This online calculator converts angular velocity from degrees per second (°/s, deg/s) to radians per second (rad/s). The conversion is fixed by the definition of the degree relative to the radian, so the same input always produces the same result.
Degrees per Second (°/s) to Radians per Second (rad/s) Converter
Enter a value in °/s in the field below and press the button to convert it to rad/s.
Degrees per Second (°/s)
Result in Radians per Second (rad/s)
How to use the calculator
- Enter the angular speed in Degrees per Second (°/s).
- Set Decimal Places to choose how many digits to keep in the result.
- Click Convert to get the value in Radians per Second (rad/s).
- Use Copy Result to copy the output value.
- Use Swap to switch the conversion direction when you want the opposite calculation.
- Use Clear All to reset the input, output, rounding, and the displayed calculation.
Definitions of measurement units
Degrees per second (°/s, deg/s) is an angular velocity unit that tells how many degrees of rotation occur each second. The degree (symbol °) is a non-SI unit accepted for use with SI. Since 360° equals 2π radians, 1 °/s = π/180 rad/s, which is approximately 0.01745329252 rad/s. It is commonly used in user interfaces, robotics settings, and specifications where degrees are easier to read.
Radians per second (rad/s) is an angular velocity unit based on the radian (rad), the coherent SI unit for plane angle. One radian is defined from circle geometry as the angle that subtends an arc equal in length to the radius. From the same 360° equals 2π rad relationship, 1 rad/s = 180/π °/s, which is approximately 57.295779513 °/s. It is the standard unit in many physics and engineering equations (dynamics, control, vibration).
Conversion formula
rad/s = (°/s) × (π/180)
Source: NIST Guide to the SI, Chapter 5 (lists the exact relationship 1° = (π/180) rad).
Conversion table
| Degrees per second (°/s) | Radians per second (rad/s) |
|---|---|
| 0 | 0.000000000 |
| 0.01 | 0.000174533 |
| 0.05 | 0.000872665 |
| 0.1 | 0.001745329 |
| 0.5 | 0.008726646 |
| 1 | 0.017453293 |
| 2 | 0.034906585 |
| 5 | 0.087266463 |
| 10 | 0.174532925 |
| 15 | 0.261799388 |
| 30 | 0.523598776 |
| 45 | 0.785398163 |
| 60 | 1.047197551 |
| 90 | 1.570796327 |
| 120 | 2.094395102 |
| 180 | 3.141592654 |
| 270 | 4.712388980 |
| 360 | 6.283185307 |
| 1000 | 17.453292520 |
| 10000 | 174.532925199 |
Real World Examples
- Analog clock second hand: 6 °/s = 0.104719755 rad/s
- Analog clock minute hand: 0.1 °/s = 0.001745329 rad/s
- Analog clock hour hand: 0.008333333 °/s = 0.000145444 rad/s
- Turntable at 33⅓ rpm: 200 °/s = 3.490658504 rad/s
- Turntable at 45 rpm: 270 °/s = 4.712388980 rad/s
- Turntable at 78 rpm: 468 °/s = 8.168140899 rad/s
- AC electrical phase rotation at 50 Hz: 18000 °/s = 314.159265359 rad/s
- AC electrical phase rotation at 60 Hz: 21600 °/s = 376.991118431 rad/s
- Aircraft AC electrical phase rotation at 400 Hz: 144000 °/s = 2513.274122872 rad/s
- Hard drive spindle at 7200 rpm: 43200 °/s = 753.982236862 rad/s
What do you use this calculator for? If there is another unit conversion tool you want us to add, please tell us in the comments.
CalcuLife.com
Leave A Comment