Quick answer
The area of a circle is A = πr². With a radius of 3, the area is 28.2743, the diameter 6 and the circumference 18.8496.
Choose which measurement you know (radius, diameter, circumference or area). The calculator returns the others.
Related tools: Circle Calculator: Radius, diameter, circumference and area of a circle from any one of them. Circumference Calculator: Circumference of a circle. Circle Diameter Calculator: Diameter of a circle from radius, circumference or area.
How to use the Area of a 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 = 3.
| Result | Value |
|---|---|
| Area | 28.274334 |
| Radius | 3 |
| Diameter | 6 |
| Circumference | 18.849556 |
Example 2
Inputs: I know the = Diameter; Value = 2.
| Result | Value |
|---|---|
| Area | 3.141593 |
| Radius | 1 |
| Diameter | 2 |
| Circumference | 6.283185 |
The first line is the headline result (area). Below it the area of a 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.
Why r squared
Doubling the radius quadruples the area: r = 6 gives 113.1, four times 28.27. A circle of diameter d has area π d²/4.
Units and uses
The area is in squared units of the input. Use it for pizzas, pipes, circular gardens and pool covers. If you know the circumference, r = C ÷ 2π.
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 |
|---|---|---|---|
| 1.5 | 7.068583 | 1.5 | 3 |
| 3 | 28.274334 | 3 | 6 |
| 6 | 113.097336 | 6 | 12 |
| 12 | 452.389342 | 12 | 24 |
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 Area of a 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 |
|---|---|---|
| [Circle Calculator](/math/circle-calculator/) | 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 Segment Area Calculator](/math/segment-area/) | radius and central angle | Segment area |
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
What is the area of a circle with radius 10?
A radius of 10 gives A = π × 100 ≈ 314.16 square units.
How do I find area from diameter?
Halve the diameter first, then use A = π × (d ÷ 2)²; a 6 cm diameter gives 28.27 cm².
What is π?
π is the ratio of a circle's circumference to its diameter, about 3.14159.
What does the Area of a Circle Calculator calculate?
Area of a circle from its radius, diameter or circumference. It returns Area, Radius, Diameter and Circumference.
What formula does the Area of a 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 area of a Circle is worked out. The choices are Radius, Diameter, Circumference and Area.
What is an example of a area of a Circle result?
With i know the Radius and value 3, the area is 28.274334.
Related calculators
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- 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 Segment Area Calculator — Area of a circular segment from radius and central angle.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Sector Area Calculator — Area and arc length of a circular sector.
- Ellipse Calculator — Area and approximate perimeter of an ellipse.
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.