A worked example
For a regular hexagon with side 5, area is 6 × 5² ÷ (4 tan(π/6)), approximately 64.9519 square units. The familiar hexagon formula 3√3s²/2 is equivalent. This Regular Polygon Area example can be compared with other shape areas.
Math calculator
Regular Polygon Area Calculator
Compute area from a regular polygon's side count and common side length. Its area sits beside the working formula for a quick arithmetic check.
Regular Polygon Area inputs
Set up the calculation
What the formula is measuring
A regular polygon has equal sides and equal angles. Joining its center to every vertex creates congruent isosceles triangles whose combined area can be expressed with n, side length s, and tan(π/n). For a connected concept in Regular Polygon Area, see interior angles.
The roles assigned to number of sides and side length explain the operation that produces area.
Reproducing the answer
Convert the central angle to π/n inside the tangent, square the side length, multiply by the side count, and divide by four times the tangent. Keep the calculator in radian mode for π/n.
Mistakes worth catching
The side count must be a whole number and the figure must be regular. Irregular polygons with the same side count and side length can have different areas.
A rough estimate made before calculating gives the finished area a useful plausibility check.
Problems this can answer
The formula supports symmetric paving pieces, signs, table tops, frames, and geometric models when a common side measurement is easier to obtain than an apothem.
Interpreting changes in the inputs
Treat each labeled field as part of the definition, not merely an empty box. The field assignment determines what the displayed area describes. Convert measured values to compatible units first and retain their original precision until the final rounding choice.
With side count fixed, multiplying side length by k multiplies area by k². With side length fixed, adding sides changes both perimeter and central geometry. Predict that movement before recalculating the area; disagreement points to an input-role or sign issue.
Report the area at a precision justified by the inputs. A long browser decimal is computational detail, not evidence that the source values were measured that accurately. When an exact symbolic form is conventional, keep it beside the rounded value so later work is not forced to reuse an early approximation.
Side length alone determines area only because regularity fixes every angle. An irregular polygon needs additional dimensions, coordinates, diagonals, or a decomposition into simpler shapes. Here the requested quantity is specifically area.
Keep the supplied inputs with the result, including any units and the final rounding place. The displayed formula then preserves how the area was obtained.
Questions people ask
What units does the answer use?
Square units based on the entered side unit, such as square centimeters.
Can I enter a noninteger side count?
No. A polygon has a whole number of sides.
Does the formula work for a square?
Yes. With n = 4 it simplifies to side squared.
What is an apothem?
It is the perpendicular distance from a regular polygon's center to a side.