Hexagon Radius Calculator

Reviewed by Bojan Žugec, Mathematics (FOI) • Last updated 2026-03-30

The Hexagon Radius Calculator calculates the circumradius or inradius of a regular hexagon from side length, area, or perimeter.

Hexagon Radius Calculator

Given Choose what you know; we compute radius (circumradius) and other values.

Value Enter a positive number.

Unit Outputs use the same unit.

Rounding Formatting only; calculations keep full precision.

For a regular hexagon: circumradius R equals side length s. Also: apothem a = (√3/2)s, corner-to-corner diameter D = 2R, perimeter P = 6s, area A = (3√3/2)s². Note: Results assume a perfect regular hexagon (all sides/angles equal). For fabrication/engineering use, verify tolerances and local safety requirements.

Example Presets

Presets only fill inputs; click Calculate to run.

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About the Hexagon Radius Calculator

This tool computes either the circumradius or the apothem of a regular hexagon. It also returns related values, such as side length, area, and perimeter. Regular means all sides and angles are equal. The formulas are exact and come from basic geometry.

The calculator accepts many starting points. You can enter side length, area, perimeter, apothem, or circumradius. It then solves for the rest. This is useful when you measure one feature at a job site or in a design and need everything else.

The interface is designed for quick checks and classroom use. It shows steps so you can follow the reasoning. You can treat it as a worked example generator for homework or quality checks in the field.

How to Use Hexagon Radius (Step by Step)

Hexagon radius can mean circumradius or apothem. Choose which one you need before you start. Then give the calculator one known dimension. It will compute the others using exact relationships.

Select the quantity you know, such as side length or area.
Pick the units, for example, millimeters or inches.
Enter the value and set a precision if needed.
Choose the radius type to report: circumradius or apothem.
Press Calculate to view the result and steps.

The tool labeled Calculator will show the computed radius, along with side length, area, and perimeter. It will also display the formula used and a brief derivation so you can verify each step.

Hexagon Radius Formulas & Derivations

For a regular hexagon, let s be side length, R be circumradius, and r be apothem. The circumradius R is the distance from the center to any vertex. The apothem r is the perpendicular distance from the center to a side. These quantities are linked by right triangles formed by drawing radii and altitudes.

Side and circumradius: R = s. A regular hexagon can be split into six equilateral triangles with side s. The triangle radius equals s, so the vertex lies on a circle of radius s.
Apothem in terms of side: r = (√3/2) s. In each equilateral triangle, drop an altitude. It splits the triangle into two 30-60-90 triangles. The altitude equals s√3/2, which is the apothem.
Side in terms of apothem: s = 2r/√3. This is the inverse of the prior relation.
Apothem in terms of circumradius: r = (√3/2) R, since R = s for a regular hexagon.
Perimeter: P = 6s. A hexagon has six equal sides.
Area: A = (1/2) P r = (3√3/2) s². Using the apothem formula or summing the areas of six equilateral triangles gives the same result.

These results come from simple geometry. Each step uses properties of equilateral triangles and 30-60-90 triangles. The calculator applies these identities exactly and then rounds to your chosen precision.

What You Need to Use the Hexagon Radius Calculator

You only need one dimension from your hexagon to compute the radius and other values. Pick the dimension you trust most. Then choose whether you want the circumradius or apothem as the primary output.

Side length s
Perimeter P
Area A
Circumradius R
Apothem r
Units and desired decimal precision

Values must be positive. Zero or negative inputs are invalid. The calculator assumes a regular hexagon. Irregular shapes will not match these formulas. Very large or very small values are supported, but floating-point rounding may affect the last digit.

Using the Hexagon Radius Calculator: A Walkthrough

Here’s a concise overview before we dive into the key points:

Open the Calculator and choose your input type, such as side length.
Select units for both input and output.
Enter the known value and set the number of decimal places.
Choose which radius you want to see first: circumradius or apothem.
Click Calculate to compute the result.
Review the steps and confirm the formulas used.

These points provide quick orientation—use them alongside the full explanations in this page.

