Arc Length Calculator
Find the arc length and chord of a circular arc.
Results update as you type.
How it works
An arc is a portion of a circle's circumference, and this calculator finds both the arc length and the straight-line chord connecting its endpoints from the radius and the central angle. You enter the radius and the angle the arc subtends at the centre, in degrees, and it returns the curved arc length and the chord length. The arc length is a simple fraction of the whole circumference: the central angle over 360 degrees, times two pi times the radius. The chord, the straight segment between the arc's two ends, is found with trigonometry as twice the radius times the sine of half the angle. The arc is always a little longer than the chord because it bows outward, and the two get closer as the angle shrinks. These calculations matter in construction and engineering for curved beams, roads, and railways, in manufacturing for bending materials, in navigation, and in geometry class. The distinction between arc and chord is important: the arc is the distance travelled along the curve, while the chord is the shortest straight-line distance between the same two points. Enter the radius and central angle to compute the arc length and chord length.
Arc = (θ/360)·2πr; Chord = 2r·sin(θ/2)
The arc length is the fraction of the full circumference that the arc spans: the central angle divided by 360 degrees, times two pi times the radius. The chord, the straight line joining the arc's two endpoints, equals twice the radius times the sine of half the central angle. The arc is always slightly longer than its chord.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter radius and central angle.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Arc length updates instantly as you type — no button to press.
Frequently asked questions
How do you calculate arc length?
Take the central angle divided by 360, then multiply by the full circumference, which is two pi times the radius. This gives the fraction of the circle's edge that the arc covers. For a radius of two and a 90-degree angle, the arc length is pi, about 3.14 units, which the calculator computes instantly.
What is the difference between an arc and a chord?
An arc is the curved distance along the circle between two points, while a chord is the straight-line distance directly between those same two points. The arc is always longer than the chord because it follows the curve. As the central angle gets smaller, the arc and chord lengths become nearly equal.
How is chord length found?
The chord length equals twice the radius multiplied by the sine of half the central angle. This comes from splitting the triangle formed by the two radii and the chord into two right triangles. For a radius of two and a 90-degree angle, the chord is about 2.83 units, shorter than the 3.14-unit arc.
Do I need radians or degrees?
This calculator takes the central angle in degrees, which is the more familiar unit for most people. Internally it converts to the correct proportion of the circle. If you have an angle in radians, multiply it by 180 and divide by pi to convert to degrees before entering it, or the result will be wrong.
Where is arc length used?
Arc length is essential in engineering and construction for curved roads, railway tracks, bridges, and arches, in manufacturing for bending pipes and sheet metal, and in navigation for distances along curved paths. It also appears in design, robotics for circular motion, and mathematics whenever a length along a curve must be measured.