Hexagon Calculator
Calculate the area, perimeter, inradius, circumradius and diagonals of a regular hexagon from its side length.
Area
93.53
Perimeter
36
Inradius (apothem)
5.2
Distance from centre to the middle of a side
Circumradius
6
Equal to the side length
Long diagonal
12
Spans two opposite vertices
Short diagonal
10.39
Between non-adjacent vertices
For a regular hexagon, area = (3√3/2) × side². All six sides and all six angles are equal.
Hexagon Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Calculate the area, perimeter, inradius, circumradius and diagonals of a regular hexagon from its side length. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: hexagon calculator · area of a hexagon · regular hexagon
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard mathematical formulas — the same ones taught in school and used in exams — verified by our team. All calculations are performed instantly in your browser using JavaScript, so no data is sent to any server.
The formulas follow standard mathematical definitions and conventions used in textbooks and by educational boards. Results are rounded transparently and shown with the exact formula on this page.
When to Use This Calculator
Regular hexagons appear in Indian workshops, kitchens and classrooms more than people notice. Machinists turn hexagonal stock for bolts and nuts and need the flat-to-flat width (the short diagonal) to match spanner sizes, while the long diagonal matters when estimating bar diameter. Tilers lay hexagonal vitrified tiles in Mumbai and Delhi homes, where the per-tile area feeds the order quantity. Architects use hexagons for honeycomb facades and shading screens, and product designers choose them for cable-organiser grids because they pack without gaps. Beekeeping extension projects in rural areas calculate comb-frame dimensions from hexagon geometry. Students meet the 30-60-90 triangles hidden inside a hexagon — each of its six sectors is equilateral — making this calculator a quick check for homework and design projects alike.
How to Use This Calculator
- Step 1: Measure one side of the regular hexagon — all six sides are equal.
- Step 2: Enter the side length in millimetres, centimetres, inches or any unit.
- Step 3: Read the area, perimeter, inradius, circumradius and both diagonals.
- Step 4: All six values are derived from the single side length, so nothing else needs measuring.
Worked Example
A CNC workshop in Coimbatore cuts hexagonal brass nuts whose flat-to-flat distance, the inradius doubled, must suit an 11 mm spanner. For a side of 6 mm the calculator reports an inradius of about 5.20 mm, so the flat-to-flat width is about 10.39 mm. The same hexagon has an area of about 93.53 mm², a perimeter of 36 mm, and a circumradius of 6 mm. A floor laid with hexagonal tiles of side 0.2 m uses tiles of area about 0.10 m² each — the tool confirms this before ordering hundreds of pieces.
Tips and Common Mistakes
- •Tip 1: Measure the side, not the diagonal — spanner size is the short diagonal (flat-to-flat), which the tool lists separately.
- •Tip 2: A hexagon of side s fits inside a circle of radius s, which matters when laser-cutting hex blanks from round stock.
- •Tip 3: For tiling, divide the floor area by the hexagon area to estimate the number of tiles needed.
- ✗Mistake 1: Assuming the circumradius equals the short diagonal — it equals the side length instead.
- ✗Mistake 2: Using the area formula for a regular hexagon on an irregular six-sided shape, which has no simple closed form.
Frequently Asked Questions
What is a regular hexagon?
A regular hexagon has six equal sides and six equal angles of 120°. It is the shape of honeycomb cells, many floor tiles, and the cross-section of nuts and bolts, where the flat sides grip a spanner.
How is the area of a regular hexagon calculated?
Area = (3√3/2) × side². For a side of 6 units, that works out to about 93.53 square units. You can also split it into six equilateral triangles and add their areas.
What are the inradius and circumradius?
The inradius (apothem) is the distance from the centre to the middle of a side, about 5.20 for a side of 6. The circumradius is the distance from the centre to a vertex, which equals the side length — 6 here.
What are the long and short diagonals of a hexagon?
The long diagonal spans opposite vertices and equals twice the side (12 for side 6). The short diagonal connects non-adjacent vertices and equals √3 times the side, about 10.39.
Why are hexagons so common in design?
Hexagons tessellate without gaps and enclose more area for their perimeter than squares, which is why honeybees use them. Architects and tile makers in India use hexagonal tiles for the same efficiency and look.
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