Angular Acceleration Converter
What this converter does
Angular acceleration, α, is the rate at which rotational speed changes. Physics texts and control software usually work in radians per second squared, while drive manuals describe ramps as "rpm per second" and some machinery data uses revolutions per minute squared. This page changes the unit of an angular acceleration you already know. It does not compute acceleration from torque, inertia or a speed profile.
How the conversion works
The converter expresses every input in rad/s² and then in the target unit. The relationships follow from one revolution being exactly 2π radians and one minute being 60 seconds:
- 1 rev/s² = 2π rad/s² ≈ 6.283185 rad/s²
- 1 rev/min per second (rpm/s) = 2π ÷ 60 rad/s² ≈ 0.104720 rad/s²
- 1 rev/min² = 2π ÷ 3,600 rad/s² ≈ 0.00174533 rad/s²
- 1 rad/min² = 1 ÷ 3,600 rad/s² ≈ 0.000277778 rad/s²
SoupCalc evaluates these factors from π itself instead of storing truncated decimals, so a round trip such as rad/s² → rev/s² → rad/s² returns the original value.
Worked example
A spindle drive is set to ramp from rest to 3,000 rpm in 2 seconds. The average ramp rate is 3,000 ÷ 2 = 1,500 rpm per second. Multiplying by 2π ÷ 60 gives 157.08 rad/s², the value a motion controller expects.
For a physics exercise stating α = 5 rad/s², dividing by 2π gives 0.7958 rev/s². A very slow turntable accelerating at 10 rev/min² corresponds to only 0.01745 rad/s².
What the result means
The number represents the same change in rotational speed per unit of time. In rpm/s it answers "how many rpm are gained each second"; in rad/s² it plugs directly into τ = I α and ω = ω₀ + α t. The radian is dimensionless, so rad/s² is sometimes printed simply as s⁻²; confirm the context before assuming the "per second squared" figure is a revolution-based unit.
Accuracy and limitations
- A single conversion describes an average or constant acceleration. Real drives often use S-curve profiles whose instantaneous α varies.
- Rotational acceleration is not the same as the tangential acceleration of a point on the rim; multiply by the radius to obtain the linear value in m/s².
- The page does not check whether a motor or load can physically achieve the converted value.
Sources
- BIPM SI Brochure — the radian and the coherent unit rad/s².
- NIST SP 811 Appendix B.9 — factors for angular quantities grouped by physical quantity.
Editorial record
Written and reviewed by the SoupCalc Editorial Team. Last reviewed: September 25, 2026.