How to use this calculator
- Identify the measurements labelled Area A. Check whether the figure satisfies the assumptions described below.
- Enter positive measurements in a common unit. Use the degree symbol convention for angles. Ratios such as eccentricity have no unit.
- Select Calculate. Inspect the result labels: lengths, areas and volumes have different dimensions. Copy the output or print the page if you need a record.
The formula
a = √[4A tan(π/n)/n]
Area A = 50
Worked example
For Area A = 50 cm², applying the displayed relationship gives side ≈ 4.3869134 cm. The remaining related measurements appear in the result panel. The example uses ideal dimensions and rounds only for display.
Model and limitations
Every interior angle is 120 degrees. The distance across opposite vertices is 2a, while the distance across opposite parallel sides is √3a. Its apothem is √3a/2.
The circumradius equals a side only for the regular hexagon, not for all regular polygons. Inputs are limited to 10⁹ for lengths, 10¹⁸ for areas and 10²⁷ for volumes. Extremely thin or nearly degenerate figures may lose numerical accuracy; avoid treating displayed rounding as a measurement tolerance.