Circumference to Radius Calculator
Enter the circumference of a circle to find its radius, or the radius to find the circumference.
Updated
Circumference to Radius Calculator
Our Circumference to Radius Calculator turns the distance around a circle into the distance from its centre to its edge, and back again. Divide the circumference by 2π to get the radius, or multiply the radius by 2π to get the circumference. The working, the exact answer, the diameter, the area and a drawing are shown as you type.
Quick answer
The radius of a circle is circumference ÷ 2π: r = 50 cm ÷ 2π ≈ 7.96 cm.
- Back the other way: C = 2π × r, so 5 cm gives ≈ 31.42 cm
- Rule of thumb: the radius is about a sixth of the circumference (× 0.1592)
- Diameter: twice the radius, d = C ÷ π
- Units: both are lengths, so cm stays cm
Circumference and Radius
The circumference (C) is the distance all the way around a circle. The radius (r) is the straight distance from the centre to any point on the edge, half the diameter. For every circle, big or small, the circumference is 2π times the radius, about 6.2832 times.
Conversion Formulas
One multiplication or division by 2π converts either way.
| You want | Formula |
|---|---|
| Radius from C | r = C ÷ 2π |
| Circumference from r | C = 2π × r |
| Diameter from C | d = C ÷ π |
| Area from C | A = C² ÷ 4π |
r = 50 ÷ 2π ≈ 7.9577 cm
d = 2 × r ≈ 15.9155 cm
Why You Divide by 2π
π is the circumference divided by the diameter, so C = πd. The diameter is two radii, so C = π × 2r = 2πr. Undo the multiplication and you get r = C ÷ 2π. Laid out flat, the edge of any circle is a little more than 6 radii long.
Circumference to Radius Examples
| Circumference | Radius |
|---|---|
| C = 1 m | ≈ 0.1592 m |
| C = 10π cm | 5 cm exactly |
| C = 20 in | ≈ 3.18 in |
| C = 50 cm | ≈ 7.96 cm |
| C = 100 ft | ≈ 15.92 ft |
Going the other way, a radius of 5 cm gives 10π ≈ 31.42 cm and 12 ft gives 24π ≈ 75.40 ft. Typing 31.42 back in gives 5.000648 rather than exactly 5, because 31.42 is already a rounded value.
Measuring Round Objects
It is often easier to wrap a tape around something than to find its centre. Divide that reading by 2π to get the radius.
- Trees: a trunk 2 m around has a radius of about 31.8 cm.
- Round tables and rugs: an edge 20 in around means a radius of about 3.18 in.
- Pipes and wheels: a wheel 62.83 cm around has a radius of about 10 cm.
- The Earth: 40,075 km around the equator gives a radius of about 6,378 km.
Common Mistakes
- Dividing by π only: that gives the diameter, twice the radius.
- Dividing by 2, then multiplying by π: 50 ÷ 2 × π is about 78.5, not 7.96. Divide by both 2 and π.
- Rounding π too early: 50 ÷ 6.28 gives 7.962 instead of 7.958.
- Square units: both measurements are lengths (cm, m, ft), never cm².
Key Terms
- Circumference
- The distance around a circle, C.
- Diameter
- Across the circle through the centre, d = 2r.
- Radius
- From the centre to the edge, r = d ÷ 2.
- Pi (π)
- Circumference ÷ diameter for every circle, about 3.14159.
How to Use the Circumference to Radius Calculator
- Choose what you know. Pick Circumference to find the radius, or Radius to find the circumference.
- Enter the value. Type the number, such as 50, 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 answer appears as you type, with the working, the exact form, the diameter, the area and the result in other units. Press Copy to copy it, or Clear or Esc to start again.
Example: a tape measure wrapped around a tree trunk reads 2 m. Choose Circumference, enter 2 and pick m. The radius is about 0.318 m (31.8 cm), so the trunk is about 63.7 cm across.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you convert circumference to radius?
Divide the circumference by 2π: r = C ÷ 2π. A circumference of 50 cm gives a radius of about 7.96 cm.
How do you convert radius to circumference?
Multiply the radius by 2π: C = 2πr. A radius of 5 cm gives 10π ≈ 31.42 cm.
What is the radius of a circle with a circumference of 1?
1 ÷ 2π, which is about 0.1592. So the radius is always a little less than a sixth of the circumference.
How do you get the diameter from the circumference?
Divide by π: d = C ÷ π. A circumference of 50 cm gives a diameter of about 15.92 cm, twice the radius.
Why is the circumference 2π times the radius?
π is the ratio of a circle's circumference to its diameter, so C = πd. The diameter is two radii, so C = 2πr and r = C ÷ 2π.
Is the Circumference to Radius Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Circumference to Radius Calculator to turn a measurement around any circle into its radius.