Circle Calculator (area + circumference + sector + arc)
All four classic circle quantities in one tool — area πr², circumference 2πr, sector area (½r²θ), arc length (rθ).
Result
- Radius r5.0000
- Diameter (2r)10.0000
- Area (πr²)78.539816
- Circumference (2πr)31.415927
- Sector angle60° (= 1.0472 rad)
- Sector area (½r²θ)13.089969
- Arc length (rθ)5.235988
- Chord length (2r sin(θ/2))5.000000
- Sector as fraction of circle16.67% (= 60/360)
Step-by-step
- Area = πr² = π · 5² = 78.5398.
- Circumference = 2πr = 2π · 5 = 31.4159.
- Convert angle: 60° × π/180 = 1.0472 rad.
- Sector area = ½r²θ (radian) = ½ · 5² · 1.0472 = 13.0900.
- Arc length = rθ = 5 · 1.0472 = 5.2360.
How to use this calculator
- Enter the radius — for a sector calculation, enter the angle in degrees too.
- Set angle = 360 to get the full-circle area and circumference; sector and arc become the full area and circumference.
- Set angle = 90 for a quarter-circle (¼ area, ¼ circumference).
About this calculator
Four classic circle quantities, all derived from radius r. Area A = πr². Circumference C = 2πr = πd. For a sector subtending angle θ (in radians): sector area = ½·r²·θ; arc length = r·θ. Convert degrees to radians by multiplying by π/180; or use the equivalent fraction-of-circle formulation: sector area = (deg/360)·πr², arc length = (deg/360)·2πr. The chord length connecting the two endpoints of an arc is 2·r·sin(θ/2), which is useful in trigonometry and design layout. π is irrational but well-approximated by 3.14159265358979; modern computers carry ~16 significant digits, so circle calculations on this tool are limited by IEEE 754 floating-point precision, not π precision.