Circumference Calculator
Enter a circle's radius, diameter or area to find its circumference and the full circle profile.
Updated
Circumference Calculator
Our Circumference Calculator finds the distance around a circle from whichever measurement you already have: the radius, the diameter or the area. It then fills in the rest of the circle's profile, with the working, the exact answer in terms of π, the result in other units and a drawing.
Quick answer
The circumference of a circle is 2 × π × radius: C = 2π × 5 cm ≈ 31.42 cm.
- From the diameter: C = π × d, so 10 cm gives ≈ 31.42 cm
- From the area: C = 2√(πA), so 100 cm² gives ≈ 35.45 cm
- Exact form: a radius of 5 gives exactly 10π
- Units: the circumference is a length, so cm stays cm (cm² becomes cm)
What Is Circumference?
The circumference (C) of a circle is the total distance around its edge: its perimeter. It depends only on the size of the circle, given by the radius r (centre to edge) or the diameter d = 2r (right across through the centre), and the constant π, about 3.1416.
Circumference Formulas
Use the formula that matches what you know.
| You know | Formula |
|---|---|
| The radius | C = 2πr |
| The diameter | C = πd |
| The area | C = 2√(πA) |
Once you have the circumference, the rest follows: r = C ÷ 2π, d = C ÷ π and A = C² ÷ 4π.
Circumference From the Area
The area A = πr² gives the radius back: r = √(A ÷ π). Multiply that by 2π and the two steps fold into one formula, C = 2√(πA).
r = √(100 ÷ π) ≈ 5.6419 cm
C = 2√(100π) ≈ 35.45 cm
Why the Circumference Is π Times the Diameter
Roll a circle along a straight line for exactly one turn. However big the circle is, the distance covered is always about 3.14 times its diameter. That ratio is π, so C = πd, and since d = 2r, C = 2πr.
Circumference Examples
| Known | Exact | Circumference |
|---|---|---|
| r = 5 cm | 10π | ≈ 31.42 cm |
| d = 10 m | 10π | ≈ 31.42 m |
| r = 2.5 in | 5π | ≈ 15.71 in |
| d = 24 ft | 24π | ≈ 75.40 ft |
| A = 100 cm² | 2√(100π) | ≈ 35.45 cm |
Leaving π as a letter keeps the answer exact: a radius of 5 gives 10π. Multiply by 3.14159 only at the end, so rounding does not creep in.
Circumference in Real Life
- Wheels: a wheel 0.6 m across moves π × 0.6 ≈ 1.885 m each turn.
- Pizza and baking: a 30 cm pizza has a crust about 94.25 cm long.
- Fencing a round garden: a 20 m² circular bed needs about 15.85 m of edging.
- The Earth: a mean radius of 6,371 km gives a circumference of about 40,030 km.
Common Mistakes
- Using πr²: that is the area. The circumference is 2πr.
- Mixing up r and d: 2πr and πd are equal. Using 2π with the diameter doubles the answer.
- Square units: circumference is a length (cm, m, ft), not an area (cm²).
- Rounding π too early: 3.14 instead of π gives 31.40 instead of 31.42 for r = 5.
- From the area: take the square root. C = 2√(πA), not 2πA.
Key Terms
- Circumference
- The distance around a circle, C.
- Radius
- From the centre to the edge, r.
- Diameter
- Across the circle through the centre, d = 2r.
- Area
- The space inside the circle, A = πr².
- Pi (π)
- Circumference ÷ diameter for every circle, about 3.14159.
How to Use the Circumference Calculator
- Choose what you know. Pick Radius, Diameter or Area.
- Enter the value. Type the number, such as 5, and pick a unit if you want one (mm, cm, m, km, in, ft, yd or mi; squared for an area). Decimals and fractions such as 3/4 work.
- Read and copy the result. The circumference appears as you type, with the working, the exact answer, the radius, diameter and area, and the result in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a round flower bed covers 20 m². Choose Area, enter 20 and pick m. The circumference is about 15.85 m, so that is how much edging you need.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is the formula for circumference?
C = 2πr, or C = πd with the diameter. A radius of 5 cm gives 10π ≈ 31.42 cm.
How do you find the circumference from the diameter?
Multiply the diameter by π: C = πd. A diameter of 10 cm gives 10π ≈ 31.42 cm.
How do you find the circumference from the area?
Use C = 2√(πA). An area of 100 cm² gives a radius of √(100 ÷ π) ≈ 5.64 cm and a circumference of about 35.45 cm.
Is circumference the same as perimeter?
Yes. Circumference is the name for the perimeter of a circle: the distance all the way around its edge.
What unit is circumference in?
The same length unit as the radius or diameter. A radius in cm gives a circumference in cm, not cm², because it is a distance, not an area.
What is the circumference of a circle with a radius of 1?
2π, which is about 6.283. A circle with a diameter of 1 has a circumference of π, about 3.142.
Is the Circumference Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Circumference Calculator to get a circle's full measurements from just one known value.