Geometry Formulas

2D flat shapes

• Square: $A = s^2$, $P = 4s$ (where s = side length)
• Rectangle: $A = lw$, $P = 2(l + w)$ (where l, w = length, width)
• Triangle: $A = \tfrac12 bh$, $P = a + b + c$ (where b = base, h = height)
• Circle: $A = \pi r^2$, $C = 2\pi r$ (where r = radius)
• Parallelogram: $A = bh$, $P = 2(a + b)$ (where b = base, h = height)
• Trapezoid: $A = \tfrac12 (a + b)h$ (where a, b = parallel sides)
• Rhombus: $A = \tfrac12 d_1 d_2$ (where d₁, d₂ = diagonals)
• Regular polygon: $A = \tfrac12 a P$ (where a = apothem, P = perimeter)

3D solid shapes

• Cube: $V = s^3$, $SA = 6s^2$ (where s = edge)
• Rectangular prism: $V = lwh$, $SA = 2(lw + lh + wh)$ (where l, w, h)
• Cylinder: $V = \pi r^2 h$, $SA = 2\pi r(r + h)$ (where r = radius, h = height)
• Cone: $V = \tfrac13\pi r^2 h$, $SA = \pi r(r + \ell)$ (where ℓ = slant height)
• Sphere: $V = \tfrac43\pi r^3$, $SA = 4\pi r^2$ (where r = radius)
• Pyramid: $V = \tfrac13 b^2 h$, $SA = b^2 + 2b\ell$ (where b = base edge, ℓ = slant)

Key theorems

• Pythagorean theorem: $a^2 + b^2 = c^2$ (legs a, b; hypotenuse c)
• Distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ (between two points)
• Midpoint formula: $M = \left(\tfrac{x_1 + x_2}{2}, \tfrac{y_1 + y_2}{2}\right)$ (midpoint of a segment)
• Slope: $m = \dfrac{y_2 - y_1}{x_2 - x_1}$ (steepness of a line)

Geometry formulas sheet

Every common 2D and 3D shape on one page — diagram and formula together. Save it, print it, or use it as a revision poster. Free to share with attribution.

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Variable glossary

The same symbols are used site-wide so the notation never shifts under you.

• a, b, cside lengths
• l, w, hlength, width, height
• rradius
• ddiameter (d = 2r)
• sside length or slant height
• ℓslant height
• bbase
• Pperimeter
• Ccircumference
• Aarea
• SAsurface area
• Vvolume
• θcentral angle (degrees)