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 | 43.011935 cm² |
| Perimeter | 25 cm |
| Apothem / inradius | 3.4409548 cm |
| Circumradius | 4.253254 cm |
| Interior angle | 108° |
From circumradius
Given: Circumradius R = 5.
a = 2R sin(π/n)
| Measurement | Calculated value |
|---|---|
| Side | 5.8778525 cm |
| Area | 59.441032 cm² |
| Perimeter | 29.389263 cm |
| Apothem / inradius | 4.045085 cm |
| Circumradius | 5 cm |
| Interior angle | 108° |
From the apothem
Given: Apothem r = 5.
a = 2r tan(π/n)
| Measurement | Calculated value |
|---|---|
| Side | 7.2654253 cm |
| Area | 90.817816 cm² |
| Perimeter | 36.327126 cm |
| Apothem / inradius | 5 cm |
| Circumradius | 6.1803399 cm |
| Interior angle | 108° |
From area
Given: Area A = 50.
a = √[4A tan(π/n)/n]
| Measurement | Calculated value |
|---|---|
| Side | 5.3908906 cm |
| Area | 50 cm² |
| Perimeter | 26.954453 cm |
| Apothem / inradius | 3.7099622 cm |
| Circumradius | 4.5857654 cm |
| Interior angle | 108° |
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.