This angular acceleration converter changes how fast a rotation speeds up between radians per second squared, degrees per second squared, rpm per second and revolutions per second squared. All values go through rad/s², the SI unit. The factors come from 1 revolution = 2π rad = 360°, so 1 deg/s² = π/180 rad/s² and 1 rpm/s = 2π/60 rad/s².
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How to use the angular acceleration converter
- Enter the value, for example 500 rpm/s.
- In the angular acceleration converter, choose its unit and the target unit, such as rpm/s to rad/s².
- Read the angular acceleration converter result: 500 rpm/s = 52.36 rad/s².
For rad/s² to deg/s², multiply by 180/π (about 57.2958).
What is angular acceleration?
Angular acceleration is how quickly rotational speed changes. Its SI unit is the radian per second squared (rad/s²). It is used for motors, flywheels, robot joints and anything that spins up or slows down.
Conversion formula
The angular acceleration converter stores every unit as a multiple of the base unit, the radian per second squared (rad/s²). To convert:
value in target unit = value × (factor of source unit ÷ factor of target unit)
where each factor is the size of the unit in radians per second squared.
Common angular acceleration conversions
| From | To | 1 unit equals |
|---|---|---|
| degree per second squared (°/s²) | radian per second squared (rad/s²) | 0.01745329 rad/s² |
| revolution per minute per second (rpm/s) | radian per second squared (rad/s²) | 0.1047198 rad/s² |
| radian per second squared (rad/s²) | degree per second squared (°/s²) | 57.29578 °/s² |
Angular acceleration converter worked example
Convert 25 degrees per second squared to radians per second squared:
- Factor of °/s² = 0.017453293 rad/s²
- Factor of rad/s² = 1 rad/s²
- 25 × 0.017453293 ÷ 1 = 0.4363323 rad/s²
Angular acceleration unit reference
| Unit | Symbol | Group | Equals (rad/s²) |
|---|---|---|---|
| Radian per Second Squared | rad/s² | SI | 1 |
| Degree per Second Squared | °/s² | Common | 0.01745329252 |
| Revolution per Minute per Second | rpm/s | Common | 0.1047197551 |
| Revolution per Second Squared | rps² | Common | 6.283185307 |
| Degree per Second per Second | °/s/s | Common | 0.01745329252 |
Reverse factors for each angular acceleration unit
The reference table gives each unit in radian per second squareds. To go the other way, divide by that factor; the list below does the division for you.
- Degree per Second Squared (°/s²), Common: 1 °/s² = 0.01745329 rad/s², so 1 rad/s² = 57.29578 °/s².
- Revolution per Minute per Second (rpm/s), Common: 1 rpm/s = 0.1047198 rad/s², so 1 rad/s² = 9.549297 rpm/s.
- Revolution per Second Squared (rps²), Common: 1 rps² = 6.283185 rad/s², so 1 rad/s² = 0.1591549 rps².
- Degree per Second per Second (°/s/s), Common: 1 °/s/s = 0.01745329 rad/s², so 1 rad/s² = 57.29578 °/s/s.
Motor spin-up examples
Average angular acceleration is the change in rotation speed divided by time. Some example spin-ups, assuming steady acceleration:
| Spin-up | rpm/s | rad/s² | deg/s² |
|---|---|---|---|
| 0 to 1,000 rpm in 5 s | 200 | 20.94 | 1,200 |
| 0 to 3,000 rpm in 2 s | 1,500 | 157.08 | 9,000 |
| 0 to 7,200 rpm in 4 s | 1,800 | 188.5 | 10,800 |
| 0 to 60 rpm in 1 s | 60 | 6.28 | 360 |
To get rpm/s, divide the speed change by the seconds; then multiply by 0.10472 for rad/s².
Torque and angular acceleration
Newton’s second law for rotation is τ = I × α: torque equals moment of inertia times angular acceleration, with α in rad/s². A flywheel with I = 0.5 kg·m² driven by 10 N·m accelerates at 20 rad/s², about 1,146 deg/s². Use the torque converter and the moment of inertia converter to put inputs in SI units first. Deg/s² to rad/s² is multiply by π/180.
Units in motor specifications
Motor and drive data sheets often state acceleration in rpm per second rather than rad/s². To convert, multiply by 2π and divide by 60. A fan that reaches 1,200 rpm in 4 seconds accelerates at 300 rpm/s; the angular acceleration converter gives 31.42 rad/s², or 1,800 deg/s². A washing machine drum that spins up to 1,400 rpm over 20 seconds averages 70 rpm/s, about 7.33 rad/s².
These are average values. Real motors accelerate fastest at low speed and slow down as they approach their top speed, so peak angular acceleration is higher than the average. When sizing a motor, work in rad/s² because torque = moment of inertia × angular acceleration only holds in SI units. Use the angular acceleration converter to get rad/s² from the data sheet value, then apply the formula.
Common mistakes
- Treating rpm/s as rad/s². The values differ by a factor of about 9.55.
- Mixing degrees and radians in a torque calculation.
- Forgetting that a drive’s acceleration ramp is often set in seconds to full speed, not as an angular acceleration.
Related converters and calculators
Related rotation tools:
- Angular velocity converter: rpm and rad/s
- Acceleration converter: linear acceleration
- Torque converter: N·m and lbf·ft
- Moment of inertia converter: kg·m²
- Angle converter: degrees and radians
Sources
BIPM: SI Brochure; NIST Special Publication 811, Appendix B.
Questions about this calculator
What is the SI unit of angular acceleration?
Radians per second squared (rad/s²).
How do I convert rad/s² to deg/s²?
Multiply by 180/π, about 57.2958. For example, 2 rad/s² = 114.59 deg/s².
How do I convert deg/s² to rad/s²?
Multiply by π/180, about 0.0174533. For example, 90 deg/s² = 1.5708 rad/s².
How do I convert rpm/s to rad/s²?
Multiply by 2π/60, about 0.10472. For example, 100 rpm/s = 10.47 rad/s².
How do I calculate angular acceleration?
Divide the change in angular velocity by the time taken: α = Δω ÷ Δt. Going from 0 to 30 rad/s in 3 s gives 10 rad/s².
How is angular acceleration related to torque?
Torque = moment of inertia × angular acceleration (τ = Iα), with α in rad/s².
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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