Geometry
Circumference Calculator
Find the distance around a circle from its radius, diameter, area — or work backwards from the circumference itself. Every property is reported alongside, with the working shown step by step.
What do you know?
C = 2πrCircumference
31.4159
Radius
5 cm
Diameter
10 cm
Circumference
31.4159 cm
Area
78.5398 cm²
π taken as 3.14159…
Try an example
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The basics
What is circumference?
The circumference is the distance all the way around a circle — its perimeter. Because every circle is the same shape scaled up or down, that distance is always the same multiple of the width across: a little over three times. That fixed multiple is π, and it is the whole reason a single measurement is enough to describe a circle completely.
C = 2πr
From the radius
The radius is the distance from the centre to the edge. Double it and multiply by π to walk all the way around.
r = 5 → C = 2 × π × 5 ≈ 31.4159
C = πd
From the diameter
The diameter is the width straight across through the centre — twice the radius. Times π gives the circumference directly.
d = 10 → C = π × 10 ≈ 31.4159
The constant
Why π shows up
Take any circle, measure its circumference and its diameter, and divide one by the other. You always get the same number — about 3.14159 — no matter how big or small the circle is. That ratio is what we call π.
π = C ÷ d
A ratio, not a length
π is defined as circumference divided by diameter, so it has no units. It is the same for a coin and for the equator.
π ≈ 3.14159
Irrational
The digits never end and never repeat. We round it for arithmetic, but the true value cannot be written as a fraction.
22/7 ≈ 3.143
Handy approximations
22/7 and 3.14 are close enough for most by-hand work; this tool uses full precision.
Method
How to calculate it by hand
Three steps, whether you start from the radius or the diameter.
- 1
Identify what you know
Spot whether you have the radius r (centre to edge) or the diameter d (all the way across). If you only have one, the other is just half or double.
d = 2r · r = d ÷ 2 - 2
Pick the matching formula
Use C = 2πr with a radius, or C = πd with a diameter. They give exactly the same answer.
C = 2πr or C = πd - 3
Multiply through by π
Substitute your number and multiply by π ≈ 3.14159. Keep the unit of length — the answer comes out in the same unit you measured in.
C = 2 × π × 5 ≈ 31.4159
Worked examples
See it from any starting point
The same circle, reached from the radius, the diameter, or even backwards from the circumference. Switch tabs to follow each route.
Given r = 7
C = 2πr
C = 2 × π × 7
C = 6.2832 × 7
C = 43.9823
Cross-check: a circle here has diameter 14, circumference 43.9823, and area 153.938 — every property follows from the one value you started with.
Where it shows up
Why circumference matters
Circumference is one of the most practical numbers in geometry — anywhere something rolls, wraps, or curves.
distance = C × turns
Wheels & gears
A wheel travels one circumference per turn, so a bike or car wheel's size sets how far each rotation carries you.
C = πd
Pipes & rings
The length of material to wrap a pipe, build a ring, or hoop a barrel is its circumference — a single multiplication.
40,075 km
Planets & orbits
Eratosthenes measured Earth's circumference from shadows over 2,000 years ago; the same formula sizes orbits today.
Reference
Every formula in one place
Each circle property can be found from any other. Pick the row that matches what you already know.
| You know | Find circumference | Find the rest |
|---|---|---|
| Radius r | C = 2πr | d = 2r, A = πr² |
| Diameter d | C = πd | r = d ÷ 2, A = π(d/2)² |
| Area A | C = 2√(πA) | r = √(A ÷ π) |
| Circumference C | — | r = C ÷ 2π, d = C ÷ π |
Worth knowing
Rules worth remembering
A handful of relationships make circle problems quick once you see them.
C ÷ d = π
Always the same ratio
Divide any circle's circumference by its diameter and you get π. This is the definition, and it never changes.
d = 2r
Diameter is double the radius
Mixing up r and d is the most common slip — double a radius or halve a diameter before you plug in.
2× r → 2× C
Circumference scales linearly
Double the radius and the circumference doubles too. Unlike area, it grows in direct proportion to size.
