Circle Formula Calculator — Area, Circumference, Arc, Sector & More
Enter a circle's radius and a central angle to compute every circle formula in one place: area, circumference, diameter, arc length, sector area, chord length, and circular segment area.
°
A = πr² — total area enclosed by the circle
- 1
Square the radius
r² = 6² = 36 - 2
Area = π × r²
π × 36 = 113.0973
How does this calculator work?
For a circle of radius r: A = πr², C = 2πr, d = 2r. For central angle θ (radians): arc = rθ, sector = ½r²θ, chord = 2r·sin(θ/2), segment = ½r²(θ−sin θ). Enter radius and angle to compute all formulas at once.
Formula
How this is calculated
The circle is fully defined by a single measurement: its radius r. The full-circle quantities follow directly: area A = πr², circumference C = 2πr, and diameter d = 2r. These are among the most fundamental formulas in geometry and arise constantly in engineering, physics, and everyday calculation.
For any arc or sector defined by a central angle θ, scale the full-circle values by the fraction θ/(2π) in radian terms. This gives arc length = rθ and sector area = ½r²θ. A chord is the straight line between the two endpoints of the arc, with length 2r·sin(θ/2) from the half-angle in the isosceles triangle formed with the two radii. The circular segment — the region between the chord and the arc — has area equal to the sector minus the triangle: ½r²(θ − sin θ).
All formulas use θ in radians internally; the input angle in degrees is converted automatically. As a sanity check, when θ = 360° the arc length equals the full circumference and the sector area equals the full circle area.
Frequently asked questions
A sector is a "pie slice" bounded by two radii and the arc between them. A segment is the smaller region between the chord (straight line connecting the two arc endpoints) and the arc itself. Segment area = sector area minus the triangle formed by the two radii and the chord.
Multiply degrees by π/180. For example 90° × π/180 = π/2 ≈ 1.5708 rad. The calculator converts automatically — enter your angle in degrees.
The sector has area ½r²θ. The isosceles triangle formed by the two radii and the chord has area ½r²·sin θ (using the formula ½ab·sin C for a triangle). Subtracting the triangle from the sector leaves the segment: ½r²θ − ½r²·sin θ = ½r²(θ − sin θ).
Also known as
TG we-Calculate Editorial Team. (2026). Circle Formula Calculator — Area, Circumference, Arc, Sector & More [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/circle-formula-calculator
TG we-Calculate Editorial Team. "Circle Formula Calculator — Area, Circumference, Arc, Sector & More." TG we-Calculate. 2026. https://we-calculate.com/calculator/circle-formula-calculator.
TG we-Calculate Editorial Team, "Circle Formula Calculator — Area, Circumference, Arc, Sector & More," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/circle-formula-calculator
@misc{wecalculate_circle_formula_calculator, title = {Circle Formula Calculator — Area, Circumference, Arc, Sector & More}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/circle-formula-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?