How a circle is defined by its radius
A circle is the set of all points sitting the same distance from a single centre point. That fixed distance is the radius, and it is the only measurement you need — every other property of the circle follows from it.
Because all the formulas are built from the radius, doubling the radius doubles the diameter and circumference but quadruples the area, since area depends on the radius squared.
What each output means
The calculator reports four related quantities:
- Radius: the distance from the centre to the edge, the value you entered.
- Diameter: the full width across the centre, exactly twice the radius.
- Circumference: the distance once around the edge, equal to 2·π·r.
- Area: the flat space enclosed inside the circle, equal to π·r².
Working from a different measurement
If you only know the diameter, halve it and enter the result as the radius. If you know the circumference, divide it by 2·π to recover the radius before entering it.
The constant π is irrational, so any answer involving it is an approximation. The calculator uses a high-precision value of π internally and rounds only the displayed figure, which is accurate enough for any practical measurement.
Formula
diameter = 2·r; circumference = 2·π·r; area = π·r²Frequently asked questions
- I only have the diameter — what do I enter?
- Halve the diameter and enter it as the radius (radius = diameter / 2).