Angular Acceleration Converter: rad/s², r/s², r/(min·s) & More

What is angular acceleration?

Angular acceleration is the rate at which angular velocity changes—how quickly rotation speeds up or slows down. It’s the rotational analogue of linear acceleration (m/s²): instead of meters per second squared, you have radians per second squared (rad/s²), revolutions per second squared (r/s²), or revolution per minute per second (r/(min·s)). In physics and engineering, angular acceleration (often written α) appears in τ = Iα (torque = moment of inertia × angular acceleration) and in any analysis of spinning bodies that change speed. The SI unit is radian per square second (rad/s²); dimension is angle/time², or 1/time² when the radian is omitted.

This converter lets you switch between six common ways to express angular acceleration: rad/s², rad/min², °/s², r/s², r/(min·s), and r/min². Every value is normalized to rad/s² under the hood, so you can convert from datasheet units (e.g. r/(min·s)) to SI for formulas in one step.

How angular acceleration conversion works

To convert between any two angular acceleration units, we express both in rad/s². Multiply your value by the source unit’s factor (how many rad/s² one unit equals), then divide by the target unit’s factor:

Example: convert 1 r/s² to rad/s². One revolution per square second = 2π rad/s², so 1 r/s² = 2π ≈ 6.283 rad/s². Another: convert 10 r/(min·s) to rad/s². One revolution per minute per second = (2π/60) rad/s², so 10 r/(min·s) = 10 × (2π/60) ≈ 1.047 rad/s². The tool above does this for all six units.

Key angular acceleration units explained

Each unit’s factor to rad/s². 1 revolution = 2π radians; 1° = π/180 radians. “Per square second” means per s²; “per minute per second” means per (min·s).

When to use rad/s² vs r/s² vs r/(min·s)

Rad/s² is the SI unit and is preferred in physics and textbook formulas (e.g. α = τ/I). r/s² (revolution per square second) appears in specs for fast-accelerating rotors or when “revolutions” are natural. r/(min·s) (revolution per minute per second) is common on motor and drive nameplates: “angular acceleration 100 r/(min·s)” means RPM increases by 100 every second. Converting r/(min·s) to rad/s² is often needed to plug into τ = Iα. rad/min² and r/min² are used when time scales are in minutes. This converter supports all six so you can match datasheet units and formula units.

Who uses an angular acceleration converter?

Mechanical and electrical engineers convert motor or drive specs (often in r/(min·s)) to rad/s² for torque and inertia calculations. Students and educators use it to check homework (e.g. “convert 50 r/s² to rad/s²”) and to relate τ = Iα (in rad/s²) to real-world units. Motion control and robotics may specify angular acceleration in °/s² or r/(min·s); converting to rad/s² is needed for simulation or dynamics libraries. Automotive and aerospace work with rotating components (turbochargers, flywheels) where angular acceleration in rad/s² or r/s² appears. All conversions run in your browser—no data is sent to a server.

Why radian per square second is the SI unit

Angular acceleration α = dω/dt (rate of change of angular velocity). Angular velocity ω has dimension 1/time (rad/s), so α has dimension 1/time². The SI coherent unit is therefore rad/s². The radian is dimensionless, so rad/s² is dimensionally equivalent to s⁻². The BIPM and CGPM use rad/s² for angular acceleration; degrees and revolutions are accepted for use with SI but are not part of the coherent set. Using rad/s² keeps τ = Iα and other rotational equations dimensionally consistent. This converter uses rad/s² as the internal base so every result is traceable to SI.

Common angular acceleration conversions at a glance

Handy reference for rad/s² to r/s², r/(min·s) to rad/s², and other everyday conversions.

Avoiding common mistakes

Don’t confuse angular acceleration (α, in rad/s²) with angular velocity (ω, in rad/s): acceleration is rate of change of velocity. Don’t mix units in τ = Iα—use rad/s² for α when I is in kg·m² and τ in N·m. “Revolution per minute per second” (r/(min·s)) means (rev/min)/s, i.e. change in RPM per second; it is not the same as “revolution per square minute” (r/min²). When in doubt, convert everything to rad/s² with this tool, then apply your formulas.

Angular Acceleration Conversion FAQ