Diameter of a Circle Calculator
Created by: Emma Collins
Last updated:
To find the diameter of a circle, double the radius (d = 2r), divide the circumference by π (d = C ÷ π), or from the area take d = 2√(A ÷ π). A circle with a 5 inch radius is 10 inches across; one with a 31.4 inch circumference is 10 inches across; one with an area of 78.54 square inches is also 10 inches across. If you only have part of the circle, measure a chord and the arc height.
Diameter of a Circle Calculator
MathFind the diameter from the radius, circumference, area, or a chord and arc height.
How to find the diameter of a circle
From radius: d = 2r
From circumference: d = C ÷ π
From area: d = 2 × √(A ÷ π)
From a chord and arc height: d = c² ÷ 4h + h
Worked examples
- Radius 7 cm: d = 2 × 7 = 14 cm.
- Circumference 50 in: d = 50 ÷ 3.14159 = 15.92 in.
- Area 200 ft²: 200 ÷ π = 63.66, √63.66 = 7.98, d = 15.96 ft.
- Chord 10 m with a 2 m arc height: d = 100 ÷ 8 + 2 = 14.5 m.
Area to diameter chart
Diameter = 2√(area ÷ π). Works in any unit: square inches give inches, square meters give meters.
| Area | Diameter | Radius | Circumference |
|---|---|---|---|
| 1 | 1.128 | 0.564 | 3.545 |
| 2 | 1.596 | 0.798 | 5.013 |
| 5 | 2.523 | 1.262 | 7.927 |
| 10 | 3.568 | 1.784 | 11.210 |
| 12 | 3.909 | 1.954 | 12.280 |
| 20 | 5.046 | 2.523 | 15.853 |
| 25 | 5.642 | 2.821 | 17.725 |
| 28.27 | 6.000 | 3.000 | 18.848 |
| 50 | 7.979 | 3.989 | 25.066 |
| 78.54 | 10.000 | 5.000 | 31.416 |
| 100 | 11.284 | 5.642 | 35.449 |
| 113.1 | 12.000 | 6.000 | 37.700 |
| 150 | 13.820 | 6.910 | 43.416 |
| 200 | 15.958 | 7.979 | 50.133 |
| 250 | 17.841 | 8.921 | 56.050 |
| 314.16 | 20.000 | 10.000 | 62.832 |
| 500 | 25.231 | 12.616 | 79.267 |
| 1000 | 35.682 | 17.841 | 112.100 |
Pi is irrational, so most of these results are rounded. Areas like 78.54 and 314.16 are exact circles with diameters of 10 and 20.
Frequently Asked Questions
How do you find the diameter of a circle?
It depends on what you know. From the radius, double it (d = 2r). From the circumference, divide by π (d = C ÷ π). From the area, divide by π, take the square root and double it (d = 2√(A ÷ π)).
How do I find the diameter from the area?
Divide the area by π, take the square root to get the radius, then double it. For an area of 50 cm²: 50 ÷ 3.14159 = 15.92, √15.92 = 3.99 cm radius, so the diameter is 7.98 cm.
How do I find the diameter from the circumference?
Divide the circumference by π. A circle with a 31.4 inch circumference has a diameter of 31.4 ÷ 3.14159 = 10.0 inches.
How do I find the diameter of a circle from part of an arc?
Measure a straight chord across the arc and the arc height (sagitta), the distance from the middle of the chord to the arc. Then D = chord² ÷ (4 × height) + height. A 24 inch chord with a 3 inch rise gives 576 ÷ 12 + 3 = 51 inches.
Is the diameter twice the radius?
Yes. The radius runs from the center to the edge and the diameter runs edge to edge through the center, so d = 2r and r = d ÷ 2.
How do I measure the diameter of a round object?
For a pipe, tree or post, wrap a tape around it and divide the circumference by π; this averages out slight ovality. For a hole or a flat disc, measure across in two or three directions through the widest point and average the readings.
Sources and References
- Weisstein, Eric W. “Circle.” MathWorld. Relations between radius, diameter, circumference and area.
- Weisstein, Eric W. “Sagitta.” MathWorld. Radius from chord length and sagitta: r = c²/(8s) + s/2.