About the Circle Calculator
A circle calculator finds the area, circumference, and diameter from the radius. Circles appear everywhere from pipe cross-sections to wheel travel to pizza value comparisons, and every one of their properties follows from the radius through π.
The formula
A = πr², C = 2πr, d = 2rr is the radius from centre to edge, d the diameter across the full width, and π ≈ 3.14159 the constant ratio of any circle's circumference to its diameter.
How to use this calculator
- 1Enter your Radius. The field starts at
5, which you can overwrite. - 2Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Radius | 5 |
Result
Area: 78.5398 units²
Circumference: 31.4159 units
Diameter: 10 units
Quarter Arc Length: 7.8540 units
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Circumference scales linearly with radius while area scales with its square, and that difference produces most of the surprising results about circles. Doubling the radius doubles the perimeter but quadruples the area — which is why a 16-inch pizza has more than twice the food of a 12-inch one, and why pipe capacity rises so sharply with diameter.
π is irrational, so every circle calculation is an approximation at some level of precision. Three decimal places is ample for construction; NASA uses about fifteen for interplanetary navigation. The constant is the same for every circle, which is what makes these formulas universal.
Things worth knowing
- Check whether a given measurement is the radius or the diameter. Confusing them is the most common error, and it changes area by a factor of four.
- Area scales with the square of radius: 1.4 times the radius gives roughly double the area.
- The area of a sector is the full area times the fraction of 360 degrees it spans.
- A circle encloses more area than any other shape of the same perimeter.
- For pipes and cables, cross-sectional area governs capacity, so it grows with the square of diameter.
Frequently asked questions
How do I find the area of a circle?+
Square the radius and multiply by π. A radius of 5 gives 25 × 3.14159 ≈ 78.54 square units. If you have the diameter, halve it first.
What is the difference between radius and diameter?+
The radius runs from the centre to the edge; the diameter runs edge to edge through the centre and is twice the radius. Mixing them up is the commonest source of error.
Why does a larger pizza give so much more food?+
Because area grows with the square of the radius. A 16-inch pizza has about 1.8 times the area of a 12-inch one, so it is usually far better value per square inch even at a higher price.
What exactly is π?+
The ratio of any circle's circumference to its diameter, approximately 3.14159. It is the same for every circle and irrational, so its decimal expansion never terminates or repeats.