Follow a worked example.
Every example below can be loaded using its calculator’s Reset example button. Inputs use centimetres, square centimetres or cubic centimetres as labelled, while angles use degrees.
From a side
Given: Side a = 5.
A = na²/[4 tan(π/n)]; P = na
| Measurement | Calculated value |
|---|---|
| Side | 5 cm |
| Area | 120.71068 cm² |
| Perimeter | 40 cm |
| Apothem / inradius | 6.0355339 cm |
| Circumradius | 6.5328148 cm |
| Interior angle | 135° |
From circumradius
Given: Circumradius R = 5.
a = 2R sin(π/n)
| Measurement | Calculated value |
|---|---|
| Side | 3.8268343 cm |
| Area | 70.710678 cm² |
| Perimeter | 30.614675 cm |
| Apothem / inradius | 4.6193977 cm |
| Circumradius | 5 cm |
| Interior angle | 135° |
From the apothem
Given: Apothem r = 5.
a = 2r tan(π/n)
| Measurement | Calculated value |
|---|---|
| Side | 4.1421356 cm |
| Area | 82.842712 cm² |
| Perimeter | 33.137085 cm |
| Apothem / inradius | 5 cm |
| Circumradius | 5.411961 cm |
| Interior angle | 135° |
From area
Given: Area A = 50.
a = √[4A tan(π/n)/n]
| Measurement | Calculated value |
|---|---|
| Side | 3.2179713 cm |
| Area | 50 cm² |
| Perimeter | 25.74377 cm |
| Apothem / inradius | 3.8844349 cm |
| Circumradius | 4.2044821 cm |
| Interior angle | 135° |
Check the answer’s dimensions
An area contains a product of two lengths, while volume contains three. A perimeter or radius is still a length. If your input measurements are mixed between metres and centimetres, convert them to a common unit first. A realistic-looking number can still be wrong if the units were inconsistent.