Perimeter of Regular Hexagon Calculator
Enter the side length of a regular hexagon, or its apothem, circumradius or area, to find its perimeter.
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Perimeter of Regular Hexagon Calculator
Our Perimeter of Regular Hexagon Calculator finds the total length around a six-sided shape with equal sides and equal angles. Enter the side length, or switch to the apothem, the circumradius or the area, and it shows the perimeter with the working, the other hexagon measurements and the perimeter in other units.
Quick answer
The perimeter of a regular hexagon is P = 6 × s: a 6 cm side gives 36 cm.
- From the circumradius: P = 6 × R (the radius equals the side)
- From the apothem: P = 4√3 × a ≈ 6.928203 × a
- From the area: P ≈ 3.722419 × √A
- Side from the perimeter: s = P ÷ 6
What Is a Regular Hexagon?
A regular hexagon is a polygon with six equal sides and six equal interior angles of 120°. Its perimeter is the distance all the way around it: the sum of the six sides. Because the sides are equal, one side is all you need.
Perimeter of a Regular Hexagon Formula
P = 6 × s
- Measure one side. All six sides are equal, say 6 cm.
- Multiply by 6. 6 × 6 = 36.
- Keep the unit. The perimeter is 36 cm, in the same unit as the side.
A perimeter is a length, so it is never in square units. Square units (cm², m²) are for the area of a regular hexagon.
Hexagon Perimeter Examples
| Side | Perimeter |
|---|---|
| 4 cm | 24 cm |
| 7.5 mm | 45 mm |
| 10 m | 60 m |
| 12 in | 72 in |
| 2.3 km | 13.8 km |
Doubling the side doubles the perimeter. (The area, by contrast, goes up four times.)
Perimeter From the Circumradius
The circumradius R runs from the centre to a corner. Lines from the centre to every corner split a regular hexagon into six equilateral triangles, so the circumradius is exactly the same length as a side:
P = 6 × R
R = 4 cm: P = 24 cm
The hexagon perimeter is a little shorter than the circle around it: 6 × R against 2π × R ≈ 6.283185 × R.
Perimeter From the Apothem
The apothem a runs from the centre to the middle of a side. It is the height of one of the six equilateral triangles, so a = s × √3 ÷ 2 and the side is s = 2a ÷ √3:
P ≈ 6.928203 × a
a = 5 m: P = 20√3 ≈ 34.641 m
Perimeter From the Area
The area of a regular hexagon is A = (3√3 ÷ 2) × s² ≈ 2.598076 × s². Undo that to get the side, then multiply by 6:
A = 60 cm²: s ≈ 4.806 cm
P ≈ 6 × 4.806 ≈ 28.83 cm
In one step, P ≈ 3.722419 × √A. For the square root, the Square Root Calculator gives as many digits as you need.
Side Length From the Perimeter
Work backwards by dividing the perimeter by 6:
45 m ÷ 6 = 7.5 m
So 45 m of edging goes round a regular hexagon with 7.5 m sides.
Common Mistakes
- Multiplying by 5 or 8. A hexagon has 6 sides, so the factor is 6.
- Using square units. Perimeter is a length: 36 cm, not 36 cm².
- Mixing units. Convert every side to one unit before adding.
- Using 6 × s on an irregular hexagon. If the sides differ, add all six lengths.
- Using the apothem as the side. The apothem is shorter (about 0.866 × s). Only the circumradius equals the side.
- Doubling the width across the corners. That width is the long diagonal, 2 × s, so the perimeter is 3 times it, not 2 times.
Key Terms
- Perimeter
- Total length around the shape, P.
- Side
- Any of the six equal edges, s.
- Apothem
- Centre to the middle of a side, a.
- Circumradius
- Centre to a corner, R (equal to s).
- Diagonals
- Long 2 × s, short √3 × s.
How to Use the Perimeter of Regular Hexagon Calculator
- Choose what you know. Pick Side, Apothem, Radius (the circumradius) or Area. Side is the usual choice; the others work the side out first.
- Enter the value. Type it, such as 6, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi). Decimals and fractions such as 3/4 work.
- Read and copy the result. The perimeter appears as you type, with a drawing, the working, the side, apothem, circumradius, both diagonals, area and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a hexagonal garden bed has 12 ft sides. Enter 12 and pick ft. The perimeter is 72 ft (21.9456 m), which is the length of edging you need.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a regular hexagon?
Multiply the side length by 6. A regular hexagon with 6 cm sides has a perimeter of 6 × 6 = 36 cm.
What is the formula for the perimeter of a regular hexagon?
P = 6 × s, where s is the length of one side. It is the six equal sides added together.
How do you find the perimeter of a hexagon from the radius?
Multiply the circumradius R (centre to a corner) by 6. In a regular hexagon the circumradius equals the side, so a 4 cm radius gives a perimeter of 24 cm.
How do you find the perimeter of a hexagon with the apothem?
Use P = 4√3 × a, about 6.928203 × a. An apothem of 5 m gives a side of about 5.774 m and a perimeter of 20√3, about 34.641 m.
How do you find the perimeter of a hexagon from its area?
Find the side with s = √(A ÷ 2.598076), then multiply by 6. An area of 60 cm² gives a side of about 4.806 cm and a perimeter of about 28.83 cm.
How do you find the side of a regular hexagon from its perimeter?
Divide the perimeter by 6. A perimeter of 45 m gives sides of 7.5 m.
What units is the perimeter of a hexagon in?
The same length unit as the side, such as cm, m or ft. Perimeter is never in square units; those are for area.
Does P = 6 × s work for any hexagon?
No. It only works for a regular hexagon, where all six sides are equal. For an irregular hexagon, add the six side lengths.
Is the Perimeter of Regular Hexagon Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Perimeter of Regular Hexagon Calculator to find the perimeter of any regular hexagon from its side, apothem, circumradius or area, in any units.