(x - h)^{2} + (y - k)^{2} = r^{2}$ Circle

Related calculators

Circle Calculator