The formula
How it works
A circle is defined by a single measurement. Give the calculator any one of the radius, diameter, circumference or area, and it works out the other three — plus the constant π that ties them all together.
FAQ
What is π?
Pi (π ≈ 3.14159) is the ratio of a circle’s circumference to its diameter. It is the same for every circle, which is why one measurement is enough to find all the others.
Radius or diameter — which do I need?
Either works. The diameter is the full width across the centre, and the radius is half of it. Pick whichever you know from the menu and enter it.
Why is area measured in square units and circumference in plain units?
Circumference is a length — a distance around the edge — so it keeps whatever unit you entered, like metres or feet. Area covers a surface, so it is measured in that unit squared, like square metres, because it is built from two lengths multiplied together.
How do I find the area of just part of a circle?
That is a sector, found with \(A = \frac{\theta}{360} \pi r^2\) for an angle θ in degrees, or a fraction of the full circle’s area for any wedge. This calculator handles the whole circle; for a slice, scale its area result by the fraction of the circle the slice represents.
What is the difference between a circle and a sphere?
A circle is a flat, two-dimensional shape with an area and a circumference; a sphere is its three-dimensional counterpart, like a ball, with a surface area and a volume instead. If you are working with a round solid rather than a flat shape, use a sphere calculator instead of this one.
Can I enter a negative or zero value?
A zero value gives a circle with no size — everything comes back as zero — and a negative value is not physically meaningful for a radius, diameter, circumference or area, so the calculator treats it as zero. Enter a positive number for a meaningful result.
Does the calculator work with any unit of measurement?
Yes — it does not assume inches, metres or anything else. Whatever unit you type the value in, the radius, diameter and circumference come back in that same unit, and the area comes back in that unit squared.
About the circle calculator
This calculator finds every basic property of a circle — radius, diameter, circumference and area — from just one of them. A circle is the set of points the same distance from a centre, and that single distance, the radius, fixes its whole size. Because all four measurements are linked by the constant π, knowing any one lets you calculate the rest exactly.
How to use it
Use the menu to say which measurement you already have, then type its value. If you enter a radius of 5, the calculator returns a diameter of 10, a circumference of about 31.4 and an area of about 78.5. Choose Area or Circumference from the menu instead to work backwards to the radius. Keep your units consistent: whatever unit you enter, lengths come back in the same unit and the area in that unit squared.
The formula
The area of a circle is and its circumference is , where is the radius and . The diameter is simply . To go the other way, rearrange: from area, ; from circumference, . Once you have the radius, every other property follows from these two short formulas.
Where it is used
Circles are everywhere in design and construction, so these formulas turn up constantly. Builders use area to order enough material for a round patio or pond liner, and engineers use it to size pipes and cylinders by their cross-section. Circumference tells you the length of a running track, the distance a wheel travels in one turn, or how much edging a circular garden bed needs. The same maths scales up to gears, lenses and satellite orbits.