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Geometry cheat sheet

All 22 formulas on one page. Print it or save it as a PDF; it fits on 3 sides of A4 or Letter.

Pythagorean theorem

a2+b2=c2
Hypotenusec=a2+b2
A shorter sidea=c2−b2
  • a one of the two shorter sides (legs), which meet at the right angle
  • b the other shorter side
  • c the hypotenuse: the longest side, opposite the right angle

Area of a rectangle

A=l×w
PerimeterP=2(l+w)
Square of side sA=s2
  • A the area, in square units (cm², m²)
  • l the length
  • w the width

Area of a triangle

A=12bh
  • A the area
  • b the base: any side you choose
  • h the perpendicular height: the distance from the base (or its extension) to the opposite corner, at right angles to the base

Heron's formula

A=s(s−a)(s−b)(s−c), s=a+b+c2
  • A the area of the triangle
  • a the first side
  • b the second side
  • c the third side
  • s the semi-perimeter: half of a+b+c

Area of a parallelogram

A=bh
  • A the area
  • b the base: one of the sides
  • h the perpendicular height between the base and the opposite side

Area of a trapezoid (trapezium)

A=a+b2h
  • A the area
  • a one of the parallel sides
  • b the other parallel side
  • h the perpendicular height: the distance between the parallel sides

Area of a circle

A=πr2
From the diameterA=πd24
  • A the area inside the circle
  • r the radius: centre to edge (half the diameter)
  • π pi, about 3.14159: the ratio of any circle's circumference to its diameter

Circumference of a circle

C=2πr
From the diameterC=πd
  • C the circumference: the perimeter of the circle
  • r the radius
  • π pi, about 3.14159

Arc length

s=rθ(θ in radians), s=θ360×2πr(θ in degrees)
  • s the arc length: the distance along the curved edge
  • r the radius of the circle
  • θ the central angle at the centre of the circle, in degrees or radians (use the toggle)

Area of a sector

A=12r2θ(θ in radians), A=θ360πr2(θ in degrees)
  • A the area of the sector
  • r the radius of the circle
  • θ the central angle, in degrees or radians (use the toggle)

Area of an ellipse

A=πab
  • A the area of the ellipse
  • a the semi-major axis: half the longest width
  • b the semi-minor axis: half the shortest width

Area of a regular polygon

A=ns24tan⁡(πn)
Using the apothem aA=12×perimeter×a=12nsa
  • A the area
  • n the number of sides (3 or more)
  • s the length of each side
  • tan⁡(πn) the tangent of π/n radians (that is 180°/n)

Interior angles of a polygon

S=(n−2)×180°
Each angle of a regular polygon(n−2)×180°n
Each exterior angle of a regular polygon360°n
  • S the sum of the interior angles, in degrees
  • n the number of sides (3 or more)

Volume of a box (cuboid)

V=lwh
Cube of side sV=s3
  • V the volume, in cubic units (cm³, m³)
  • l the length
  • w the width
  • h the height

Surface area of a box (cuboid)

S=2(lw+lh+wh)
Cube of side sS=6s2
  • S the total surface area
  • l the length
  • w the width
  • h the height

Volume of a cylinder

V=πr2h
  • V the volume
  • r the radius of the circular end
  • h the height (or length) of the cylinder

Surface area of a cylinder

S=2πr2+2πrh
Curved surface onlyScurved=2πrh
FactorisedS=2πr(r+h)
  • S the total surface area
  • r the radius
  • h the height

Volume of a cone

V=13πr2h
  • V the volume
  • r the radius of the circular base
  • h the perpendicular height, from the base straight up to the tip (not the slant height)

Surface area of a cone

S=πr2+πrl
Curved surface onlyScurved=πrl
Slant heightl=r2+h2
  • S the total surface area
  • r the radius of the base
  • l the slant height: from the edge of the base to the tip, along the surface

Volume of a sphere

V=43πr3
HemisphereV=23πr3
  • V the volume
  • r the radius: centre to surface

Surface area of a sphere

S=4πr2
Hemisphere (curved part)S=2πr2
  • S the surface area
  • r the radius

Volume of a pyramid

V=13Bh
  • V the volume
  • B the area of the base (for a square base of side s, B=s2)
  • h the perpendicular height from the base to the apex

letx.io · Geometry cheat sheet · 2026-10-31