What this calculator does
Converting circumference to diameter is a single division: divide by π. It comes up whenever a circular object has been measured around its outside, with a tape measure or a piece of string, but the figure actually needed is the straight-line distance across it.
This calculator runs the conversion in whichever direction is needed, circumference to diameter or diameter to circumference, and shows the radius and area of the same circle alongside the headline result either way.
The formula
Circumference to diameter uses d = C/π, dividing the measured circumference by π. Diameter to circumference reverses it with C = πd, multiplying the diameter by π. Both directions rely on the same fixed ratio, π, approximately 3.14159, that links every circle’s circumference to its diameter.
| Term | Meaning |
|---|---|
| C | Circumference: the distance around the outside of the circle. |
| d | Diameter: the straight-line distance across the circle through its centre. |
| π | Pi, the fixed ratio of circumference to diameter for any circle, approximately 3.14159. |
The inputs explained
| Field | What to enter |
|---|---|
| Value | Enter the circumference or the diameter, matching the direction selected below. |
| Convert | Select whether you are converting a circumference to a diameter, or a diameter to a circumference. |
When to use it
Measuring a tree, pipe or drum with a tape
Wrapping a tape measure around a trunk, pipe or drum gives the circumference directly; converting that circumference to diameter gives the figure usually needed for sizing or comparison.
Specifying a part by its across-the-middle size
Diameter to circumference conversion is useful the other way around too, when a part is specified by diameter but the length of belt, band or trim needed to go around it is what is actually being ordered.
Checking a circumference of a circle with diameter answer
A textbook problem giving one measurement and asking for the other is solved directly here, in whichever direction the question is posed.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Circumference to diameter across a range of measurements
The diameter and radius recovered from a range of measured circumference values.
| Circumference | Diameter | Radius |
|---|---|---|
| 10 | 3.183 | 1.592 |
| 20 | 6.366 | 3.183 |
| 31.4 | 9.995 | 4.997 |
| 50 | 15.915 | 7.958 |
| 100 | 31.831 | 15.915 |
| 200 | 63.662 | 31.831 |
Converting the same value both directions
The value 10 run through both directions of the conversion, to show how the "convert" setting changes what the number is taken to mean.
| Direction | Result |
|---|---|
| Circumference to diameter | 3.183 |
| Diameter to circumference | 31.416 |
Questions
How do you convert circumference to diameter?
Divide the circumference by π, approximately 3.14159. A circumference of 31.4 divided by π gives a diameter of about 10.
How do you convert diameter to circumference?
Multiply the diameter by π. A diameter of 10 multiplied by π gives a circumference of about 31.4.
What is the circumference of a circle with diameter 1?
Exactly π, approximately 3.14159, since circumference equals π times the diameter and a diameter of 1 leaves the formula unchanged.
Why does converting circumference to diameter only involve π and no other measurement?
Because π is defined as the fixed ratio between a circle’s circumference and its diameter, true for every circle regardless of size, so no other information is needed to convert between the two.
For circumference from a radius as well as a diameter, see the circumference calculator. For diameter from a radius, area or circumference, see the diameter calculator.