Circumference to Diameter Calculator
Enter the circumference of a circle to find its diameter, or the diameter to find the circumference.
Updated
Circumference to Diameter Calculator
Our Circumference to Diameter Calculator turns the distance around a circle into the distance across it, and back again. Divide the circumference by π to get the diameter, or multiply the diameter by π to get the circumference. The working, the exact answer, the radius, the area and a drawing are shown as you type.
Quick answer
The diameter of a circle is circumference ÷ π: d = 50 cm ÷ π ≈ 15.92 cm.
- Back the other way: C = π × d, so 10 cm gives ≈ 31.42 cm
- Rule of thumb: the diameter is just under a third of the circumference (× 0.3183)
- Radius: half the diameter, r = C ÷ 2π
- Units: both are lengths, so cm stays cm
Circumference and Diameter
The circumference (C) is the distance all the way around a circle. The diameter (d) is the straight distance across it through the centre, twice the radius. For every circle, big or small, the circumference is π times the diameter, about 3.1416 times.
Conversion Formulas
One multiplication or division by π converts either way.
| You want | Formula |
|---|---|
| Diameter from C | d = C ÷ π |
| Circumference from d | C = π × d |
| Radius from C | r = C ÷ 2π |
| Area from C | A = C² ÷ 4π |
d = 50 ÷ π ≈ 15.9155 cm
r = d ÷ 2 ≈ 7.9577 cm
Why You Divide by π
Roll a circle along a straight line for exactly one turn. The distance covered is its circumference, and it is always about 3.14 diameters long. That ratio is π by definition, so C = πd. Undo the multiplication and you get d = C ÷ π.
Circumference to Diameter Examples
| Circumference | Diameter |
|---|---|
| C = 1 m | ≈ 0.3183 m |
| C = 10π cm | 10 cm exactly |
| C = 50 cm | ≈ 15.92 cm |
| C = 100 ft | ≈ 31.83 ft |
| C = 54 mm | ≈ 17.19 mm |
Going the other way, a diameter of 10 cm gives 10π ≈ 31.42 cm and 24 ft gives 24π ≈ 75.40 ft. Typing 31.42 back in gives 10.0013 rather than exactly 10, because 31.42 is already a rounded value.
Measuring Round Objects
It is often easier to wrap a tape around something than to measure straight through it. Divide that reading by π to get the width.
- Trees: a trunk 2 m around is about 63.7 cm across.
- Ring sizes: a finger 54 mm around needs a ring about 17.19 mm wide inside.
- Pipes and posts: a pipe 15.7 cm around is about 5 cm in diameter.
- The Earth: 40,075 km around the equator gives a diameter of about 12,756 km.
Common Mistakes
- Dividing by 2π: that gives the radius, half the diameter.
- Multiplying instead of dividing: the diameter is always smaller than the circumference.
- Rounding π too early: 50 ÷ 3.14 gives 15.92, but 100 ÷ 3.14 gives 31.85 instead of 31.83.
- 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 Diameter Calculator
- Choose what you know. Pick Circumference to find the diameter, or Diameter 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 radius, 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 trunk is about 0.637 m (63.7 cm) across.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you convert circumference to diameter?
Divide the circumference by π: d = C ÷ π. A circumference of 50 cm gives a diameter of about 15.92 cm.
How do you convert diameter to circumference?
Multiply the diameter by π: C = πd. A diameter of 10 cm gives 10π ≈ 31.42 cm.
What is the diameter of a circle with a circumference of 1?
1 ÷ π, which is about 0.3183. So the diameter is always a little less than a third of the circumference.
How do you get the radius from the circumference?
Divide by 2π: r = C ÷ 2π. A circumference of 50 cm gives a radius of about 7.96 cm, half the diameter.
Why is the circumference π times the diameter?
π is defined as the ratio of a circle's circumference to its diameter. Every circle has the same ratio, about 3.14159, so C = πd and d = C ÷ π.
Is the Circumference to Diameter 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 Diameter Calculator to turn a measurement around any circle into the width across it.