Circle Calculator
Enter any one of a circle’s radius, diameter, circumference or area and get the other three, plus a sector, arc and chord.
Result
Area: 78.5398 ft²
A measurement, not a material estimate. Nothing is added for waste.
- Radius
- 5 ft (60 in, 1.524 m)
- Diameter
- 10 ft (120 in, 3.048 m)
- Circumference
- 31.4159 ft (376.9911 in, 9.5756 m)
https://calcgallery.com/geometry/circle-calculator/
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How to use the Circle Calculator
- Choose which measurement you have, radius, diameter, circumference or area.
- Enter it in any unit.
- Optionally enter a central angle to get the sector area, the arc length and the chord for that slice of the circle.
The four measurements
Every circle has one free size. Fix any one of these four and the other three follow:
| Measurement | From the radius | Back to the radius |
|---|---|---|
| Diameter | d = 2r | r = d ÷ 2 |
| Circumference | C = 2πr | r = C ÷ 2π |
| Area | A = πr² | r = √(A ÷ π) |
The page first works out the radius from whatever you entered, then calculates the other three from that one radius. Calculating each pair separately can give answers that disagree in the last digit, even though each looks right.
Sectors, arcs and chords
A central angle θ cuts a slice from the circle, like a slice of pie. For that slice:
- Sector area = ½ × r² × θ
- Arc length = r × θ, the curved edge
- Chord length = 2 × r × sin(θ ÷ 2), the straight edge across the open end
The first two formulas need θ in radians, where a full turn is 2π instead of 360 degrees. You can type the angle in degrees; the page converts it. A quarter circle is 90 degrees, or π ÷ 2 radians, and its sector area is exactly a quarter of the circle’s.
Units
A length entered in inches or centimetres is converted before anything is calculated, so the area comes out correctly in square feet or square metres. Remember that an area scales with the square of the length. A circle twice as wide has four times the area, which is why a 16-inch pizza is nearly twice the size of a 12-inch one.
With your numbers
- Radius = diameter ÷ 2 = 5 ft
- Diameter = 2 × 5 ft = 10 ft
- Circumference = 2 × π × 5 ft = 31.42 ft
- Area = π × 5 ft² = 78.54 ft²
Quick reference
A measurement, not a material estimate. Nothing is added for waste.
| Example | Area |
|---|---|
| Radius 2.5 m | 19.635 m² |
| Diameter 10 ft | 78.5398 ft² |
| Diameter 12 ft | 113.0973 ft² |
| Circumference 3 m | 0.7162 m² |
| Area 100 ft² | 100 ft² |
| Area 1 m² | 1 m² |
| Quarter circle, radius 3 m | 28.2743 m² |
| Radius 2.5 m, 60° slice | 19.635 m² |
Common questions about the Circle Calculator
- What is the difference between radius and diameter?
- The radius runs from the centre to the edge. The diameter runs right across through the centre, so it is always twice the radius. Most real measurements are diameters, because it is easier to measure across a pipe, a table or a tree than to find the centre.
- Where does 2πr come from?
- π is defined as the ratio of any circle’s circumference to its diameter, about 3.14159. So the circumference is π times the diameter, and since the diameter is 2r, that is 2πr. The area formula πr² follows from it: cut a circle into thin wedges and lay them head to tail, and they form a shape close to a rectangle πr long and r high.
- How do I find the radius from the area?
- Divide the area by π and take the square root. A circle of 100 square feet has a radius of √(100 ÷ π), a little under 5.65 feet. Choose Area above and the page does this for you.
- How do I measure a circle I cannot reach across?
- Wrap a tape round it to get the circumference, then choose Circumference above. That is the usual way to size a tree trunk, a column or a tank. Dividing by π gives the diameter.
- What is a chord?
- A straight line joining two points on the circle. For a slice with a given central angle, the chord is the straight edge across the open end, 2r × sin(θ ÷ 2). At 60 degrees it equals the radius, and at 180 degrees it is the diameter.