List of formulas in elementary geometry

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Geometric shapes[edit]

This is a short list of some common mathematical shapes and figures and the formulas that describe them.

Two-dimensional shapes[edit]

Shape Area Perimeter/Circumference
Square A = side^2 P = 4 x side
Rectangle A = l × w P = 2l + 2w
Circle A = π × r^2 C = 2 × π × r
Ellipse (where a is the semimajor axis and b is the semiminor axis) A = π × a × b
Triangle A = ½ × b × h P = a + b + c
Parallelogram b = base, h = height, a = side A = b × h P = 2a + 2b
Trapezoid (where a and b are the bases) A = ½(a + b) × h
Sources:[1][2]

Three-dimensional shapes[edit]

Shape Volume Surface area
Cube V=s^3 6s^2
Rectangular Prism l = length, h = height, w = width V = l × w × h S = 2lw + 2lh + 2wh
Sphere V = (4/3) π r^3 r^2
Right Circular Cylinder V = π × r^2 × h S = 2π rh + 2π r^2
Sources:[3]

LaTeX markup (for writer/editors)[edit]

Circle (area and circumference)[edit]

C = \,2\pi r

A = \,\pi r^2

dA = \,\mathrm{d}r\,\mathrm{d}\theta

Sphere (area and volume)[edit]

A = 4\pi r^2

V = \frac{4}{3}\pi r^3

dA = r^2 \sin\theta\, d\theta\, d\phi

\mathrm{d}V=r^2\sin\theta\,\mathrm{d}r\,\mathrm{d}\theta\,\mathrm{d}\varphi

References[edit]