Geometry desk
Circle Area Calculator
Find the area of a circle from its radius.
Circle Area Calculator: Work out how much flat space a circular disc covers from the distance between its centre and edge. Enter the radius to find an area in square units, useful for comparing round panels, lids or patches of ground. Runs 100% locally in your browser with zero server file uploads.
- Category
- Calculators
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Area
78.54 cm²
Area = π × radius²- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Area = π × radius²
A worked example with sample values:
| Inputs | |
|---|---|
| Radius | 5 cm |
| Results | |
|---|---|
| Area | 78.54 cm² |
Why the area is π times radius squared
Let A be the area and r the radius. The formula is A = π × r². Imagine cutting the disc into many narrow sectors and arranging them with alternate tips pointing up and down. As the sectors get narrower, the arrangement approaches a rectangle of height r and length half the circumference, πr. Multiplying these lengths gives πr².
For radius 5 cm, square the radius: 5 × 5 = 25 cm². Multiply by π to obtain 25π = 78.539816… cm². The calculator displays Area = 78.54 cm². This is the area inside the boundary, so it answers a coverage question rather than the length of trim needed around the edge.
The circle equations in OpenStax Prealgebra 2e (https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures) distinguish area from circumference. Doubling r multiplies coverage by four.
Converting a disc's area
A square centimetre is a square with sides of 1 cm. Because 1 m contains 100 cm, a square metre contains 100 × 100 = 10,000 cm². Divide an area in cm² by 10,000 to express it in m²; dividing by only 100 treats area as a length and gives the wrong result. A zero radius describes a degenerate disc mathematically, but this form requires a positive radius.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
Related tools
Frequently asked questions
I measured the diameter. What should I enter for circle area?
Halve it first. A circle 10 cm across has radius 5 cm. Entering 10 as the radius makes the calculated area four times too large, because the radius is squared.
How do I recover the radius from a known area?
Rearrange A = πr² to r = √(A ÷ π). An area of 25π cm² gives radius 5 cm and diameter 10 cm. Use the unrounded area when available; a rounded area gives an approximate radius.
Does choosing metres convert my existing centimetre radius?
The unit selector labels the measurement; it does not rescale the number. Replace 5 cm with 0.05 m before calculating in metres. The corresponding area is about 0.007854 m², rather than 78.54 m².
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