Angular Velocity Conversion Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/10/2026
To convert an angular velocity, it is reduced to radians per second, then converted into the target unit. A speed of 100 revolutions per minute equals about 10.47 rad/s.
Explanation
Three units are commonly used to express a rotational speed. The radian per second (rad/s) is the SI unit, used directly in mechanics formulas (rotational kinetic energy, angular momentum) — it is the one expected by most physics and engineering calculations, including our angular velocity calculator. The revolution per minute (rpm) is the most intuitive and most commonly read unit in everyday life: it appears on engine tachometers, hard drive specs, and washing machine spin cycles. The degree per second (°/s) is sometimes used in robotics and animation to express a slower rotational speed that is more intuitive to visualize than radians, on the same principle as our angle conversion calculator for a static angle rather than a rotational speed. Conversion between these units is purely proportional: one full turn always corresponds to 2π radians, 360°, or 1 revolution, whatever the unit of time chosen.
Example: converting 100 rpm to rad/s
Inputs
Value: 100. Starting unit: revolutions per minute. Target unit: radians per second.
Calculation
100 rpm equals 100 × (2π ÷ 60) = 100 × 0.10472 ≈ 10.471976 rad/s.
Result
100 rpm equal about 10.47 radians per second.
Frequently asked questions
Why is rad/s used in mechanics formulas?
The radian is the natural unit of angle in mathematics: it simplifies rotational mechanics formulas, such as rotational kinetic energy or the linear speed of a point (v = ω × r, valid only if ω is expressed in rad/s). This is why engineering calculations almost always use rad/s rather than rpm or °/s.
How do you quickly go from rpm to rad/s in your head?
A useful benchmark: multiply by π/30 (about 0.1047). For example, 3,000 rpm × 0.1047 ≈ 314.16 rad/s. This calculator gives the exact decimal value for any speed.
Does this conversion apply to any rotating object?
Yes, angular velocity depends only on the angle covered per unit of time, not on the size of the rotating object. The linear speed of a point on that object, however, also depends on its distance from the axis of rotation (the radius): two points at different distances from the same axis have the same angular velocity but different linear speeds.