Perimeter of Regular Pentagon Calculator
Enter the side length of a regular pentagon, or its apothem, circumradius or area, to find its perimeter.
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Perimeter of Regular Pentagon Calculator
Our Perimeter of Regular Pentagon Calculator finds the total length around a five-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 pentagon measurements and the perimeter in other units.
Quick answer
The perimeter of a regular pentagon is P = 5 × s: a 6 cm side gives 30 cm.
- From the apothem: P = 10 × a × tan 36° ≈ 7.265425 × a
- From the circumradius: P = 10 × R × sin 36° ≈ 5.877853 × R
- From the area: P ≈ 3.811935 × √A
- Side from the perimeter: s = P ÷ 5
What Is a Regular Pentagon?
A regular pentagon is a polygon with five equal sides and five equal interior angles of 108°. Its perimeter is the distance all the way around it: the sum of the five sides. Because the sides are equal, one side is all you need.
Perimeter of a Regular Pentagon Formula
P = 5 × s
- Measure one side. All five sides are equal, say 6 cm.
- Multiply by 5. 5 × 6 = 30.
- Keep the unit. The perimeter is 30 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 pentagon.
Pentagon Perimeter Examples
| Side | Perimeter |
|---|---|
| 4 cm | 20 cm |
| 7.5 mm | 37.5 mm |
| 10 m | 50 m |
| 12 in | 60 in |
| 2.3 km | 11.5 km |
Doubling the side doubles the perimeter. (The area, by contrast, goes up four times.)
Perimeter From the Apothem
The apothem a runs from the centre to the middle of a side. Half a side and the apothem make a right triangle with a 36° angle at the centre, so the side is s = 2a × tan 36°:
P ≈ 7.265425 × a
a = 5 m: P ≈ 36.327 m
Perimeter From the Circumradius
The circumradius R runs from the centre to a corner, so it is the radius of the circle drawn through all five corners. Each side is s = 2R × sin 36°:
P ≈ 5.877853 × R
R = 4 cm: P ≈ 23.511 cm
The pentagon perimeter is a little shorter than the circle around it: 5.877853 × R against 2π × R ≈ 6.283185 × R.
Perimeter From the Area
The area of a regular pentagon is A ≈ 1.720477 × s². Undo that to get the side, then multiply by 5:
A = 60 cm²: s ≈ 5.905 cm
P ≈ 5 × 5.905 ≈ 29.53 cm
In one step, P ≈ 3.811935 × √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 5:
47 m ÷ 5 = 9.4 m
So 47 m of edging goes round a regular pentagon with 9.4 m sides.
Common Mistakes
- Multiplying by 6 or 4. A pentagon has 5 sides, so the factor is 5.
- Using square units. Perimeter is a length: 30 cm, not 30 cm².
- Mixing units. Convert every side to one unit before adding.
- Using 5 × s on an irregular pentagon. If the sides differ, add all five lengths.
- Confusing the apothem with the circumradius. The apothem goes to the middle of a side, the circumradius to a corner, and they give different perimeters.
Key Terms
- Perimeter
- Total length around the shape, P.
- Side
- Any of the five equal edges, s.
- Apothem
- Centre to the middle of a side, a.
- Circumradius
- Centre to a corner, R.
- Diagonal
- Corner to a non-adjacent corner, φ × s.
How to Use the Perimeter of Regular Pentagon 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, diagonal, area and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a pentagonal garden bed has 12 ft sides. Enter 12 and pick ft. The perimeter is 60 ft (18.288 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 pentagon?
Multiply the side length by 5. A regular pentagon with 6 cm sides has a perimeter of 5 × 6 = 30 cm.
What is the formula for the perimeter of a regular pentagon?
P = 5 × s, where s is the length of one side. It is the five equal sides added together.
How do you find the perimeter of a pentagon with the apothem?
Use P = 10 × a × tan 36°, about 7.265425 × a. An apothem of 5 m gives a side of about 7.265 m and a perimeter of about 36.327 m.
How do you find the perimeter of a pentagon from the radius?
With the circumradius R (centre to a corner), each side is 2R × sin 36°, so P = 10 × R × sin 36°, about 5.877853 × R. A 4 cm radius gives about 23.511 cm.
How do you find the perimeter of a pentagon from its area?
Find the side with s = √(A ÷ 1.720477), then multiply by 5. An area of 60 cm² gives a side of about 5.905 cm and a perimeter of about 29.53 cm.
How do you find the side of a regular pentagon from its perimeter?
Divide the perimeter by 5. A perimeter of 47 m gives sides of 9.4 m.
What units is the perimeter of a pentagon 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 = 5 × s work for any pentagon?
No. It only works for a regular pentagon, where all five sides are equal. For an irregular pentagon, add the five side lengths.
Is the Perimeter of Regular Pentagon 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 Pentagon Calculator to find the perimeter of any regular pentagon from its side, apothem, circumradius or area, in any units.