How to use it
- Choose which measurement you have – radius, diameter, circumference or area – and type it with its unit.
- Read the other three values. Switching the “given” selector keeps the same circle and shows that quantity in the field.
- For a slice of the circle, enter the central angle in degrees or radians to get the arc length, chord, sector and segment area.
- Copy the summary or share the link.
Example
Area 78.54 cm²: r = √(78.54 ÷ π) = √25.0 = 5.00 cm, so d = 10 cm and C = 2π × 5 = 31.42 cm. A 90° sector of that circle: θ = π/2 = 1.5708 rad, arc = 5 × 1.5708 = 7.85 cm, sector area = ½ × 25 × 1.5708 = 19.63 cm² (a quarter of 78.54), chord = 2 × 5 × sin 45° = 7.07 cm, and the segment between the chord and the arc is 19.63 − 12.5 = 7.13 cm².
Formulas
d = 2r C = 2πr = πd A = πr²
from C: r = C / (2π) from A: r = √(A / π)
sector (θ in radians, degrees × π/180):
arc s = r·θ area = ½·r²·θ chord = 2r·sin(θ/2) segment = ½·r²·(θ − sin θ)The unit is a label: all lengths come out in the unit you choose and areas in that unit squared; the formulas are exact. Angles above 360° (2π) are rejected because a sector cannot exceed the full circle.
Sources: Wolfram MathWorld – Circle, Wolfram MathWorld – Circular sector and segment.
Questions
- How do I find the radius from the circumference?
- Divide by 2π. A circumference of 31.42 cm gives r = 31.42 ÷ 6.2832 = 5 cm. Select "Circumference" and type the value – the radius is computed exactly.
- What is the area of a circle with a diameter of 10?
- Halve the diameter first: r = 5, A = π × 25 = 78.54 square units. Using the diameter directly in πr² is the most common mistake and gives four times the true area.
- How much pizza is in a 12-inch versus two 8-inch pizzas?
- Area grows with the square of the diameter: a 12-inch is 113.1 in², two 8-inch pizzas are 2 × 50.3 = 100.5 in². The single large one is bigger.