Enter any single circle property — radius, diameter, circumference, or area — to compute all other properties instantly. Optionally add a central angle to get arc length and sector area.
How to use this calculator
Select which property you already know: radius, diameter, circumference, or area.
Enter its value — the other three properties compute instantly.
Optionally enter a central angle (in degrees) to get the arc length and sector area for that slice.
Formula & method
Circle properties from radius
d = 2r · C = 2πr · A = πr² · Arc length = (θ/360) × 2πr · Sector area = (θ/360) × πr²
r = radius, d = diameter, C = circumference, A = area, θ = central angle in degrees.
Example
Circle with r = 5: d = 10, C = 2π × 5 ≈ 31.42, A = π × 25 ≈ 78.54. 60° sector: arc ≈ 5.24, sector area ≈ 13.09.
Key insights
π ≈ 3.14159 is the ratio C / d for every circle regardless of size.
Doubling the radius quadruples the area (A = πr²), but only doubles the circumference.
A sector is a 'pizza slice'. Its area is (θ/360) × πr² and its arc length is (θ/360) × 2πr.
The circle is the unique shape that maximises area for a given perimeter.
How to interpret your result
Circumference vs diameter
Their ratio is always π ≈ 3.14159. Knowing one uniquely determines the other.
Sector vs segment
A sector is the pie-slice bounded by two radii and an arc. A segment is the region between a chord and an arc — computed by subtracting the triangle from the sector.
Frequently asked questions
How do I find the radius from the circumference?
r = C / (2π). Example: if C = 31.42, then r = 31.42 / 6.2832 ≈ 5.
What is a sector of a circle?
A sector is the region bounded by two radii and the arc between them, like a slice of pie. Its area = (θ / 360) × πr².
Is diameter the same as circumference?
No. Diameter d = 2r is a straight line through the centre. Circumference C = πd is the total curved perimeter.
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