Circle Calculator
Enter any one circle property to calculate radius, diameter, area, and circumference instantly
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Quick summary
A circle calculator derives all four main circle properties from any single known value. Circumference (perimeter) uses C = 2πr, area uses A = πr², diameter uses d = 2r. For sectors, the same formulas scale by the fraction θ/360.
Reviewed by Simple Calculators TeamLast reviewed
How to use this calculator
- Enter the inputs requested by the calculator.
- Choose the units or options that match your situation and review the assumptions.
- Run or update the calculation to see the result.
- Review the result, breakdown, and formulas shown on the page.
- Check the inputs, units, dates, and limitations before saving or sharing the result.
Circle Formulas & Examples
Circle — Core Properties
- r
- Radius
- d
- Diameter = 2r
- A
- Area = πr²
- C
- Circumference = 2πr
Worked example
Circle with radius 7
- Given
- r = 7
- Calculation
- Result
- Area ≈ 153.94, Circumference ≈ 43.98
Sector (Pie Slice)
- θ
- Central angle in degrees
- r
- Radius
Worked example
90° sector of circle with radius 6
- Given
- θ = 90°r = 6
- Calculation
- Result
- ≈ 28.27 units²
Frequently asked questions
How do I find circumference from area?
First find the radius: r = √(A/π). Then compute circumference: C = 2πr. For example, if area = 50.27, then r = √(50.27/π) ≈ 4, and C = 2π×4 ≈ 25.13.
What is a sector of a circle?
A sector is a "pie slice" of a circle bounded by two radii and an arc. Its area is proportional to the central angle: A = (θ/360) × πr².
What is the difference between circumference and perimeter?
Circumference specifically refers to the perimeter of a circle — the total length around its boundary. For non-circular shapes, the term "perimeter" is used.
How precise is π in these calculations?
The calculator uses JavaScript's Math.PI which is accurate to 15-16 significant digits (π ≈ 3.141592653589793). For most practical purposes, this is far more than enough precision.
Key terms
- Radius (r)
- The distance from the center of a circle to any point on its circumference.
- Diameter (d)
- The longest chord of a circle, passing through the center. d = 2r.
- Circumference (C)
- The perimeter of a circle: C = 2πr.
- Sector
- A region bounded by two radii and the arc between them, like a pizza slice.
Methodology, sources & limitations
This page shows the formula, assumptions, and limitations used for this estimate. Rates, thresholds, and other time-sensitive inputs can change, so verify them against the relevant official source before relying on a result.
For our review approach and the primary sources we consult, see the methodology and source policy. If you spot an outdated figure or formula, please contact us with a correction.