About the Circle Calculator
This circle calculator solves a circle from any single measurement. Choose whether you know the radius, the diameter, the circumference or the area, type the value, and the calculator returns all four properties at once. It saves you from rearranging formulas such as r = C ÷ 2π or r = √(A ÷ π) by hand.
Students use it to check geometry homework, and it is just as handy for practical jobs: working out the diameter of a tree from a tape measured around the trunk, the area of a round table top, the length of edging for a circular flower bed or the size of a pipe from its circumference.
The results are in the same unit as your input — lengths in that unit and area in that unit squared. π is used at full double precision (3.14159265…), so answers may differ slightly from textbook answers that round π to 3.14.
With the default inputs, the area (a) is 78.5398 units². Change any value above to recalculate instantly.
How to use the circle calculator
- 1Choose which measurement you already know.
- 2Enter its value (area in square units, the others in length units).
- 3Read the area, radius, diameter and circumference.
- 4Keep the units consistent — the results use the same unit as your input.
Formula and method
Everything about a circle follows from its radius. The diameter is twice the radius, the circumference is the diameter multiplied by π (about 3.14159), and the area is π times the radius squared. π is the fixed ratio of any circle’s circumference to its diameter.
When you enter something other than the radius, the calculator first converts it back to r: dividing a diameter by 2, a circumference by 2π, or taking the square root of the area divided by π. It then applies the forward formulas, so all four results are always consistent with each other.
- r
- Radius — centre to edge
- d
- Diameter — edge to edge through the centre
- C
- Circumference — distance around the circle
- A
- Area enclosed by the circle
- π
- ≈ 3.14159265, the ratio C ÷ d
Worked examples
Circle with a 5 cm radius
With r = 5, the diameter is 10, the circumference is 2π × 5 ≈ 31.42 and the area is π × 25 ≈ 78.54 square units.
Tree trunk measuring 100 cm around
Dividing the 100 cm circumference by π gives a diameter of about 31.8 cm, so the radius is 15.92 cm and the cross-section is roughly 796 cm².
Round table top with an area of 50 sq ft
r = √(50 ÷ π) ≈ 3.99 ft, so the table is about 7.98 ft across and its edge is 25.07 ft long.
Frequently asked questions
How do you find the area of a circle?+
Square the radius and multiply by π: A = πr². If you only have the diameter, halve it first; for example, a 10 cm diameter gives r = 5 and an area of about 78.54 cm².
How do I find the radius from the circumference?+
Divide the circumference by 2π (about 6.2832). A circumference of 31.4 cm gives a radius of about 5 cm, and a diameter of about 10 cm.
What is the difference between radius and diameter?+
The radius runs from the centre to the edge; the diameter runs all the way across through the centre, so it is always exactly twice the radius.
Why is π used for circles?+
π is the constant ratio between every circle’s circumference and its diameter, about 3.14159. Because all circles are similar shapes, the same constant appears in both the circumference and area formulas.
How do I get the radius from the area?+
Divide the area by π and take the square root: r = √(A ÷ π). An area of 100 m² gives a radius of about 5.64 m.