Hexagon Size Calculator: Side, Area & More

This calculator works out the key dimensions of a regular hexagon. You enter any one known value — side length, perimeter, area, inradius (apothem), or circumradius — and it returns the rest, including the side length if that is what you need. The first output is the side length, since that is the most common “size” question, followed by area, perimeter, and both radii.

Formula

For a regular hexagon (six equal sides and six equal angles), all the key measurements are related to the side length s:

• Perimeter P = 6s
• Area A = (3√3/2) × s² ≈ 2.5980762 × s²
• Inradius (apothem) r = (√3/2) × s ≈ 0.8660254 × s
• Circumradius R = s

Here s is the side length, P is the total distance around the hexagon, A is the two-dimensional space inside, r is the distance from the center to the midpoint of a side, and R is the distance from the center to a vertex. The circumradius equals the side length because a regular hexagon is made of six equilateral triangles.

Worked Example

Using the default values: known value = 10, and the known quantity is side length.

1. Side length s = 10 units.
2. Perimeter = 6 × 10 = 60 units.
3. Area = 2.5980762 × 10² = 2.5980762 × 100 = 259.80762 ≈ 259.81 square units.
4. Inradius = 0.8660254 × 10 = 8.660254 ≈ 8.6603 units.
5. Circumradius = 10 units (same as side).

The calculator gives the same results: side 10, area 259.81, perimeter 60, inradius 8.6603, circumradius 10.

When to Use a Hexagon Size Calculator

Hexagons appear in many practical places: floor tiles, honeycomb patterns, bolts and nuts, mirrors, garden planters, and structural components. You might need the size when ordering a custom glass hexagon, cutting a hexagon from a square board, or checking how many hex tiles fit a wall. This calculator is for regular hexagons — all sides and angles equal. If your shape is irregular (like a stretched hexagon), the formulas do not apply directly.

How to Choose the Right Input

Choose the measurement you already have. If you only know the distance across the hexagon from one vertex to the opposite vertex (the “long diagonal”), that is the circumradius doubled. If you know the distance across from the midpoint of one side to the midpoint of the opposite side (the “short diagonal”), that is the inradius doubled. The calculator accepts side, perimeter, area, inradius, or circumradius directly. For example, a bolt head often has a “width across flats” of 10 mm — that is the inradius times 2, so enter inradius = 5 mm to get the side length.

Common Mistakes and Misconceptions

• Confusing inradius and circumradius: The inradius is smaller than the circumradius. For a hexagon, the circumradius equals the side length; the inradius is about 0.866 times the side.
• Using the wrong area formula: Some people use the formula for a circle or a square. The hexagon area is roughly 2.598 times the square of the side.
• Unit mix-ups: If you enter the side in inches, the area comes out in square inches, the perimeter in inches, and the radii in inches. Do not mix feet and inches without converting first.
• Thinking all hexagons are regular: A hexagon can have unequal sides. This calculator only works for regular hexagons.

Limits of the Formula

The formulas assume a perfectly regular hexagon in a flat plane. Real-world objects may have manufacturing tolerances, rounded corners, or slight warping, so measurements will be approximate. Also, the area formula gives the mathematical area; if you are buying material, add extra for waste and cuts. The calculator gives exact mathematical values, but physical measurement always has some uncertainty.

Alternatives and Related Calculations

If you have an irregular hexagon, you can divide it into triangles and calculate each area separately. For a regular hexagon, you could also use the general polygon formulas: area = (1/2) × perimeter × apothem. That works for any regular polygon. If you need the size of a hexagon that fits inside a circle or around a circle, use the circumradius and inradius respectively. For 3D shapes like hexagonal prisms or bolts, you would also need height or thickness.

Frequently Asked Questions

How do I find the side length of a hexagon if I only know the area?

Rearrange the area formula: s = √(A / 2.5980762). For example, if the area is 100 square units, s = √(100 / 2.5980762) ≈ √38.49 ≈ 6.20 units.

What is the difference between inradius and circumradius?

The inradius (apothem) is the distance from the center to the midpoint of a side. The circumradius is the distance from the center to a vertex. In a regular hexagon, the circumradius equals the side length, and the inradius is about 0.866 times the side.

Can I use this calculator for a hexagon with unequal sides?

No. The formulas assume all six sides and angles are equal. For an irregular hexagon, you need to know more dimensions or break it into triangles.

What units should I use?

Use any consistent unit: inches, centimeters, feet, meters, etc. The side length, perimeter, and radii will be in that unit, and the area will be in that unit squared. Do not mix units without converting.

How do I measure a hexagon I already have?

Measure one side directly with a ruler. If you cannot measure a side, measure the distance across from one vertex to the opposite vertex (that is twice the circumradius) or the distance across from the middle of one side to the middle of the opposite side (that is twice the inradius).

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in a | Known value | - | 10 | 0
sel k | What is the known value? | Side length=1, Perimeter=2, Area=3, Inradius=4, Circumradius=5
out side | Side length | units | if(k==1,a, k==2,a/6, k==3,sqrt(a/(2.5980762)), k==4,a*2/sqrt(3), k==5,a) | 4
out area | Area | sq units | 2.5980762 * side^2 | 2
out perimeter | Perimeter | units | 6 * side | 2
out inradius | Inradius (apothem) | units | side * 0.8660254 | 4
out circumradius | Circumradius | units | side | 4