Angular Velocity Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
Angular velocity is calculated with ω = N × 2π ÷ 60, where N is the rotation speed in revolutions per minute. For 1,500 RPM, the angular velocity is about 157.08 rad/s.
Explanation
Angular velocity (denoted ω, the Greek letter omega) measures how fast an object rotates in radians per second, the unit consistent with the international system used in most mechanics formulas (rotational energy, angular momentum...). It differs from the rotation speed usually shown on a tachometer or spec sheet, expressed in revolutions per minute (RPM). The conversion follows directly from the definition of the radian: one full turn equals 2π radians, and a minute contains 60 seconds, giving the factor 2π ÷ 60 applied to the speed in RPM. This conversion is purely definitional, with no approximation: a motor spinning at 1,500 RPM has an angular velocity of exactly 1,500 × 2π ÷ 60 radians per second. For the kinetic energy associated with straight-line motion rather than rotation, see our kinetic energy calculator.
Example: 1,500 RPM
Inputs
Rotation speed: 1,500 RPM.
Calculation
Angular velocity = 1,500 × 2π ÷ 60 = 1,500 × 0.10472 ≈ 157.08 rad/s.
Result
This rotation speed corresponds to about 157.08 rad/s.
Frequently asked questions
Why use radians per second instead of revolutions per minute?
Radians per second is the unit consistent with the international system, directly usable in rotational mechanics formulas (rotational kinetic energy, angular momentum, mechanical power) with no extra conversion factor. Revolutions per minute stays more intuitive and readable in everyday use (on a car's tachometer, for example), which explains its widespread commercial use despite this technical drawback.
Where does the factor 2π ÷ 60 come from?
2π represents the number of radians in one full turn (360°), and 60 converts minutes to seconds. The combined factor 2π ÷ 60 (about 0.1047) therefore converts a speed in revolutions per minute directly into radians per second, with no intermediate step.
How do I convert the other way, from rad/s to RPM?
Simply invert the formula: rotation speed (RPM) = angular velocity (rad/s) × 60 ÷ 2π. This calculator is set up for the most common use (RPM to rad/s); the reverse conversion follows exactly the same factor, just applied the other way.