Acceleration - Angular Converter
Convert angular acceleration, how quickly rotation speeds up or slows down, between radians, degrees and revolutions per second squared, per minute squared and rpm per second. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
This tool converts angular acceleration (angle per time squared) only. It is not angular velocity (angle per time) and not linear acceleration (m/s²).
Angular Acceleration Formula
Every angular acceleration unit is a fixed multiple of the radian per second squared. Result = value × (source factor ÷ target factor). The building blocks are exact: 1 revolution = 2π rad, 1 degree = π/180 rad, 1 minute = 60 s, so 1 rev/min² = 2π ÷ 3,600 rad/s². The unit rev/(min·s) means “revolutions per minute gained each second” and equals 2π ÷ 60 rad/s².
What Is Angular Acceleration?
Angular acceleration is the rate at which angular velocity changes: α = Δω ÷ Δt. The SI unit is the radian per second squared (rad/s²). If a motor shaft goes from rest to 100 rad/s in 4 seconds, its average angular acceleration is 25 rad/s². Slowing a rotation down is angular acceleration with the opposite sign, so this converter accepts negative values.
The unit names combine an angle with a time squared. Revolution per second squared and revolution per minute squared are common in machinery. The revolution per minute per second (rpm per second) is very practical for drives and test benches, because the speed is read in rpm while the time is read in seconds. A degree per second squared is common for gimbals, antennas and robot joints.
Do not confuse it with related quantities. Angular acceleration is not angular velocity, which is angle per time (Velocity - Angular Converter), and it is not linear acceleration, which is length per time squared (Acceleration Converter). They are linked by the radius: the tangential acceleration of a point on a rotating body is a = α × r, valid only with α in rad/s².
Supported Units
This converter supports the following 6 angular acceleration units. The last column gives the value of each unit in the base unit, the radian per second squared. Note that rev/min² and rev/(min·s) are different units: the first divides by 60² and the second by 60.
| Unit | Symbol | Value in rad/s² |
|---|---|---|
| Radian per second squared | rad/s² | 1 |
| Degree per second squared | °/s² | 0.01745329252 |
| Radian per minute squared | rad/min² | 0.0002777777778 |
| Revolution per second squared | rev/s² | 6.283185307 |
| Revolution per minute squared | rev/min² | 0.001745329252 |
| Revolution per minute per second | rev/(min·s) | 0.1047197551 |
How to Use the Acceleration - Angular Converter
- Type the angular acceleration in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (rad/s²): 1 rev/(min·s) = 0.1047197551 rad/s² and 1 rad/s² = 1 rad/s².
- Divide the source size by the target size to get the conversion factor: 0.1047197551 ÷ 1 = 0.1047197551, so 1 rev/(min·s) = 0.1047197551 rad/s².
- Multiply by your value: 100 rev/(min·s) × 0.1047197551 = 10.47197551 rad/s².
Angular acceleration can be positive or negative (a negative value means rotation is slowing down), so a minus sign is accepted. Zero is also valid.
Common Angular Acceleration Conversions
- Motor spin-up: a drive that gains 600 rpm every second is accelerating at 62.83185307 rad/s², which is 10 rev/s².
- Revolutions per second squared: 2 rev/s² equals 12.56637061 rad/s².
- Gimbal specification: 500 °/s² equals 8.72664626 rad/s².
- Slow rotation: 1 rev/min² equals 0.001745329252 rad/s² and 0.1 °/s².
- Per minute squared to per second squared: 3,600 rev/min² equals 1 rev/s².
- Back to SI: 25 rad/s² equals 238.7324146 rev/(min·s).
Radian per Second Squared to Other Angular Acceleration Units
Quick reference for frequently used values
| rad/s² | Degree/s² | Revolution/s² | rev/(min·s) |
|---|---|---|---|
| 0.1 | 5.729577951 | 0.01591549431 | 0.9549296586 |
| 1 | 57.29577951 | 0.1591549431 | 9.549296586 |
| 5 | 286.4788976 | 0.7957747155 | 47.74648293 |
| 10 | 572.9577951 | 1.591549431 | 95.49296586 |
| 25 | 1,432.394488 | 3.978873577 | 238.7324146 |
| 50 | 2,864.788976 | 7.957747155 | 477.4648293 |
| 100 | 5,729.577951 | 15.91549431 | 954.9296586 |
| 500 | 28,647.88976 | 79.57747155 | 4,774.648293 |
Where and Why This Conversion Is Used
- Motor and drive design: ramp rates and spin-up times, where torque = moment of inertia × angular acceleration.
- Robotics and motion control: joint, gimbal and servo acceleration limits.
- Vehicles and machinery: flywheels, clutches, turbines and wheel spin during traction events.
- Testing and instrumentation: rotary tables and shaker or spin-test specifications.
- Physics education: rotational kinematics problems.
Limitations
- The converter changes units only. To get torque you need the moment of inertia: τ = I × α, with I in kg·m² and α in rad/s².
- The value is treated as the rate of change of rotation about one axis; it does not combine rotations about different axes.
Important Differences Between Related Measurements
- Angular acceleration vs angular velocity: angular velocity is how fast something spins (rad/s). Angular acceleration is how fast that spin rate changes (rad/s²). A shaft turning at a steady 1,500 rpm has zero angular acceleration.
- Angular acceleration vs linear acceleration: angular acceleration is angle per time squared. Linear acceleration is length per time squared. At radius r, a = α × r, so the same α gives a larger linear acceleration farther from the axis.
- rev/min² vs rev/(min·s): rev/min² is a revolution rate that changes once per minute. rev/(min·s) (rpm per second) is much larger numerically: 1 rev/(min·s) equals 60 rev/min².
- Angular acceleration vs torque: torque is the twisting moment that causes angular acceleration. They are related through the moment of inertia, but they are different quantities.
Each converter on this site changes units within one quantity only, and none of them mixes quantities. The related tools are: Velocity - Angular, Acceleration, Acceleration - Angular, Density, Specific Volume, Moment of Inertia, Moment of Force and Torque.