This page presents the most important geometry formulas for area, perimeter, circumference, volume, and surface area of common plane figures and solid shapes.
For a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\):
\[ a^2 + b^2 = c^2 \]
Perimeter:
\[ P = a + b + c \]Area formulas:
Using base \(b\) and height \(h\):
\[ A = \frac{1}{2} b h \]Using two sides and the included angle:
\[ A = \frac{1}{2} bc \sin A \] \[ A = \frac{1}{2} ac \sin B \] \[ A = \frac{1}{2} ab \sin C \]Heron's Formula (when all three sides are known):
\[ A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2} \]
\[
P = 2L + 2W
\]
\[
A = LW
\]
\[
A = b h
\]
\[
A = \frac{1}{2}(a + b)h
\]
\[
C = 2\pi r
\]
\[
A = \pi r^2
\]
For central angle \(t\) in radians:
\[ s = r t \] \[ A = \frac{1}{2} r^2 t \]
\[
V = LWH
\]
\[
SA = 2(LW + WH + HL)
\]
\[
V = \frac{4}{3}\pi r^3
\]
\[
SA = 4\pi r^2
\]
\[
V = \pi r^2 h
\]
\[
SA = 2\pi r h + 2\pi r^2
\]
\[
V = \frac{1}{3}\pi r^2 h
\]
\[
SA = \pi r \sqrt{r^2 + h^2}
\]