Circle Calculator
This circle calculator solves the whole circle from any single measurement. Tell it the one value you know, radius, diameter, circumference, or area, and it works out all the others instantly. Set an angle and you'll also get the arc length, chord, sector area, and segment area for that slice, drawn on a live diagram so you can see exactly what's being measured. It's every circle formula in one place, with the working shown.
- Start from any one value
- Radius, diameter, area
- Arc and sector for any angle
- Live diagram
- Formula shown
Last updated July 18, 2026 Uses pi at full precision Reviewed by the Calcowa team
90° = 1.5708 rad, a quarter of the circle.
Everything above comes from the one value you entered.
| For your 90° slice | Result |
|---|---|
| Arc length | 12.5 cm |
| Chord length | 11.254 cm |
| Sector area | 49.736 cm² |
| Segment area | 18.075 cm² |
| Sector perimeter | 28.415 cm |
Which circle formula does each result use?
Every number the tool shows comes from one of these formulas, all built on the radius. When you enter a different value, the calculator first converts it to the radius, then runs the rest of the table. The angle formulas use degrees here; in radians, arc length collapses to the tidy L = rθ.
| Quantity | Formula | Getting the radius back |
|---|---|---|
| Diameter | d = 2r | r = d / 2 |
| Circumference | C = 2πr | r = C / 2π |
| Area | A = πr² | r = √(A / π) |
| Arc length | L = (θ/360) · 2πr | needs the angle too |
| Chord | c = 2r · sin(θ/2) | needs the angle too |
| Sector area | A = (θ/360) · πr² | needs the angle too |
| Segment area | A = ½r²(θ - sin θ), θ in rad | needs the angle too |
How does this circle calculator solve everything from one value?
Every property of a circle is locked to its radius, so one measurement is genuinely all it takes. The tool converts whatever you enter into the radius first: it halves a diameter, divides a circumference by 2π, or takes the square root of an area over π. From there, the rest is direct substitution into the formulas above. The angle you set doesn't change the circle at all; it just picks how big a slice to measure for the arc, chord, sector, and segment.
Worked example: a 50 cm circumference and a 90° slice
Say you've wrapped a tape measure around a pipe and read 50 cm, and you want the radius, the area, and the arc of a quarter turn. Here's the whole chain:
- Radius: r = 50 / (2 × 3.14159) = 7.9577 cm
- Diameter: d = 2 × 7.9577 = 15.915 cm
- Area: A = π × 7.9577² = 198.94 cm²
- Arc at 90°: (90/360) × 50 = 12.5 cm
- Sector at 90°: (90/360) × 198.94 = 49.736 cm²
A couple of assumptions worth knowing: the tool treats the shape as a perfect circle, keeps everything in the one unit you pick, and caps the angle at 360° since a bigger angle just wraps around. If your real object is slightly oval, measure the circumference rather than the diameter; it averages out the error better.
Frequently asked questions
Divide the circumference by 2 times pi. A circumference of 50 cm gives 50 / 6.2832, which is about 7.96 cm, and that's your radius. Once you've got the radius, everything else follows: double it for the diameter and square it times pi for the area. This calculator runs that chain automatically whenever circumference is the value you know.
You don't need the radius directly, because both the diameter and the circumference lead straight to it. From the diameter, halve it first, so A = pi (d/2) squared. From the circumference there's an even quicker shortcut: A = C squared / (4 pi). Enter whichever value you have and the tool works the area out along with all the rest.
Arc length is the fraction of the circle the angle covers times the full circumference, so L = (angle / 360) x 2 pi r in degrees, or simply L = r x angle when the angle is in radians. A 90 degree arc is a quarter of the circle, so on a circle with a 50 cm circumference it's exactly 12.5 cm. The tool shows the arc for whatever angle you set.
A sector is the pizza-slice shape between two radii and the arc, while a segment is the region between a chord and the arc, with no point at the center. Their areas differ too: the sector is (angle/360) x pi r squared, and the segment subtracts the inner triangle, giving half r squared times (angle - sin angle) with the angle in radians. If you're cutting a slice, you want the sector; if you're working out how full a horizontal tank is, you want the segment.
Divide by pi. The circumference of any circle is always pi times its diameter, so d = C / 3.14159. A 50 cm circumference means a 15.92 cm diameter, and half of that, 7.96 cm, is the radius. It's the oldest ratio in geometry, and it doesn't change with size.
Half the full circle's area, so A = pi r squared / 2. Set the angle to 180 degrees in this calculator and the sector area is exactly the semicircle area, since a 180 degree sector is half the circle. Watch the perimeter, though: it isn't half the circumference, because the straight edge adds a full diameter on top of the curved half.
It uses the JavaScript built-in Math.PI, which is pi to about 16 digits, 3.141592653589793. Results are rounded to a sensible number of decimals for display, but the math underneath runs at full precision, so nothing drifts. That's more accurate than 3.14 or 22/7, which can be off by enough to notice on a large circle.
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Working with another shape?
Every solid and flat shape has its own calculator, formula included.