Circle calculator: circumference, area, radius and diameter

Know one measurement, get the other three

Every circle is described by four linked values: the radius, the diameter, the circumference (the distance around) and the area (the surface inside). Once you know any one of them, the rest follow. This circle calculator does the math as you type, in the unit you pick, and shows every formula with your own numbers plugged in. It also handles a circular sector (a pizza slice) and an annulus (a ring).

Use it to size a tablecloth, order edging for a round flower bed, figure out how much cover a round pool needs, check geometry homework, or work out the length of a coiled hose.

How to use it

1. Choose a "Unit" (mm, cm, m, km, inches or feet) and the number of "Decimal places". Area is shown in square units: in², ft², m² and so on.
2. In "1. Radius, diameter, circumference, area", fill in just one box: "Radius", "Diameter", "Circumference (perimeter)" or "Area". The box you type in is tagged "given"; the other three switch to "calculated" and get a dashed outline.
3. The diagram draws the value you entered as a dashed line and the calculated ones in blue. Under "Result", "Formulas step by step" lists each calculation.
4. For a slice, use "2. Circular sector": a radius and an "Angle in degrees" give the "Arc length", the "Sector area" and the "Chord".
5. For a ring, use "3. Annulus (ring)" with the "Outer radius" and the "Inner radius".

"Copy results" puts the four circle values on your clipboard. Your last entries are kept on this device.

Circle formulas

• Circumference: C = 2πr = πd
• Area: A = πr²
• Radius from circumference: r = C / 2π
• Radius from area: r = √(A / π)
• Sector with angle θ in degrees: arc s = πrθ / 180, area πr²θ / 360, chord c = 2r × sin(θ/2)
• Annulus: A = π(R² − r²)

π is 3.14159265… Rounding it to 3.14 costs about 0.05%, which is fine for a tablecloth hem and not fine for a machined part. The calculator keeps full precision and only rounds what it displays.

Worked examples

Is one 12-inch pizza more than two 8-inch pizzas? Yes. The 12-inch pizza has a 6-inch radius: π × 36 = 113.10 in². One 8-inch pizza is π × 16 = 50.27 in², so two make 100.53 in². The single large pizza gives you about 12.5% more.

A cover for an above-ground pool. A 15 ft round pool has a 7.5 ft radius, so its surface is π × 56.25 = 176.71 ft², and its rim measures π × 15 = 47.12 ft.

A gravel path around a patio. A round patio with an 8 ft radius plus a 2 ft path makes a ring of 10 ft and 8 ft: π × (100 − 64) = 113.10 ft² of path to cover.

Common mistakes

Mixing up radius and diameter is the classic one: a "48-inch round table" is measured edge to edge, so 48 inches is its diameter. Also remember that area grows with the square of the radius: double the diameter and the area is four times bigger, not two. Finally, changing the "Unit" only changes the label, it does not convert the numbers you typed.

FAQ

Is circumference the same as perimeter?

For a circle, yes. Both words mean the distance around it. Circumference is the usual term for circles; perimeter is used for any shape.

How do I find a tree's diameter with a tape measure?

Wrap the tape around the trunk and enter the reading in "Circumference (perimeter)". A trunk measuring 157 cm around has a diameter of 49.97 cm, roughly 50 cm.

Can it work out a semicircle?

Yes: use the sector with a 180° angle. For a 10 cm radius, the arc is 31.4159 cm and the area 157.0796 cm². Add the 20 cm diameter to the arc to get the full outline.

Why is the area in square units?

Area always is. Pick feet and the area appears in ft²; pick meters and it appears in m².