Mathematics · Geometry
Circle Calculator — Radius, Diameter, Circumference, Area, Arc & Sector
Enter any one measurement of a circle — radius, diameter, circumference or area — and get all the others with the working. Add a central angle to find the arc length, sector area, chord length and segment area.
Your inputs
Quick start — try a typical case
Optional — 0 to skip. 90° is a quarter circle.
Your result Live
Area
153.93804 cm²
Radius 7 cm · circumference 43.982297 cm
- Radius
- 7 cm
- Diameter
- 14 cm
- Circumference
- 43.982297 cm
- Area
- 153.93804 cm²
Working
r: Step 1 · Radius
r = 7
Expression becomes 7 cm
C: Step 2 · Circumference
2πr = 2 × π × 7
Expression becomes 43.982297 cm
A: Step 3 · Area
πr² = π × 7²
Expression becomes 153.93804 cm²
How this is calculated
d = 2r · C = 2πr · A = πr² · arc = rθ · sector = ½r²θ · chord = 2r·sin(θ/2) · segment = ½r²(θ − sin θ)
- θ
- Central angle in radians (degrees × π ÷ 180)
Everything about a circle follows from its radius. Work the radius out from whatever you know — halve the diameter, divide the circumference by 2π, or take √(area ÷ π) — then circumference is 2πr and area is πr². An arc is the same fraction of the circumference as its angle is of 360°.
Assumptions & sources
- π is used to full double precision (3.14159265…), not 22/7.
Calculator ID MATH-CIRCLE-001 · version 1.0.0
Common questions
What's the area of a circle with radius 7 cm?
π × 7² ≈ 153.94 cm² (154 cm² with π ≈ 22/7).
How do I find the radius from the circumference?
Divide the circumference by 2π. A 100 cm circumference has radius 100 ÷ 6.2832 ≈ 15.92 cm.
What's the difference between a sector and a segment?
A sector is the pizza-slice shape between two radii; a segment is the part between a chord and the arc.