These are the formulas for the standard shapes: area, perimeter, circumference, diameter, volume and surface area. Each formula has its own page, and on it there is not only the formula but where it comes from, what every letter means, two worked examples and the mistake that this particular shape invites.
A formula can be found anywhere. What is harder to find is why it is that formula — why the cone carries a third, where πr² comes from, why the semicircle adds the diameter to the arc. That is what the pages are written for.
Area
| Shape | Formula |
|---|
| Circle | A = π · r² |
| Rectangle | A = a · b |
| Square | A = a² |
| Triangle | A = ½ · a · h |
| Trapezoid | A = ½ · (a + b) · h |
| Parallelogram | A = a · h |
| Rhombus | A = ½ · d · e |
| Hexagon | A = (3√3 / 2) · a² |
| Regular polygon | A = (n · a²) / (4 · tan(π / n)) |
| Circular sector | A = (deg / 360) · π · r² |
Perimeter
| Shape | Formula |
|---|
| Rectangle | P = 2 · (a + b) |
| Square | P = 4 · a |
| Triangle | P = a + b + c |
| Regular polygon | P = n · a |
| Semicircle | P = π · r + 2 · r |
Circumference
| Shape | Formula |
|---|
| Circle | C = 2 · π · r |
Diameter
| Shape | Formula |
|---|
| Circle | d = 2 · r |
Volume
| Shape | Formula |
|---|
| Cone | V = (1/3) · π · r² · h |
| Cylinder | V = π · r² · h |
| Sphere | V = (4/3) · π · r³ |
| Cube | V = a³ |
| Rectangular prism | V = a · b · h |
| Triangular prism | V = ½ · a · h · l |
| Pyramid | V = (1/3) · a · b · h |
Surface area
| Shape | Formula |
|---|
| Cylinder | S = 2 · π · r² + 2 · π · r · h |
| Sphere | S = 4 · π · r² |
| Cube | S = 6 · a² |
| Rectangular prism | S = 2 · (a·b + a·h + b·h) |
| Cone | S = π · r² + π · r · l |
| Pyramid | S = a² + 2 · a · l |
| Triangular prism | S = a · h + 3 · a · l |
What is not here, and why
A flat figure has no volume and no surface area distinct from its area, so there are no «volume of a circle» or «surface area of a rectangle» pages here, even though people do type those. A separate address for them would print an error of subject as a fact; instead they are dealt with inside the neighbouring pages.
There is no separate page for the perimeter of a circle either — not because nobody asks for it, but because it is the same length as the circumference. One value, one address.