Hexagon Side Length Calculator: Find Side from Area

This calculator works out the side length of a regular hexagon when you enter either the area, the perimeter, or the distance across corners (circumradius). You choose what you know, type in the value, and the page returns the side length in the same unit you entered, along with the circumradius and apothem for reference.

Formula

A regular hexagon has six equal sides and six equal interior angles of 120°. The formulas below connect the side length s to the other common measurements:

• Area (A) = (3√3/2) × s², so s = √(2A / (3√3))
• Perimeter (P) = 6s, so s = P / 6
• Circumradius (R) = distance from center to a vertex = s, so s = R
• Apothem (a) = distance from center to the midpoint of a side = (√3/2) × s

All lengths are in the same unit you enter (inches, cm, meters, etc.). The area must be in that unit squared (e.g., in², cm²).

Worked Example

Using the default values from the calculator above:

1. You select Area and enter A = 100 unit².
2. Plug into the area formula: A = (3√3/2) × s².
3. Rearrange: s² = 2A / (3√3) = 200 / (5.196152) ≈ 38.490.
4. Take the square root: s ≈ 6.204 unit.

The calculator shows s ≈ 6.204 (rounded to 3 decimals). The circumradius equals the side length (6.204), and the apothem is 6.204 × 0.866025 ≈ 5.373 unit.

When to Use This Calculator

You would reach for a hexagon side calculator when you are working on a project that involves a regular hexagon but you only have one measurement. Common real-world situations include:

• Tile or paver patterns: you know the area of a hexagonal tile, and you need the side length to plan cuts or spacing.
• Hex bolts and nuts: the “across flatsâ€� dimension is the apothem times 2; if you know the across-flats, you can find the side length.
• Honeycomb or structural panels: you have the total area of a hexagonal cell and want the side length for material estimates.
• 3D modeling or CNC: you need the side length to draw a hexagon from a given area or circumradius.

The calculator assumes a regular hexagon (all sides equal, all angles 120°). If your hexagon is irregular, these formulas do not apply—you would need the actual side measurements.

How to Read the Results

The main output is the side length, which is always in the same linear unit as your input. For example, if you enter area in square meters, the side length is in meters. The secondary outputs help you double-check:

• Circumradius: the radius of the circle that passes through all six vertices. For a regular hexagon, it is exactly equal to the side length—a useful sanity check.
• Apothem: the radius of the inscribed circle that touches the midpoints of the sides. It is about 0.866 times the side length.

If you measured the “across flats� of a hex nut (the distance between two opposite flat sides), that is twice the apothem. So side length = (across flats) / √3.

Common Mistakes and How to Avoid Them

People often trip on these points:

• Unit mismatch: entering area in square inches but expecting the side in centimeters. Convert everything to the same unit system first.
• Confusing circumradius with apothem: the circumradius equals the side length, but the apothem is shorter (0.866 × side). They are not interchangeable.
• Using the formula for a regular hexagon on an irregular one: if the sides are not equal, the area formula does not hold.
• Rounding too early: if you round the side length to 2 decimals before using it in further calculations, you may compound errors. Keep full precision until the final step.

For a quick check: a regular hexagon with side length 1 has area ≈ 2.598, apothem ≈ 0.866, and circumradius = 1. If your results are wildly different from these ratios, recheck your input.

Limits of the Formula

The formulas here are exact for a perfect regular hexagon in Euclidean geometry. They do not account for:

• Material thickness, bevels, or manufacturing tolerances (for physical objects).
• Curved surfaces or projections (e.g., a hexagon drawn on a sphere).
• Irregular hexagons where sides or angles differ.

For most practical purposes—tiling, drawing, basic engineering sketches—the regular hexagon model is accurate enough. For high-precision machining, always verify with direct measurement.

Frequently Asked Questions

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

Use the formula s = √(2A / (3√3)). For example, if the area is 100 cm², then s ≈ 6.204 cm. This works only for a regular hexagon.

Is the side length of a regular hexagon equal to its circumradius?

Yes. In a regular hexagon, the distance from the center to any vertex equals the side length. This is because the hexagon can be divided into six equilateral triangles.

What is the difference between the apothem and the circumradius?

The apothem is the distance from the center to the midpoint of a side (the inscribed circle radius), while the circumradius is the distance from the center to a vertex (the circumscribed circle radius). The apothem is always shorter: apothem = (√3/2) × side.

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

No. The formulas assume all six sides are equal and all angles are 120°. For an irregular hexagon, you would need to measure each side individually or use a different method.

How do I convert “across flats� to side length?

Across flats is the distance between two opposite parallel sides, which equals 2 × apothem. So side length = (across flats) / √3. For example, a hex nut with across flats of 10 mm has a side length of 10 / 1.732 ≈ 5.77 mm.

What unit should I use for the area input?

Use the square of whatever linear unit you want the side length in. If you want the side in inches, enter area in square inches. If you enter area in square feet, the side will come out in feet.

Related

• Conduit Size Calculator: Fill & Sizing
• Compressed File Size Calculator: Estimate ZIP & RAR Sizes
• Coffee Half Life Calculator: Caffeine Half-Life

in sel | Given value | area=area, perimeter=perimeter, circumradius=circumradius | area
in a | Area | unit² | 100 | 0
in p | Perimeter | unit | 30 | 0
in r | Circumradius | unit | 5 | 0
out s | Side length | unit | (sel=="area" ? sqrt(a/(3*sqrt(3)/2)) : sel=="perimeter" ? p/6 : r) | 3
out R | Circumradius | unit | s | 3
out ap | Apothem (inradius) | unit | s*sqrt(3)/2 | 3