Math
Hexagon Calculator
The hexagon calculator solves a regular hexagon from any single measurement.
Because a regular hexagon is six equilateral triangles, its circumradius equals its side, its apothem is (√3/2)s, and its area is (3√3/2)s² — the calculator keeps those exact radicals (side 6 gives area 54√3) next to the decimals.
Apothem = center to the middle of a side. Circumradius = center to a vertex.
Area is in square units; the rest are lengths.
Pick the unit your measurements use. Area is reported in square units and volume in cubic units.
Try an example
Result
Area
—
- Side
- —
- Perimeter
- —
- Apothem (inradius)
- —
- Circumradius
- —
- Interior angle
- —
- Exterior angle
- —
More details (1 more)
- Number of diagonals
- —
Student quick launch
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Study path
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What the hexagon calculator solves
The hexagon calculator solves a regular hexagon from any single measurement. Because a regular hexagon is six equilateral triangles, its circumradius equals its side, its apothem is (√3/2)s, and its area is (3√3/2)s² — the calculator keeps those exact A root expression written with the √ symbol, such as a square root. (side 6 gives area 54√3) next to the decimals.
Formula
How to use it
- Choose which hexagon measurement you know: side, apothem, circumradius, area, or perimeter.
- Enter the value and choose its unit.
- Read the area, side, perimeter, apothem, circumradius, angles, and diagonal count; open the work for each formula.
How to read the answer
A regular hexagon has 6 equal sides and 6 equal angles of 120°. The apothem is the radius of the circle that fits inside it and the circumradius is the radius of the circle through its corners; the area is half the perimeter times the apothem.
Common mistakes and edge cases
- Mixing up apothem (center to the middle of a side) with circumradius (center to a corner). The circumradius is always longer.
- Using the interior angle formula with the wrong n. Interior angle = (n − 2) × 180° / n.
- Forgetting that area is in square units while every other result is a length.
- Zero or negative measurements cannot form a polygon and return an error.
Worked examples
Side 6 (area 54√3)
Area
93.5307
Apothem 5 cm
Area
86.6025
Circumradius 10 (side is also 10)
Area
259.8076
Area 100 square units
Area
100
Perimeter 48 ft
Area
166.2769
Decimal side 2.5 m
Area
16.238
Zero side (impossible)
Area
Error
Frequently asked questions
What is the area of a regular hexagon?+
A = (3√3/2)s² ≈ 2.598·s². For side 6 that is 54√3 ≈ 93.53. It is six equilateral triangles of area (√3/4)s² each.
Why does the circumradius equal the side?+
Joining the center to each vertex splits the hexagon into six triangles with 60° central angles. Each is equilateral, so the two radii and the side are all the same length.
What is the apothem of a hexagon?+
The distance from the center to the middle of a side: a = (√3/2)s ≈ 0.866s. It is also the height of one of the six equilateral triangles.
What are the angles of a hexagon?+
Each interior angle of a regular hexagon is 120°, and the six add up to 720°. Each exterior angle is 60°.
How many diagonals does a hexagon have?+
Nine: n(n − 3)/2 = 6 × 3 / 2. Three pass through the center (the long diagonals, length 2s) and six are shorter (length s√3).
How do I find the side from the area?+
Rearrange A = (3√3/2)s²: s = sqrt(2A / (3√3)). Area 100 gives side ≈ 6.204.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026