C grows, A grows²
Area grows faster
Area follows πr², so doubling the radius quadruples the area while only doubling the circumference.
arc = C × (θ/360)
Arc length is a fraction
A slice of the edge is just the circumference times the slice's share of the full 360 degrees.
unit in = unit out
Units carry through
Multiplying by π (a pure number) keeps your unit — measure in cm and the circumference is in cm.
Quick chart
Circumference of a circle, at a glance
The circumference, radius or diameter, and area for whole-number sizes 1 through 24. Switch between holding the diameter or the radius fixed.
| Diameter | Circumference | Radius | Area |
|---|---|---|---|
| 1 | 3.14 | 0.5 | 0.79 |
| 2 | 6.28 | 1 | 3.14 |
| 3 | 9.42 | 1.5 | 7.07 |
| 4 | 12.57 | 2 | 12.57 |
| 5 | 15.71 | 2.5 | 19.63 |
| 6 | 18.85 | 3 | 28.27 |
| 7 | 21.99 | 3.5 | 38.48 |
| 8 | 25.13 | 4 | 50.27 |
| 9 | 28.27 | 4.5 | 63.62 |
| 10 | 31.42 | 5 | 78.54 |
| 11 | 34.56 | 5.5 | 95.03 |
| 12 | 37.7 | 6 | 113.1 |
| 13 | 40.84 | 6.5 | 132.73 |
| 14 | 43.98 | 7 | 153.94 |
| 15 | 47.12 | 7.5 | 176.71 |
| 16 | 50.27 | 8 | 201.06 |
| 17 | 53.41 | 8.5 | 226.98 |
| 18 | 56.55 | 9 | 254.47 |
| 19 | 59.69 | 9.5 | 283.53 |
| 20 | 62.83 | 10 | 314.16 |
| 21 | 65.97 | 10.5 | 346.36 |
| 22 | 69.12 | 11 | 380.13 |
| 23 | 72.26 | 11.5 | 415.48 |
| 24 | 75.4 | 12 | 452.39 |
Using C = πd with π ≈ 3.14159. Values are in the same unit you measure in; area is in that unit squared.
Pitfalls
Common mistakes
The errors that turn a right method into a wrong answer.
2πr ✗ as πr
Forgetting the 2
With a radius you need 2πr, not πr. Dropping the 2 halves your answer — a classic exam slip.
πd ✗ with r
Using the wrong width
C = πd needs the diameter. Feed it a radius and you get half the true circumference. Check which one you have first.
πr² vs 2πr
Mixing circumference and area
2πr is the distance around; πr² is the space inside. The squared one is area, not circumference.
cm vs cm²
Losing the unit
Circumference is a length (cm, m, in), never a square unit. If your answer reads in cm², you computed area by mistake.
FAQ
Common questions
Multiply the radius by 2π, where π ≈ 3.14159. The formula is C = 2πr. For a radius of 5, the circumference is 2 × π × 5 ≈ 31.4159.
Multiply the diameter by π. The formula is C = πd, because the diameter is twice the radius. For a diameter of 10, the circumference is π × 10 ≈ 31.4159.
The diameter is the straight-line distance across the circle through its centre, equal to twice the radius (d = 2r). The circumference is the distance around the circle. They are linked by C = πd, so the circumference is always about 3.14159 times the diameter.
Divide the circumference by 2π. Rearranging C = 2πr gives r = C ÷ 2π. For a circumference of 100, the radius is 100 ÷ 6.2832 ≈ 15.9155.
First recover the radius with r = √(A ÷ π), then apply C = 2πr. For an area of 78.54, the radius is √(78.54 ÷ π) ≈ 5, so the circumference is about 31.4159.
π is the ratio of any circle's circumference to its diameter — the same constant for every circle, approximately 3.14159. It is irrational, so its decimal expansion never ends or repeats.
Yes — circumference is simply the word used for the perimeter of a circle. For polygons you add up the side lengths; for a circle that distance around the edge is the circumference.
For schoolwork, 3.14 or 3.14159 is plenty. Engineering rarely needs more than a handful of digits, and even NASA uses only about 15 for interplanetary navigation. This calculator uses your device's full-precision π.
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Ugo CharlesBuilt and fact-checked against our editorial standards · Last updated June 2026
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