Circle Calculator
Derive diameter, circumference, area from radius — plus arc, sector and chord.
Overview
The Circle Calculator takes any single circle measurement — radius, diameter, circumference or area — and derives the other three, along with arc, sector and chord properties when you supply an angle. Whether you need to size a round table, pour a concrete patio or solve a geometry homework problem, you get all the related numbers in one click.
Carpenters, garden designers, architects and students all reach for circle math. Hand-calculating chord length or sector area means remembering the right formula every time; the tool keeps everything consistent.
How it works
Given a radius r, the circle's diameter is 2r, circumference is 2πr and area is πr^2. Any single input pins the others through these relationships.
For an arc subtending angle θ (in radians), arc length is r * θ and sector area is 0.5 * r^2 * θ. The chord connecting the arc's endpoints has length 2 * r * sin(θ / 2). Angles in degrees are converted with θ_rad = θ_deg * π / 180.
Examples
radius 5 → diameter 10, circumference ≈ 31.42, area ≈ 78.54
diameter 12 → radius 6, circumference ≈ 37.70, area ≈ 113.10
radius 10, angle 60° → arc ≈ 10.47, sector area ≈ 52.36, chord 10
area 50 → radius ≈ 3.99, circumference ≈ 25.07
FAQ
Is the calculator exact?
The arithmetic is exact up to double-precision rounding. Areas using π carry the same approximation as the rest of double-precision math.
Why is my chord length the same as the radius for a 60° angle?
Because at 60° the triangle formed by two radii and the chord is equilateral. A handy mental check.
Can I enter angles in radians?
Yes — the tool accepts both degrees (with a ° toggle) and radians. Pick one and stay consistent.
What's the difference between arc and chord?
Arc length is along the curve of the circle. Chord is the straight line between the same two endpoints. The chord is always shorter unless the arc spans 0 or 360 degrees.
Does it handle ellipses?
No, this tool is circle-only. Ellipse perimeter doesn't have a clean closed form — it needs an elliptic integral or a Ramanujan approximation.