Engineering converters
Velocity - Angular Converter
Convert rpm, radians per second, degrees per second and revolutions per hour.
Result
104.72 rad/s
1000 rpm = 104.72 rad/s
All units for this value
| Unit | Symbol | Value |
|---|---|---|
| Radian per second | rad/s | 104.72 |
| Radian per minute | rad/min | 6283.19 |
| Radian per hour | rad/h | 376991 |
| Degree per second | °/s | 6000 |
| Degree per minute | °/min | 360000 |
| Degree per hour | °/h | 21600000 |
| Gradian per second | grad/s | 6666.67 |
| Revolution per second | rev/s | 16.6667 |
| Revolution per minute | rpm | 1000 |
| Revolution per hour | rev/h | 60000 |
About this calculator
Angular velocity describes how fast something spins or rotates, expressed as an angle covered per unit of time. This converter switches between radians per second, revolutions per minute (rpm), degrees per second, and related units, so readings from motors, turbines, and rotating machinery can all be compared on the same scale.
How it works in plain English
Every angular velocity unit combines an angle measure — radians, degrees, or full revolutions — with a time measure, such as seconds, minutes, or hours. The converter treats radians per second as the common anchor, multiplying your entered value by a fixed factor to reach that anchor and then applying a second factor to reach your target unit. This keeps every pairing of angle and time unit consistent without needing a separate formula for each combination.
Revolutions per minute is the most familiar unit in this group, showing up on engine tachometers, motor spec sheets, and drill speeds. One full revolution equals 2π radians, so converting rpm to radians per second means multiplying by 2π and dividing by 60 to also convert minutes into seconds. Degrees per second is common in robotics and camera pan-tilt systems, where π radians equal 180 degrees.
Select your starting unit and target unit from the from and to menus, type a value, and the converted figure appears immediately. A full table lists that same angular velocity across every supported unit at once, a precision control adjusts how many decimal places are shown, and a swap button reverses the two chosen units in one click.
The formula
- value_in_target = value_in_source × (source factor to rad/s) ÷ (target factor to rad/s)
- 1 rpm = 2π ÷ 60 rad/s ≈ 0.104720 rad/s
- 1 rev/s = 2π rad/s ≈ 6.283185 rad/s
- 1 deg/s = π ÷ 180 rad/s ≈ 0.017453 rad/s
- 1 rad/s = 60 ÷ 2π rpm ≈ 9.549297 rpm
Worked example
Suppose a motor spins at 1,500 rpm and you want that speed in radians per second. First convert to the common anchor: 1,500 rpm × (2π ÷ 60) = 1,500 × 0.104720 = 157.08 rad/s. That single multiplication captures both the revolution-to-radian and minute-to-second scaling in one step.
Typing 1,500 into the rpm field with rad/s selected as the target shows 157.08 rad/s right away. The full unit table displayed alongside it also confirms this equals about 9,000 degrees per second and 25 revolutions per second, all computed from the same entered value.
Common angular velocity unit equivalents
| Unit | Equal to (rad/s) |
|---|---|
| 1 rad/s | 1 |
| 1 rad/min | 0.016667 |
| 1 rad/h | 0.000278 |
| 1 deg/s | 0.017453 |
| 1 deg/min | 0.000291 |
| 1 deg/h | 0.00000485 |
| 1 rev/s | 6.283185 |
| 1 rpm | 0.104720 |
| 1 rev/h | 0.001745 |
Standard unit definitions
Frequently asked questions
Why is rpm converted using 2π instead of 360?
Radians measure angle using the arc length of a circle relative to its radius, and one full turn equals exactly 2π radians rather than 360. Since rpm counts full revolutions per minute, converting it to radians per second requires multiplying by 2π to switch from revolutions to radians, then dividing by 60 to switch from minutes to seconds.
What's the difference between rpm and rev/s?
Both count full revolutions, but rpm measures them per minute while rev/s measures them per second. Since there are 60 seconds in a minute, 1 rev/s equals exactly 60 rpm. Tachometers and motor ratings typically use rpm, while some physics and engineering formulas prefer rev/s or radians per second directly.
Where is angular velocity used in practice?
It describes the rotational speed of engines, turbines, fans, wheels, drills, and rotating shafts in machinery. Engineers use it to calculate torque, power transmission, and centripetal effects, while robotics and camera systems often use degrees per second for smaller, more intuitive rotational movements like panning or tilting.
Can I convert directly between degrees per second and rpm?
Yes. Choose degrees per second as the from unit and rpm as the to unit, and the converter applies both the degree-to-radian factor and the revolution-to-time factor in a single calculation. There's no need to manually pass through radians per second first, since that anchor conversion happens automatically behind the scenes.
How precise are the converted results?
Conversions rely on the exact mathematical constant π along with defined time-unit relationships, so results are accurate to as many decimal places as you choose to display. The precision control lets you widen or narrow the number of digits shown, which helps when comparing very close rotational speeds.
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