Quick answer
A circle's diameter is 2r, its circumference is 2πr and its area is πr². From a radius of 5: diameter 10, circumference 31.4159 and area 78.5398.
Choose which measurement you know (radius, diameter, circumference or area) and enter it. The calculator returns the other three.
Related tools: Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Circumference Calculator: Circumference of a circle. Circle Diameter Calculator: Diameter of a circle from radius, circumference or area.
How to use the Circle Calculator
- Choose i know the: Radius, Diameter, Circumference and Area.
- Enter value (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| I know the | Choose one: Radius; Diameter; Circumference; Area | Starts at Radius |
| Value | A number | > 0 |
Formula and method
Formula
d = 2r; C = 2πr; A = πr²
IEEE-754 double precision; shown to at most 6 decimal places.
Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: I know the = Radius; Value = 5.
| Result | Value |
|---|---|
| Area | 78.539816 |
| Radius | 5 |
| Diameter | 10 |
| Circumference | 31.415927 |
Example 2
Inputs: I know the = Circumference; Value = 6.283185307179586.
| Result | Value |
|---|---|
| Area | 3.141593 |
| Radius | 1 |
| Diameter | 2 |
| Circumference | 6.283185 |
The first line is the headline result (area). Below it the circle Calculator lists radius, diameter and circumference, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Working backwards
From the area, r = √(A ÷ π); from the circumference, r = C ÷ 2π. For an area of 78.54, r = √(78.54 ÷ 3.14159) = 5.
Why π
π ≈ 3.14159 is the ratio of any circle's circumference to its diameter. Using 3.14 instead gives an area of 78.5 for r = 5, which is accurate to three figures.
How the result changes with value
Holding every other input at the first worked example, this table changes only value. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Value | Area | Radius | Diameter |
|---|---|---|---|
| 2.5 | 19.634954 | 2.5 | 5 |
| 5 | 78.539816 | 5 | 10 |
| 10 | 314.159265 | 10 | 20 |
| 20 | 1,256.637061 | 20 | 40 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "0" shows "Value must be greater than 0." beside that field and no result.
Choosing between the Circle Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Circumference Calculator](/math/circumference/) | i know the and value | Circumference |
| [Circle Diameter Calculator](/math/circle-diameter/) | i know the and value | Diameter |
| [Radius Calculator](/math/radius-calculator/) | i know the and value | Radius |
| [Circle Perimeter Calculator](/math/circle-perimeter/) | radius | Circle Perimeter |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Value must be positive
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
How do I get area from the diameter?
Halve it to get the radius, then use πr².
What are the units of area?
Squared units of the input length.
What is the circumference of a circle with radius 1?
It is 2π, about 6.2832 units.
What does the Circle Calculator calculate?
Radius, diameter, circumference and area of a circle from any one of them. It returns Area, Radius, Diameter and Circumference.
What formula does the Circle Calculator use?
d = 2r; C = 2πr; A = πr². Every quantity is derived from the radius: r = d/2 = C/2π = √(A/π).
What does the “I know the” option change?
It sets how the circle is worked out. The choices are Radius, Diameter, Circumference and Area.
What is an example of a circle result?
With i know the Radius and value 5, the area is 78.539816.
Related calculators
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Circumference Calculator — Circumference of a circle.
- Circle Diameter Calculator — Diameter of a circle from radius, circumference or area.
- Radius Calculator — Radius of a circle from diameter, circumference or area.
- Circle Perimeter Calculator — Perimeter (circumference) of a circle from its radius.
- Circle Equation Calculator — Equation of a circle from its centre and radius.
- Circle Segment Area Calculator — Area of a circular segment from radius and central angle.
- Unit Circle Calculator — Coordinates on the unit circle for an angle.
- Octagon Calculator — Area, perimeter and angles of a regular 8-sided polygon.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.