Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Radius and diameter get used interchangeably in casual conversation, and the area formula doesn't forgive that. Since area scales with the square of the radius, plugging a diameter into a formula expecting a radius doesn't just double the answer: it quadruples it, a mistake that's easy to make and easy to miss because the resulting number still looks plausible.
Before you rely on it
What to check
Confirm whether the measurement you have is a radius or a diameter before entering it. Halve a diameter to get the radius this calculator expects.
The common error
Where people go wrong with circle area & circumference calculator
Entering a diameter directly as the radius. The area comes out four times too large, and because the number still looks like a reasonable size for a circle, the error tends to go unnoticed until something built from it doesn't fit.
Sensitivity evidence
How radius changes the area
| Radius | Area | Circumference |
|---|---|---|
| 4 | 50.3 | 25.1 |
| 4.5 | 63.6 | 28.3 |
| 5worked example | 78.5 | 31.4 |
| 5.5 | 95 | 34.6 |
| 6 | 113.1 | 37.7 |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Radius | 5 |
| Area | 78.5 |
| Circumference | 31.4 |
Where the inputs come from
Enter the radius, the distance from the center to the edge. If you know the diameter, divide it by two, and if you know the circumference, divide it by two pi. Use one unit throughout. Measure carefully, since area depends on the square of the radius, so a small error in radius becomes a larger error in area. The calculator returns both area and circumference.
When the result stops applying
Measure the true radius rather than assuming it from a diameter that includes a rim or wall thickness. Ovals and ellipses need a different formula, and partial circles need the sector formulas.
What to compare it with
Cut out a hole or ring on the annulus calculator, work with parts of circles on the arc length and sector page, and find volumes on the sphere, cylinder and cone pages. The ellipse calculator handles ovals, and the regular polygon page covers shapes with straight sides. The unit conversion pages change units.
People also ask
Frequently asked questions
What is the formula for the area of a circle?
Pi times the radius squared. A circle with a radius of 5 has an area of about 78.5 square units, and doubling the radius quadruples the area.
How do I find the radius from the diameter?
Divide the diameter by two. A 10-inch diameter circle has a 5-inch radius, and the same halving works for any unit of length.
Why does doubling the radius quadruple the area?
Because area depends on the square of the radius, so doubling gives four times the area.