Arc Length Calculator
Enter a radius and central angle — in degrees or radians — and get the exact length of the arc, plus the chord and sector area that go with it.
Example: with Radius (r) 10 · Central angle (θ) 60 · Angle unit Degrees → Arc length (L): 10.47.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outArc length formula: radians vs degrees
The arc length formula depends on how the central angle is measured. In radians it’s simply L = rθ: a radius of 10 and a 1.5 rad angle give an arc of 10 × 1.5 = 15. In degrees, scale the full circumference by the angle’s share of 360°: L = 2πr × (θ/360). For r = 10 and θ = 60°, that’s 2π × 10 × (60/360) ≈ 10.47.
To find the length of an arc of a circle you only ever need those two numbers — radius and central angle. If you have the diameter, halve it first. A quick sanity check: at 360° the “arc” is the whole circumference (2πr), and at 180° it’s exactly half, so a valid answer always sits between 0 and 2πr.
How it’s calculated
Radians: L = rθ. Degrees: L = 2πr × (θ/360). The chord is 2r × sin(θ/2) and the sector area is ½r²θ, both with θ in radians. Degrees are converted by multiplying by π/180, using JavaScript’s full-precision π ≈ 3.14159 (Math.PI); nothing is rounded until display.
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Plugging a degree angle into L = rθ — that form needs radians; convert with θ × π/180 first.
- Using the diameter as r — halve the diameter before applying the formula.
- Confusing arc length with the chord — the straight line between the endpoints is always shorter than the arc.
- Entering an angle over 360° (2π rad) — a circular arc can't be longer than the full circumference.
Frequently asked questions
What is the arc length formula?
L = rθ when the central angle θ is in radians, or L = 2πr × (θ/360) when it’s in degrees. Both give the same answer once the angle is converted.
How do I find the length of an arc with degrees?
Multiply the full circumference 2πr by θ/360. Example: r = 10 and θ = 60° gives 2π × 10 × (60/360) ≈ 10.47.
How do I find arc length without the angle?
If you know the sector area A instead, use L = 2A ÷ r. With A = 52.36 and r = 10, L = 104.72 ÷ 10 ≈ 10.47.
Is arc length the same as the chord?
No. The chord is the straight segment between the arc’s endpoints and is always shorter: at r = 10 and 60°, the chord is exactly 10 while the arc is 10.47.
Can an arc be longer than the circumference?
Not on a circle — the largest possible arc is the full circumference 2πr, reached at 360° (2π radians).