Comprimento de Arco (rad)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
s = rθ
About this calculator
The arc length calculator (radians) computes the length of a circular arc using the formula s = r·θ, where r is the radius and θ is the central angle in radians. The result is given in the same unit as the radius, making it useful for geometry, engineering, and physics. Simply enter the radius and angle to get the arc length instantly.
It works by directly applying the formula s = r·θ, without unit conversion. The radius must be in a linear unit (meters, centimeters, etc.) and the angle must be in radians. If the angle is in degrees, convert it to radians first (multiply by π/180). The calculator assumes the angle is already in radians.
Use this calculator whenever you need to find the length of a circular arc, such as in architectural arcs, curve distances, gear design, or trigonometry and calculus problems. It is helpful for students, engineers, and professionals working with circle geometry.
Cautions: ensure the radius and angle are in the correct units. Angles in degrees must be converted to radians. Remember that the angle should be at most 2π radians (one full revolution). For angles greater than 2π, the arc corresponds to multiple revolutions. The formula s = r·θ is valid only for angles in radians.
Frequently asked questions
What if the angle is in degrees?
Convert degrees to radians by multiplying by π/180 before using the calculator. For example, 60° equals 60 × π/180 = π/3 radians.
Can I use any unit for the radius?
Yes, but the arc length will be in the same unit. If the radius is in meters, the arc will be in meters. Keep units consistent.
Does the formula work for angles greater than 2π?
Yes, the arc length is proportional to the angle. For example, θ = 4π gives an arc of two full revolutions (s = 4πr).
What is the difference between arc and chord?
The arc is the curved length between two points on a circle, while the chord is the straight line distance. This calculator gives the arc.
Do I need to know π to use the calculator?
No, the calculator uses π internally if needed. Just enter the angle in radians (which may include π, like π/2).