Circle Calculator — Area, Circumference, Diameter, Radius
Pick an input mode, type one value, and this calculator derives radius, diameter, area, circumference, and — if you supply a central angle — arc length and sector area. Works for any units; just keep them consistent.
- Area (A)
- 78.539816
- Circumference (C)
- 31.415927
How it works
The four fundamental circle measurements
Every circle is fully described by a single number. Give the calculator any one of the four standard measurements and it derives the rest using exact formulas. Radius r is the distance from the center to the edge. Diameter d = 2r spans the full width. Circumference C = 2πr is the perimeter — the distance around the circle. Area A = πr² is the surface enclosed.
These four quantities are locked together by π ≈ 3.14159265358979. Once you fix one, the other three follow immediately. The calculator carries ten or more significant digits internally and rounds the display to six decimal places — enough for engineering work, well beyond what any ruler can measure.
Unit consistency is your responsibility: if you enter a radius in centimeters, all results are in centimeters (linear) or square centimeters (area). There is no unit conversion built in — keep all inputs in the same unit system.
Arc length and sector area
A central angle θ cuts the circle into a sector — a pie-slice shape. The arc length L is the curved portion of the circumference that the sector spans: L = (θ / 360) × C = (θ / 360) × 2πr. For a full circle (θ = 360°) this equals C, as expected.
The sector area As is the fraction of the full disk enclosed by the sector: As = (θ / 360) × A = (θ / 360) × πr². For a semicircle (θ = 180°) this gives πr²/2, exactly half the full area.
These formulas are used everywhere from pizza geometry and pie charts to engineering problems involving gears, lenses, and circular segments. Enter the central angle in the optional field to add arc length and sector area to the results.
Practical uses and worked examples
Landscaping: a circular flower bed with a 3-meter radius has area A = π × 3² ≈ 28.274 m². Need to edge it? The circumference is 2π × 3 ≈ 18.850 m of edging material.
Construction: a round window with a 45 cm diameter has radius 22.5 cm. Its area ≈ 1590.4 cm². A pipe with a 10 cm circumference has radius C / (2π) ≈ 1.592 cm and cross-sectional area ≈ 7.958 cm².
Data visualization: a pie chart sector representing 25% of data corresponds to a 90° central angle. For a chart with radius 150 px, the sector area is (90/360) × π × 150² ≈ 17671 px² and the arc length is (90/360) × 2π × 150 ≈ 235.6 px.
Frequently asked questions
›What is the formula for the area of a circle?
A = πr², where r is the radius and π ≈ 3.14159265358979. Equivalently, A = π(d/2)² = πd²/4 if you know the diameter.
›How do I find the circumference from the area?
Derive radius first: r = √(A/π). Then C = 2πr = 2π√(A/π) = 2√(πA). Enter the area in this calculator and the circumference is computed automatically.
›What is the difference between circumference and perimeter?
For a circle, circumference IS the perimeter — the distance around the boundary. Perimeter is the general term for any closed shape; circumference is the specific word for circles.
›How accurate are the results?
JavaScript's 64-bit floating-point arithmetic gives about 15-17 significant digits. The display rounds to 6 decimal places. This far exceeds the precision of any physical measurement tool.
›What central angle gives a half-circle?
180 degrees. Half the circumference is πr (the arc) and half the area is πr²/2. This shape is called a semicircle.
›Can I use any unit?
Yes. The calculator is unit-agnostic. If you enter a radius in inches, all lengths are in inches and area is in square inches. Just be consistent — do not mix meters and centimeters.
›What is a sector?
A sector is the pie-slice region bounded by two radii and the arc between them. Its area is a fraction (θ/360) of the full circle area. A quarter-circle is a 90° sector.
›Does the data stay private?
All calculations run in your browser. Nothing is sent to any server.
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