Circle Area Calculator
Enter a circle's radius to find the space inside it using A = πr². Use any length unit and the answer is in that unit squared.
The shape behind the formula
Schematic diagram; proportions are not to scale. Use the formula and current values below for the numerical result.
About this calculation
Circle Area: find area from radius. A radius runs from a circle’s center to its edge; the diameter crosses the center and equals twice the radius. Area and circumference measure different aspects of the circle.
Formula
A = πr²
Worked example
With Radius: 5 units, area is 78.539816 square units.
Calculation method
The rule is A = πr².
Area grows with the square of the radius. Doubling radius makes a circle four times as large in area.
For this circle area example, changing radius from 5 units to 6 units while keeping the other inputs fixed changes area from 78.539816 square units to 113.097336 square units.
Reading area
Circumference has linear units, whereas area has square units. Doubling a radius doubles circumference but quadruples area. In the worked values on this page, radius 5 units produce area 78.539816 square units.
Practical use
Use circle measurements for wheels, round plots, containers, and construction layouts. The specific task here is to find area from radius.
Limits and common mistakes
Do not enter diameter where a formula expects radius. Check whether the result should describe a boundary or an enclosed surface. Verify radius in units before interpreting area; a value measured on another basis would answer a different question.
Why the relationship works
A circle is determined by its radius, the center-to-edge distance. Diameter is twice that length; circumference follows the boundary; area covers the interior. Radius enters area squared but circumference only once. If the input is a measured diameter, divide it by two before using a radius-based rule. The circle area rule uses radius (units) in A = πr²; read each symbol as the field named on this page.
Interpreting another set of values
For circle area, the fields labeled radius (units) are the known quantities. The calculator solves for area in square units using A = πr². A radius, diameter, and circumference are lengths; area covers the inside. Check that the output unit changes appropriately if a length is squared, and distinguish the radius entered from the full width. When comparing two calculations, keep their units and input definitions identical.
For a second circle area check, keep the other default inputs fixed and change radius from 5 units to 7 units. Area changes from 78.539816 square units to 153.93804 square units. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.
Checks and limits
Keep linear and square units distinct. A result for circumference, diameter, or radius is a length, while area is in square units. Squaring a unit as well as a number is necessary: a circle with radius in centimeters has area in square centimeters. Round only after the calculation if a measurement is approximate. The reported area is an area. If the input lengths were centimeters, its unit would be square centimeters; the numerical 78.539816 square units therefore describes covering rather than edge length.
Inputs
- Radius (units)