Engineering converters
Acceleration - Angular Converter
Convert rad/s², degrees per second squared and revolutions per minute squared.
Result
572.958 rev/min²
1 rad/s² = 572.958 rev/min²
All units for this value
| Unit | Symbol | Value |
|---|---|---|
| Radian per second squared | rad/s² | 1 |
| Radian per minute squared | rad/min² | 3600 |
| Radian per hour squared | rad/h² | 12960000 |
| Degree per second squared | °/s² | 57.2958 |
| Degree per minute squared | °/min² | 206265 |
| Revolution per second squared | rev/s² | 0.159155 |
| Revolution per minute squared | rev/min² | 572.958 |
| Revolution per hour squared | rev/h² | 2062650 |
About this calculator
Angular acceleration measures how quickly a rotational speed changes over time, expressed as an angular velocity unit per unit of time. This converter switches between radians per second squared, degrees per second squared, and revolution-based units like revolutions per minute squared, used in motor control, robotics, and rotational dynamics.
How it works in plain English
Just as linear acceleration describes a changing speed, angular acceleration describes a changing rotational speed, and it's built from an angle unit divided by time squared. The converter uses radians per second squared as its common anchor, multiplying your entered value by a fixed factor to reach that anchor and then dividing by the target unit's factor to produce the final figure. This approach keeps every combination of angle and time-squared unit consistent.
Because time appears squared in these units, converting from a minute-based or hour-based unit involves squaring the time-scaling factor as well as applying the angle conversion. For example, going from revolutions per minute squared to radians per second squared requires multiplying by 2π for the revolution-to-radian step and dividing by 3,600 (60 squared) for the minutes-to-seconds step, since both minute factors in the denominator get squared.
Choose your source and target units in the from and to menus, enter a value, and the converted result appears at once. A complete table shows that same angular acceleration in every supported unit simultaneously, a precision control adjusts the number of decimal places shown, and a swap button reverses the two chosen units instantly.
The formula
- value_in_target = value_in_source × (source factor to rad/s²) ÷ (target factor to rad/s²)
- 1 rev/min² = 2π ÷ 3600 rad/s² ≈ 0.001745 rad/s²
- 1 rev/s² = 2π rad/s² ≈ 6.283185 rad/s²
- 1 deg/s² = π ÷ 180 rad/s² ≈ 0.017453 rad/s²
- 1 rad/s² = 3600 ÷ 2π rev/min² ≈ 572.958 rev/min²
Worked example
Suppose a motor's speed ramps up at a rate of 300 revolutions per minute squared and you want that in radians per second squared. Multiply by the combined factor: 300 rev/min² × (2π ÷ 3600) = 300 × 0.001745 = 0.5236 rad/s². This single step handles both the revolution-to-radian conversion and the minutes-squared-to-seconds-squared scaling.
Typing 300 into the rev/min² field with rad/s² selected as the target shows 0.5236 rad/s² immediately. The accompanying unit table also confirms this equals about 30 degrees per second squared and roughly 0.0833 revolutions per second squared, all derived from the same entered value.
Common angular acceleration unit equivalents
| Unit | Equal to (rad/s²) |
|---|---|
| 1 rad/s² | 1 |
| 1 rad/min² | 0.000278 |
| 1 rad/h² | 0.0000000772 |
| 1 deg/s² | 0.017453 |
| 1 deg/min² | 0.00000485 |
| 1 rev/s² | 6.283185 |
| 1 rev/min² | 0.001745 |
| 1 rev/h² | 0.000000485 |
Standard unit definitions
Frequently asked questions
Why does squaring time matter so much in these conversions?
Angular acceleration units include time in the denominator raised to the second power, so any time-unit conversion factor, like 60 seconds per minute, must also be squared when switching between units. This is why converting rev/min² to rad/s² divides by 3,600 rather than 60, since both minute factors in the original unit get converted.
Where does angular acceleration matter in practice?
It's used in motor and drive system design to describe how quickly a spinning shaft speeds up or slows down, in robotics to control joint movements smoothly, and in rotational dynamics problems involving torque and moment of inertia, since torque equals moment of inertia multiplied by angular acceleration.
How is angular acceleration related to angular velocity?
Angular velocity describes how fast something is rotating at a given moment, while angular acceleration describes how quickly that rotational speed is changing over time. If a motor's rpm increases steadily, its angular acceleration is constant; if the rpm holds steady, the angular acceleration is zero.
Can negative angular acceleration be entered?
Yes, negative values represent deceleration, meaning the rotational speed is decreasing over time. The converter applies the same multiply-then-divide process to negative numbers as it does to positive ones, so a negative rev/min² value converts to a correspondingly negative rad/s² value.
How precise are the converted results?
Conversions rely on the exact constant π and defined time-unit relationships, so results are accurate to as many decimal places as you choose to show. The precision control lets you widen or narrow that display, which is useful when comparing very small or very close angular acceleration values.
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