Perimeter of Circle Calculator
Enter the radius, diameter or area of a circle to find its perimeter (circumference).
Updated
Perimeter of Circle Calculator
Our Perimeter of Circle Calculator finds the perimeter of a circle, also called its circumference, from the radius, the diameter or the area. It shows the working, the exact answer in terms of π, the matching radius, diameter and area, and a drawing.
Quick answer
The perimeter of a circle is 2 × π × radius: C = 2π × 7 cm ≈ 43.98 cm.
- From the diameter: C = π × d, so 12 m gives ≈ 37.70 m
- From the area: C = 2√(πA), so 100 cm² gives ≈ 35.45 cm
- Radius from the perimeter: r = C ÷ 2π
- Units: the perimeter is a length, so cm stays cm (not cm²)
What Is the Perimeter of a Circle?
The perimeter of a circle is the distance all the way around its edge. For circles it has a special name, the circumference, so the two words mean the same thing. The radius r runs from the centre to the edge, and the diameter d = 2r runs right across through the centre.
Perimeter of a Circle Formulas
Use the formula that matches what you know. All three give the same perimeter for the same circle.
| You know | Formula |
|---|---|
| The radius | C = 2πr |
| The diameter | C = πd |
| The area | C = 2√(πA) |
π (pi) is about 3.14159. It is the same for every circle: the perimeter is always a little more than 3 times the diameter.
Why the Perimeter Is π Times the Diameter
If you roll a circle along a flat line for one full turn, the distance it travels is its perimeter. For a circle with a diameter of 1, that distance is π ≈ 3.14. Double the diameter and the perimeter doubles too, so C = π × d. Since d = 2r, this is the same as C = 2πr.
Circle Perimeter Examples
| Known | Exact | Perimeter |
|---|---|---|
| r = 7 cm | 14π | ≈ 43.98 cm |
| d = 12 m | 12π | ≈ 37.70 m |
| r = 4.5 in | 9π | ≈ 28.27 in |
| d = 20 ft | 20π | ≈ 62.83 ft |
| A = 100 cm² | 2√(100π) | ≈ 35.45 cm |
Leaving π as a letter keeps the answer exact: a radius of 7 gives 14π. Multiply by 3.14159 only at the end, so rounding does not creep in.
Perimeter From the Area
If you only know the area, find the radius first. An area of 100 cm² gives r = √(100 ÷ π) ≈ 5.642 cm, so C = 2π × 5.642 ≈ 35.45 cm. In one step this is C = 2√(πA).
Finding the Radius or Diameter From the Perimeter
Turn the formula around. Divide the perimeter by π to get the diameter, and by 2π to get the radius. A perimeter of 44 cm gives d = 44 ÷ π ≈ 14.01 cm and r ≈ 7.003 cm.
Common Mistakes
- Using πr²: that is the area. The perimeter is 2πr.
- Mixing up r and d: 2πr and πd are equal. Using 2π with the diameter doubles the answer.
- Square units: a perimeter is a length (cm, m, ft), not an area (cm²).
- Rounding π too early: 3.14 instead of π gives 43.96 instead of 43.98 for r = 7.
- Using 22/7 as exact: it is close to π, but not equal to it.
Key Terms
- Perimeter
- The distance around the circle, also called the circumference, C.
- Radius
- From the centre to the edge, r.
- Diameter
- Across the circle through the centre, d = 2r.
- Pi (π)
- Perimeter ÷ diameter for every circle, about 3.14159.
How to Use the Perimeter of Circle Calculator
- Choose what you know. Pick Radius, Diameter or Area.
- Enter the value. Type the number, such as 7, 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 the working, the exact answer in terms of π, the radius, diameter and area, and the perimeter in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a round table has a diameter of 1.2 m. Choose Diameter, enter 1.2 and pick m. The perimeter is about 3.77 m, the length of trim you need for its edge.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you find the perimeter of a circle?
Multiply the radius by 2π, or the diameter by π. A radius of 7 cm gives 2π × 7 = 14π ≈ 43.98 cm.
Is the perimeter of a circle the same as its circumference?
Yes. Circumference is the special name for the perimeter of a circle: the distance all the way around it.
What is the formula for the perimeter of a circle?
C = 2πr with the radius, C = πd with the diameter, or C = 2√(πA) with the area.
How do you find the perimeter of a circle from its area?
Find the radius with r = √(A ÷ π), then use C = 2πr. An area of 100 cm² gives r ≈ 5.642 cm and C ≈ 35.45 cm.
How do you find the radius from the perimeter?
Divide the perimeter by 2π: r = C ÷ 2π. A perimeter of 44 cm gives r ≈ 7.003 cm, and the diameter is C ÷ π ≈ 14.01 cm.
What is the perimeter of a circle with a radius of 1?
2π, which is about 6.283. A circle with a diameter of 1 has a perimeter of π, about 3.142.
Is the Perimeter of Circle 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 Circle Calculator to find the perimeter (circumference) of any circle from its radius, its diameter, or its area.