Example Scenarios

A woodworker needs to cut a hexagonal tabletop and knows the side length is 18 inches. Because R = s for a regular hexagon, the circumradius is 18 inches. The apothem is r = (√3/2) × 18 ≈ 15.588 inches. Area follows as A = (3√3/2) × 18² ≈ 840.9 square inches. What this means: the tabletop fits a circle of radius 18 inches, and the minimum distance from center to a side is about 15.59 inches.

A civil engineer checks a bolt pattern shaped as a regular hexagon with perimeter 1.2 meters. The side length is s = P/6 = 1.2/6 = 0.2 meters. Therefore R = s = 0.2 meters, and the apothem is r = (√3/2) × 0.2 ≈ 0.1732 meters. The area of the pattern footprint is A = (3√3/2) × 0.2² ≈ 0.1039 square meters. What this means: a clearance circle of radius 0.2 meters covers the bolt heads, and the gap to the inner edge follows from the apothem.

Accuracy & Limitations

The formulas are exact for a regular hexagon. The main sources of error come from measurement noise, unit choice, and rounding. The calculator also assumes a flat, planar shape without deformation.

Regularity is required. Irregular hexagons need different methods.
Measurement error propagates through the formulas. Small input errors can affect area more.
Rounding occurs at your selected precision. Keep more decimals for tight tolerances.
Unit mismatches can cause large errors. Always confirm units before entering data.
Very large or tiny values may show floating-point limits in extreme cases.

If you suspect an error, recheck the input and units. You can also compute the side length from one value and verify the others by hand. The displayed steps help you audit the path from input to result.

Units & Conversions

Units matter because all hexagon formulas are homogeneous. If you enter length in inches, the radius will come out in inches, and area in square inches. Keeping consistent units avoids errors and makes your result easy to interpret.

Common length units for hexagon radius and their conversion to meters
Unit	Symbol	To meters (multiply)	Example
Millimeter	mm	0.001	250 mm = 0.25 m
Centimeter	cm	0.01	50 cm = 0.5 m
Meter	m	1	2 m = 2 m
Inch	in	0.0254	20 in ≈ 0.508 m
Foot	ft	0.3048	3 ft ≈ 0.9144 m

Use the table to convert your measurement to meters if needed, or keep everything in your preferred unit. The calculator handles conversions internally, but matching units across all inputs and outputs keeps the steps and checks clear.

Tips If Results Look Off

Most odd results come from a unit mix-up or typing error. If the radius seems too large or too small, verify the input and the chosen unit. Then check which radius you asked for, circumradius or apothem.

Confirm side length equals circumradius for regular hexagons.
Re-enter the value with more decimals if rounding matters.
Switch the output to the other radius type to compare.
Compute side from one value, then recompute area as a check.

When you recheck, follow the steps shown under the result. If your measured shape is not regular, the numbers will not match these formulas. In that case, consider measuring multiple sides and angles or using a different model.

FAQ about Hexagon Radius Calculator

Is the circumradius always equal to the side length?

Yes, for a regular hexagon, the circumradius equals the side length. This follows from splitting the hexagon into six equilateral triangles.

What is the difference between apothem and circumradius?

The apothem is the distance from the center to a side, perpendicular to that side. The circumradius is the distance from the center to any vertex.

Can I compute the radius from area only?

Yes. From A = (3√3/2) s², solve s = √(2A/(3√3)). The circumradius is s, and the apothem is (√3/2) s.

Does this work for irregular hexagons?

No. The formulas assume all sides and angles are equal. Irregular hexagons require coordinate methods or triangle decomposition with measured lengths.

Key Terms in Hexagon Radius

Regular hexagon

A six-sided polygon with all sides and interior angles equal. It can be divided into six congruent equilateral triangles.

Circumradius

The radius of the circumscribed circle that passes through all vertices. For a regular hexagon, it equals the side length.

Apothem

The perpendicular distance from the center to any side. It equals (√3/2) times the side length in a regular hexagon.

Side length

The common length of any edge of a regular hexagon. It sets the scale for radius, perimeter, and area.

Perimeter

The total length around the hexagon. For a regular hexagon, it equals six times the side length.

Area

The surface covered by the hexagon. It equals (3√3/2) times the square of the side length.

Central angle

The angle at the center between radii to adjacent vertices. In a regular hexagon, it is 360°/6 = 60°.

Long diagonal

The distance between opposite vertices across the center. In a regular hexagon, it equals twice the side length.

References