Circle Calculator
Enter the radius, diameter, circumference, or area of any circle — the other three fill in instantly, with the formula used shown below.
For display only — values aren't converted between units. Enter numbers in whichever unit you're already working with.
Enter any one value above — the other three fill in automatically.
Enter a positive number — a circle can't have a negative radius, diameter, circumference, or area.
Formulas used for this circle
A radius of 0 is a single point — every measurement collapses to 0.
Every calculation runs in your browser — nothing is sent to a server.
The four circle measurements, and how they relate
A circle is fully described by a single number — its radius — but people rarely think in radius alone. Depending on what you're measuring, you might know the diameter (the width straight across), the circumference (the distance around the edge), or the area (the space inside). Because all four values are tied to the same radius through fixed formulas, knowing any one of them is enough to work out the other three exactly.
The formulas behind every circle calculation
Every value in this calculator comes from these six relationships. π (pi) is a constant, approximately 3.14159, that appears anywhere a circle's curvature is involved:
- Diameter = 2 × r
- Circumference = 2 × π × r (equivalently, π × d)
- Area = π × r²
- Radius from diameter: r = d ÷ 2
- Radius from circumference: r = C ÷ (2 × π)
- Radius from area: r = √(A ÷ π)
Example 1 — starting from the radius. A circle with a radius of 5 cm has a diameter of 2 × 5 = 10 cm, a circumference of 2 × π × 5 ≈ 31.42 cm, and an area of π × 5² ≈ 78.54 cm².
Example 2 — starting from the circumference. A wheel with a circumference of 200 cm has a diameter of 200 ÷ π ≈ 63.66 cm and a radius of 200 ÷ (2π) ≈ 31.83 cm — useful when you've measured the distance a wheel travels in one rotation and need to work backward to its size.
Example 3 — starting from the area. A circular table with 1.5 m² of surface area has a radius of √(1.5 ÷ π) ≈ 0.69 m, a diameter of about 1.38 m, and a circumference of about 4.34 m — handy for checking whether the table will fit through a doorway.
Where π comes from, and why the decimals never end
π is the ratio of any circle's circumference to its diameter — it's the same number whether the circle is a coin or a planet's orbit, because circumference and diameter always scale together. π is irrational, so its decimal digits never repeat or terminate; 3.14159 is accurate enough for nearly any everyday calculation, and this calculator uses JavaScript's full built-in precision (about 15 significant digits) internally before rounding the display to whichever number of decimal places you choose.
Common mistakes when calculating circles
- Confusing radius and diameter: the most common error is plugging the diameter into a formula that expects the radius, or vice versa — since area uses r² but not d², that's an easy factor-of-4 mistake to make. Enter whichever one you actually have and let the calculator sort out the rest.
- Squaring the wrong quantity: circumference is proportional to r, but area is proportional to r² — doubling the radius doubles the circumference but quadruples the area.
- Mixing units mid-calculation: the formulas assume every value is in the same unit. If the radius is in centimeters, the area comes out in square centimeters, not square meters — convert first if you need a different unit.
Sources & further reading
Frequently asked questions
How do I calculate the area of a circle from the radius?
Multiply π (about 3.14159) by the radius squared: Area = π × r². For example, a circle with a 5 cm radius has an area of π × 5² ≈ 78.54 cm². Enter the radius into this circle calculator and the area, diameter, and circumference are computed and displayed instantly, with the formula shown for each.
How do I find the diameter or radius from the circumference?
Divide the circumference by π to get the diameter (d = C ÷ π), or by 2π to get the radius (r = C ÷ 2π). For example, a circumference of 31.42 cm gives a diameter of about 10 cm and a radius of about 5 cm. Type the circumference into this calculator and both are filled in automatically.
How do I calculate the circumference from the area of a circle, or the area from the circumference?
First solve for the radius, then plug it into the other formula. From area: r = √(A ÷ π), then circumference = 2πr. For example, an area of 100 cm² gives a radius of about 5.64 cm and a circumference of about 35.45 cm. This calculator does both steps for you — enter the area and the circumference, diameter, and radius all appear at once.
Does this calculator convert between units like centimeters and inches?
No. The unit label is for display only — it's attached to the numbers you see, but no unit conversion happens. Enter your radius, diameter, circumference, or area in whichever unit you're working with (centimeters, inches, meters, or anything else), and the results come back in that same unit. If you need to convert between units first, use a dedicated length converter before entering the number here.
Is my data sent to a server when I use this circle calculator?
No. Every calculation runs locally in your browser using JavaScript — the numbers you enter are never uploaded or transmitted anywhere. The only thing saved is your last input, unit label, and decimal-place preference, stored in your browser's localStorage so they're there next time you open the page on the same device.