Circle Calculator
- Radius r = 5 in.
- Diameter d = 2 × r = 2 × 5 = 10 in.
- Circumference C = 2π × r = 2 × 3.1416 × 5 = 31.4159 in.
- Area A = π × r² = 3.1416 × 5² = 78.5398 in².
- Arc length: 7.854 in
- Sector area: 19.635 in²
- Chord length: 7.0711 in
- Segment area: 7.135 in²
- Area in mm²: 50,670.7479
- Area in cm²: 506.7075
- Area in m²: 0.0507
- Area in ft²: 0.5454
- C ÷ d = π: 3.14159, matches 3.14159.
- A = C × r ÷ 2: 78.5398 in², equal to π × r². Confirmed.
- In terms of π: C = 10π in, A = 25π in².
Circle Calculator: Area, Circumference, Radius and Diameter
This free circle calculator finds the radius, diameter, circumference and area of a circle from any one of them. Enter the value you know, choose a unit, and the other three appear straight away with the working shown. You can also set an angle to get the arc length, sector area, chord length and segment area, and a diagram redraws as you change the numbers.
Quick answer: a circle with a radius of 5 inches has a diameter of 10 inches, a circumference of 31.4159 inches and an area of 78.5398 square inches.
Circle Formulas
Every measurement of a circle comes from the radius r and the constant pi, about 3.14159. The diameter is d = 2r. The circumference is C = 2πr, and the area is A = πr². Going the other way, r = C ÷ 2π and r = √(A ÷ π). The table shows the same circle reached from four different starting points.
| Known value | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| Radius 5 | 5 | 10 | 31.4159 | 78.5398 |
| Diameter 12 | 6 | 12 | 37.6991 | 113.0973 |
| Circumference 31.4159 | 5 | 10 | 31.4159 | 78.5398 |
| Area 100 | 5.6419 | 11.2838 | 35.4491 | 100 |
Radius, Diameter and Circumference
The radius is the distance from the centre to the edge, and the diameter is the full width through the centre. Circumference is the length of the edge itself, so it is what you need for fencing, edging, belts or wheel travel. Because the circumference divided by the diameter is always pi, you can estimate it by eye: a circle's edge is a little more than three times its width.
Area of a Circle
Area measures the space inside the circle, in square units. It grows with the square of the radius, so doubling the radius makes the area four times as large. This is why a 16 inch pizza has far more food than two 8 inch ones. If you are comparing areas in different units, the list under the results converts the area to square metres, feet and more. For other shapes and surfaces, use the area calculator.
Arc Length, Sector and Chord
A slice of a circle is called a sector, and the curved edge of that slice is an arc. With the angle in degrees, arc length is the circumference times the angle divided by 360, and the sector area is the circle's area times the same fraction. The chord is the straight line joining the two ends of the arc, and the segment is the area between the chord and the arc. For a radius of 3 and an angle of 90°, the arc is 4.7124, the sector is 7.0686, the chord is 4.2426 and the segment is 2.5686.
Where You Will Use It
Circle measurements come up in school geometry, woodworking, gardening, pipes and tanks, wheels and gears, and anything round that needs covering or fencing. If you need the volume of a round tank or pipe, multiply the circle's area by the length or height. For quick arithmetic with pi and other functions, the scientific calculator is handy, and the quadratic calculator helps when a circle problem leads to an equation.
How to Use This Circle Calculator
Choose what you know
Pick Radius, Diameter, Circumference or Area under Calculate from.
Enter the value and unit
Type the number or drag the slider, then choose a unit from millimetres to miles.
Set an angle if needed
Use the angle box for the arc length, sector area and chord of part of the circle.
Read the results
See all four measurements, the working, a check and a diagram of your circle.