⭕ Circle Calculator (Area, Circumference)
By ToolNimba Editorial Team · Updated 2026-06-19
Enter a value to compute the radius, diameter, circumference, and area.
This circle calculator lets you enter any one of the four common measurements of a circle (radius, diameter, circumference, or area) and works out the other three for you. Pick which value you already know, type it in, and read off the rest at once. Everything is computed in your browser using the constant π (pi), so the answers are precise and nothing is sent anywhere.
What is the Circle Calculator?
A circle is defined by a single number: its radius, the distance from the centre to the edge. Once you know the radius, every other measurement follows. The diameter is simply twice the radius, since it stretches all the way across through the centre. The circumference, the distance around the edge, is 2πr, and the area enclosed is πr². The constant π (roughly 3.14159) is the ratio of any circle's circumference to its diameter, the same for every circle no matter its size.
Because all four quantities are tied to the radius, you can start from whichever one you happen to know and recover the rest. If you know the diameter, halve it to get the radius. If you know the circumference, divide by 2π. If you know the area, divide by π and take the square root. This calculator does exactly that internally: it converts your input back to a radius first, then rebuilds the diameter, circumference, and area from it.
The one place people slip is mixing up radius and diameter, which throws off the area by a factor of four (because area depends on r squared). Reading a problem carefully to see whether you were given the radius or the diameter is half the battle. The formulas themselves never change, and that consistency is what makes circle problems so quick once the relationships click.
When to use it
- Finding the area of a circular garden bed, table top, or pizza from its radius or diameter.
- Working out how much edging, fencing, or trim you need around a circular feature (the circumference).
- Checking geometry or trigonometry homework where you are given one measurement and asked for another.
- Sizing a circular rug, pool cover, or pipe when only the area or the circumference is known.
How to use the Circle Calculator
- Choose which measurement you already know: radius, diameter, circumference, or area.
- Type that value into the box (it must be zero or positive).
- Read the radius, diameter, circumference, and area in the result boxes.
- Switch the selector to recompute from a different starting measurement at any time.
Formula & method
Worked examples
A circle with a radius of 5 units.
- diameter = 2 × 5 = 10
- circumference = 2 × π × 5 ≈ 31.415927
- area = π × 5² = π × 25 ≈ 78.539816
Result: d = 10, C ≈ 31.415927, A ≈ 78.539816
A circle with a diameter of 14 units.
- radius = 14 ÷ 2 = 7
- circumference = 2 × π × 7 ≈ 43.982297
- area = π × 7² = π × 49 ≈ 153.938040
Result: r = 7, C ≈ 43.982297, A ≈ 153.938040
A circle with an area of 78.539816 square units.
- radius = √(78.539816 ÷ π) = √25 = 5
- diameter = 2 × 5 = 10
- circumference = 2 × π × 5 ≈ 31.415927
Result: r = 5, d = 10, C ≈ 31.415927
Circumference and area for common radii (π ≈ 3.14159)
| Radius (r) | Diameter (d) | Circumference (2πr) | Area (πr²) |
|---|---|---|---|
| 1 | 2 | 6.283185 | 3.141593 |
| 2 | 4 | 12.566371 | 12.566371 |
| 3 | 6 | 18.849556 | 28.274334 |
| 4 | 8 | 25.132741 | 50.265482 |
| 5 | 10 | 31.415927 | 78.539816 |
| 10 | 20 | 62.831853 | 314.159265 |
Common mistakes to avoid
- Using the diameter where the radius belongs. The area formula is πr², not πd². If you plug the diameter in by mistake, the area comes out four times too large. Always halve the diameter to get the radius first.
- Forgetting to square the radius for area. Area is π times r squared, so the radius is multiplied by itself before multiplying by π. A radius of 5 gives π × 25, not π × 5.
- Mixing up circumference and area units. Circumference is a length (units), while area is a region (square units). They answer different questions, so check which one the problem actually wants.
Glossary
- Radius (r)
- The distance from the centre of a circle to its edge. Every other measurement is built from this.
- Diameter (d)
- The distance straight across a circle through the centre. It equals twice the radius.
- Circumference (C)
- The distance all the way around the edge of a circle, equal to 2πr.
- Area (A)
- The amount of space enclosed by a circle, equal to πr², measured in square units.
- Pi (π)
- The constant ratio of a circle's circumference to its diameter, approximately 3.14159.
Frequently asked questions
How do I find the area of a circle?
Multiply π by the radius squared: area = πr². For a radius of 5, the area is π × 25 ≈ 78.54 square units. If you only have the diameter, halve it to get the radius first.
What is the formula for the circumference of a circle?
The circumference is 2πr, where r is the radius. Equivalently it is πd, since the diameter d equals 2r. For a radius of 5 the circumference is about 31.42 units.
How do I find the radius from the area?
Divide the area by π and take the square root: r = √(A ÷ π). For example, an area of 78.54 gives √(78.54 ÷ π) = √25 = 5. This calculator does that step for you.
What is the difference between radius and diameter?
The radius runs from the centre to the edge, while the diameter runs all the way across through the centre. The diameter is exactly twice the radius, so r = d ÷ 2.
Can I enter the circumference and get the area?
Yes. Select circumference, type the value, and the tool converts it to a radius (r = C ÷ 2π) and then computes the area πr² along with the diameter, all at once.
What value of pi does this calculator use?
It uses your browser's built-in Math.PI, which is π to about 15 significant digits (3.141592653589793). Results are rounded for display but computed at full precision.