Enter any one circle measurement — radius, diameter, circumference, or area — and calculate all others, plus arc length, chord, sector area, and segment area.
| Arc Length | 5.23598776 |
| Chord Length | 5 |
| Sector Area | 13.08996939 |
| Segment Area | 2.26465184 |
| Property | Formula | Value |
|---|---|---|
| Radius (r) | — | 5 |
| Diameter (d) | 2r | 10 |
| Circumference (C) | 2πr | 31.41592654 |
| Area (A) | πr² | 78.53981634 |
| Property | Formula |
|---|---|
| Diameter | d = 2r |
| Circumference | C = 2πr = πd |
| Area | A = πr² |
| Arc length | L = rθ (θ in radians) |
| Sector area | A = ½r²θ |
| Chord length | c = 2r·sin(θ/2) |
| Segment area | A = ½r²(θ − sin θ) |
The most common circle mistake is typing the diameter into a radius box. Because area depends on r², the error does not stay small: a 4 m wide patio entered as radius 4 returns 50.27 m² instead of the true 12.57 m², exactly four times too large, and anything bought by area is four times too large with it. This calculator accepts any one of radius, diameter, circumference or area and works out the other three.
Everything on the page is derived from the radius. Diameter is d = 2r, circumference is C = 2πr (the same as πd), and area is A = πr². When you start from something else, the calculator reverses the formula first: r = d / 2, or r = C / (2π), or r = √(A / π). Note that doubling the area raises the radius only by about 41 percent, because of the square root.
The lower box adds arc, sector and chord for a central angle θ that you type in degrees, above 0 and up to 360. Internally θ is converted to radians (θ × π / 180), and then the page uses arc length L = rθ, sector area = ½r²θ, chord = 2r·sin(θ/2) and segment area = ½r²(θ − sin θ). The segment is the sliver between chord and arc, which is the sector minus its triangle.
Worked example. A circle measures 40 around, in any unit, and you want a 90° wedge. Choose Circumference and enter 40. Radius = 40 / (2π) = 6.36619772, so the diameter is 12.73239545 and the area is π × 6.36619772² = 127.3239545. With θ = 90° (π/2 radians) the arc length is 10, exactly a quarter of 40. The sector area is 31.83098862, the chord is 9.00316316 and the segment area is 11.56675189. All figures are rounded to eight decimals.
No, it uses the full-precision value built into JavaScript. For a radius of 100 the circumference is 628.3185307, while 3.14 would give 628, and the area is 31,415.92654 against 31,400. Hand calculations with 3.14 will not match to the last digits.
No. The angle field reads degrees only, from just above 0 to 360. If you type 1.0472 hoping for a 60° wedge, you get a wedge of about 1°. Multiply radians by 180 / π first. Angles above 360 produce no arc results.
A sector is the pie slice from the centre. A segment is the cap cut off by the chord, with no triangle. At 180° the chord equals the diameter and the segment is exactly half the circle. At 360° the chord shrinks to zero and the segment area equals the whole circle.
The page empties the input on purpose so a number typed for one measure is never read as another. Choose the type first, then type the value.
Results are rounded to eight decimal places, so any value below 0.000000005 shows as 0. A radius of 0.0001 shows an area of 0.00000003, and a radius of 0.00001 shows 0. Work in millimetres rather than metres for small parts.
It is exact to the display precision, but an error in the area is halved in relative terms, since r = √(A/π). A 10 percent overestimate of area produces about a 5 percent overestimate of radius. Still, measure the radius or diameter directly when you can.