Plot No. 60 · Education
Circle Calculator
Enter a circle's radius or diameter and get its area, circumference and the other measurement instantly. Area is pi times the radius squared, circumference is two times pi times the radius, and the diameter is simply twice the radius.
Area uses pi times the radius squared and circumference uses two times pi times the radius. Results are in the same units you enter (area is those units squared).
The link saves your inputs so you can bookmark or share this exact result.
Pi times the radius squared, for common radii
"Pi times r squared" is just the area formula said out loud. Square the radius first, then multiply by pi (about 3.14159). So a radius of 13.5 gives 13.5 times 13.5, which is 182.25, and 182.25 times pi is about 572.56 square units. The circumference is the distance around the edge, which is two times pi times the radius. Any radius works in the calculator above; these are the ones people look up most.
| Radius (r) | r2 | Area (pi r2) | Circumference (2 pi r) |
|---|---|---|---|
| 1 | 1.00 | 3.14 | 6.28 |
| 2 | 4.00 | 12.57 | 12.57 |
| 2.5 | 6.25 | 19.63 | 15.71 |
| 3 | 9.00 | 28.27 | 18.85 |
| 5 | 25.00 | 78.54 | 31.42 |
| 7.5 | 56.25 | 176.71 | 47.12 |
| 10 | 100.00 | 314.16 | 62.83 |
| 12.5 | 156.25 | 490.87 | 78.54 |
| 15 | 225.00 | 706.86 | 94.25 |
| 20 | 400.00 | 1,256.64 | 125.66 |
| 25 | 625.00 | 1,963.50 | 157.08 |
| 33 | 1,089.00 | 3,421.19 | 207.35 |
| 50 | 2,500.00 | 7,853.98 | 314.16 |
Rounded to two decimal places. Results are in the same units you measure the radius in, so a radius in centimetres gives an area in square centimetres. If you have the diameter rather than the radius, halve it first.
How the circle calculator works
Give the calculator either the radius or the diameter and it derives the rest of the circle. If you enter the diameter it halves it to get the radius first, since every other measurement is built from the radius. Area is pi times the radius squared, circumference is two times pi times the radius, and the diameter is twice the radius.
Pi is an irrational constant of about 3.14159, so area and circumference are never exactly whole even when the radius is. The calculator uses the full precision of pi internally and rounds area and circumference to two decimal places for display, while the radius and diameter are shown to the precision you enter.
How to use the circle calculator
- Choose whether you are entering the radius or the diameter using the toggle.
- Type the measurement. Use any unit you like; the answer stays in those units.
- Read the area and circumference, with the radius and diameter shown for reference.
Worked examples
A circle from its radius
Inputs: Radius of 5
Result: The area is pi times 25, about 78.54 square units, and the circumference is two times pi times 5, about 31.42 units.
A circle from its diameter
Inputs: Diameter of 10
Result: The radius is 5, so the results match the example above: area about 78.54 and circumference about 31.42.
Limitations and common mistakes
Edge cases and limitations
- The calculator does not attach a unit; area is always in your chosen units squared, so a radius in cm gives an area in square cm.
- Area and circumference are rounded to two decimal places, so they are close approximations rather than exact values.
- A value of zero or below is treated as invalid because a circle needs a positive radius.
Common mistakes
- Plugging the diameter into the area formula as if it were the radius, which quadruples the area; halve the diameter first.
- Forgetting to square the units for area, for example writing the answer in cm instead of square cm.
Frequently asked questions
How do you find the area of a circle?
Multiply pi (about 3.14159) by the radius squared. A circle with a radius of 5 has an area of pi times 25, which is about 78.54 square units.
What is the circumference of a circle?
The circumference is the distance around the edge. It equals two times pi times the radius, or pi times the diameter. For a radius of 5, the circumference is about 31.42.
How are radius and diameter related?
The diameter is the full width across the circle through the centre, and the radius is half of it. So if you enter a diameter of 10, the radius is 5, and every other result follows from there.
What does pi r squared mean?
It is the area formula written in shorthand: pi multiplied by the radius multiplied by itself. Squaring the radius first and then multiplying by pi (about 3.14159) gives the area enclosed by the circle, in the same units you measured the radius in, squared.
Is pi times 13.5 squared the same as the area of a circle?
Yes, as long as 13.5 is the radius. Pi times 13.5 squared means 13.5 times 13.5, which is 182.25, then multiplied by pi, giving about 572.56 square units. That is exactly the area of a circle of radius 13.5. If 13.5 is the diameter instead, halve it to 6.75 first.
Related calculators
GPA Calculator
Calculate your weighted GPA on the 4.0 scale from each course's credits and letter grade.
Final Grade Calculator
Find the score you need on your final exam to reach the overall grade you want.
Grade Calculator
Convert points earned out of points possible into a percentage and letter grade.
Average Calculator
Find the mean, median, mode, range, sum, count, min and max of a list of numbers.
See all education calculators.