- What's the formula for the area of a regular hexagon?
- Area = (3√3 / 2) × s², where s is the length of one side. The constant 3√3/2 works out to about 2.598076, so a hexagon with 10-unit sides has an area of 259.8076 square units. The reason that constant exists is worth knowing: a regular hexagon is exactly six equilateral triangles meeting at the center, and the area of one equilateral triangle is (√3/4) × s². Multiply by six and you get (6√3/4) × s², which simplifies to (3√3/2) × s². If you ever forget the constant, you can rebuild it from the triangle. This calculator also runs the formula backwards — type an area and it returns the side by taking the square root of area ÷ 2.598076.
- What does "across flats" mean, and why does it matter more than the side?
- Across flats is the distance between two opposite sides, measured straight through the middle. It's the short diagonal, and it's twice the apothem. It matters because it's the number stamped on hardware: when a nut is called M10 with a 17mm spanner size, 17mm is the across-flats measurement. Nobody measures a hex nut by its side length, because you can't get a caliper on one edge cleanly, but the flats are exactly what a wrench jaw grips. Textbooks almost always call it the short diagonal and stop there, which leaves anyone working with actual hardware doing a conversion in their head. The relationship is across flats = √3 × side, so a 17mm spanner size means a side of 9.815mm.
- What's the apothem?
- The apothem is the perpendicular distance from the center of the hexagon to the middle of any side — the radius of the largest circle that fits inside, which is why it's also called the inradius. For a regular hexagon it equals (√3/2) × side, and it's exactly half the across-flats measurement. It shows up in the other common area formula, Area = (1/2) × perimeter × apothem, which works for any regular polygon, not just hexagons. That formula is really just the six-triangles idea again: each triangle has the side as its base and the apothem as its height.
- Why is the circumradius always the same as the side?
- Because a regular hexagon is the one regular polygon where that's true, and it's a genuinely useful shortcut. The circumradius is the distance from the center to any corner. Draw lines from the center to two adjacent corners and you've made a triangle whose two long sides are both circumradii, with the hexagon's side as its base. The angle at the center is 360° ÷ 6 = 60°, and the other two angles must split the remaining 120° evenly at 60° each — so all three angles are 60° and the triangle is equilateral. All three sides are equal, which means the circumradius equals the side. That's also why you can draw a perfect hexagon with just a compass: set it to any radius, step it around the circle six times, and it closes exactly.
- Why does the result disappear when I fill in two boxes?
- Because a regular hexagon is fixed by one number, so a second one is either redundant or contradictory, and there's no safe way to guess which you meant. If you type a side of 10 and an area of 500, those describe two different hexagons — the side says the area should be 259.8076. Some calculators quietly pick one input and ignore the other, which means you get a confident answer to a question you didn't ask. This page hides the result and tells you to clear one instead. Clear the box you're less sure about and the rest solves immediately.
- How many hexagons do I need to cover an area?
- Divide the total area by the area of one hexagon, then add for waste. Hex tiles and pavers tessellate perfectly, with no gaps and no wasted interior space, which is why honeycomb and a lot of flooring use the shape — but the edges of your actual room or patio won't line up with the hexagon grid, so you'll cut some. A common allowance is 10 percent for a simple rectangular area and 15 percent where there are curves or angled walls. Work in a single unit throughout: if a paver is sold by its 300mm across-flats dimension, type 300 into Across flats, read the area in square millimeters, and convert once at the end rather than part-way through.
- Does this work for an irregular hexagon?
- No, and it's better to say so than to hand back a number that looks right. Every formula on this page assumes all six sides are equal and all six interior angles are 120°. An irregular hexagon — six sides of different lengths — has no single formula, because the sides alone don't determine its shape; you can flex it like a hinge and change the area without changing any side length. To find the area of an irregular one, split it into triangles, work out each triangle separately, and add them up. If you know the corner coordinates, the shoelace formula does it in one step.
- Why do the fixed facts never change?
- Interior angle 120°, exterior angle 60°, angle sum 720°, nine diagonals, six equilateral triangles — those hold for every regular hexagon no matter how big it is, so they sit in their own row rather than pretending to be calculated. The angle sum comes from (n − 2) × 180° with n = 6, giving 720°, split evenly across six corners for 120° each. The nine diagonals come from n(n − 3) ÷ 2: each of the six corners connects to three non-adjacent corners, and dividing by two stops you counting each line twice. Size changes every length on this page; it changes none of these.
