CALTRX

Arc Length CalculatorFind arc length from radius and central angle in degrees or radians. Useful for curved construction, circular paths, and geometry problems.

Find arc length from radius and central angle in degrees or radians. Useful for curved construction, circular paths, and geometry problems.

units
L = rθ (θ in radians) or L = (θ/360) × 2πr (θ in degrees)
L= Arc length
r= Radius
θ= Central angle

Tips & Notes

  • ✓Always check whether your angle is in degrees or radians before calculating.
  • ✓The full circumference equals the arc length when the angle is 360° or 2π radians.
  • ✓Arc length is directly proportional to both radius and angle.

Common Mistakes

  • ✗Using degrees directly in the formula L = rθ, which requires radians.
  • ✗Confusing arc length with chord length — the arc follows the curve, the chord is a straight line.
  • ✗Forgetting that a full circle is 360° or 2π radians.

Arc Length Calculator Overview

Arc Length Calculator Overview

The Arc Length Calculator computes the distance along a curved section of a circle based on the radius and the central angle. This measurement is essential in engineering, architecture, and construction whenever curved elements are involved — from designing arched doorways and circular driveways to calculating material lengths for curved trim and piping.

The mathematical relationship is elegantly simple: arc length equals radius multiplied by the angle in radians. This proportional relationship means doubling the radius doubles the arc length, and doubling the angle doubles the arc length. Understanding this proportionality helps with quick mental estimates before running precise calculations.

The calculator also provides the sector area — the region enclosed between two radii and the arc — which is useful for calculating material coverage for curved surfaces, pie chart segments, and similar applications.

Frequently Asked Questions

Arc length is the distance along the curved portion of a circle between two points. It is part of the circumference and depends on both the radius and the central angle subtended by the arc.

Multiply degrees by π/180. For example, 90° × π/180 = π/2 ≈ 1.5708 radians.

Common applications include designing curved structures, calculating distances along circular paths, determining belt lengths around pulleys, and solving geometry problems in education.

Arc length follows the curve of the circle, while chord length is the straight-line distance between the two endpoints of the arc. Arc length is always longer than chord length for the same two points.