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1 rpm equals approximately 0.1047 radians per second.
This conversion is based on the fact that one revolution per minute (rpm) is a measure of rotational speed, and to convert it to radians per second, we multiply by 2π (the radians in a full circle) and divide by 60 seconds. So, 1 rpm = (2π radians) / 60 seconds ≈ 0.1047 rad/sec.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert revolutions per minute (rpm) to radians per second (rad/sec) is: radians/sec = rpm * (2π) / 60. This works because each revolution is 2π radians, and there are 60 seconds in a minute, so multiplying rpm by 2π converts revolutions into radians, then dividing by 60 adjusts for seconds. For example, 2 rpm: 2 * (2π) / 60 = (4π)/60 ≈ 0.2094 rad/sec.
Conversion Example
- Convert 3 rpm:
- Multiply 3 by 2π: 3 * 2π = 6π ≈ 18.8496
- Divide by 60: 18.8496 / 60 ≈ 0.3142 rad/sec
- Convert 10 rpm:
- 10 * 2π = 20π ≈ 62.8319
- Divide by 60: 62.8319 / 60 ≈ 1.0472 rad/sec
- Convert 0.5 rpm:
- 0.5 * 2π = π ≈ 3.1416
- Divide by 60: 3.1416 / 60 ≈ 0.0524 rad/sec
- Convert 5 rpm:
- 5 * 2π ≈ 31.4159
- Divide by 60: ≈ 0.5236 rad/sec
Conversion Chart
This chart shows how different rpm values convert to radians per second. Use it to find quick conversions without calculations. For example, -24.0 rpm equals approximately -2.5133 rad/sec, and 26.0 rpm equals about 2.7198 rad/sec.
| rpm | rad/sec |
|---|---|
| -24.0 | -2.5133 |
| -23.0 | -2.4084 |
| -22.0 | -2.3034 |
| -21.0 | -2.1985 |
| -20.0 | -2.0935 |
| -19.0 | -1.9886 |
| -18.0 | -1.8836 |
| -17.0 | -1.7787 |
| -16.0 | -1.6737 |
| -15.0 | -1.5688 |
| -14.0 | -1.4638 |
| -13.0 | -1.3589 |
| -12.0 | -1.2539 |
| -11.0 | -1.1490 |
| -10.0 | -1.0440 |
| -9.0 | -0.9391 |
| -8.0 | -0.8341 |
| -7.0 | -0.7292 |
| -6.0 | -0.6242 |
| -5.0 | -0.5193 |
| -4.0 | -0.4143 |
| -3.0 | -0.3094 |
| -2.0 | -0.2044 |
| -1.0 | -0.0995 |
| 0.0 | 0.0 |
| 1.0 | 0.1047 |
| 2.0 | 0.2094 |
| 3.0 | 0.3142 |
| 4.0 | 0.4190 |
| 5.0 | 0.5236 |
| 6.0 | 0.6283 |
| 7.0 | 0.7330 |
| 8.0 | 0.8378 |
| 9.0 | 0.9425 |
| 10.0 | 1.0472 |
| 20.0 | 2.0944 |
| 26.0 | 2.7198 |
Related Conversion Questions
- How many radians per second are in 1 rpm?
- What is the rad/sec equivalent of 1 rpm?
- How do I convert 1 rpm to radians per second manually?
- What is the radian measure for 1 revolution per minute?
- Can I convert 1 rpm to radians per second online?
- What formula do I use to change rpm to radians in a calculation?
- Is 1 rpm the same as 0.1047 rad/sec?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes in one minute. It indicates rotational speed, with higher rpm meaning faster spinning, and is used in engines, motors, and machinery to specify how quickly they rotate.
rad
Radians are units of angular measure, where one radian equals the angle at the center of a circle subtended by an arc equal to the circle’s radius. There are 2π radians in a full circle, making radians a natural way to measure angles in mathematics and physics.
Conversion FAQs
How do I convert rpm to radians per second manually?
To convert rpm to radians/sec, multiply rpm by 2π and divide by 60. This accounts for the radians in a revolution and the seconds in a minute, giving you the rotational speed in radians per second. For example, 2 rpm: 2*(2π)/60 ≈ 0.2094 rad/sec.
Why is the factor 2π used in the conversion?
The factor 2π represents the total radians in a single revolution, because a full circle is 2π radians. Multiplying rpm by 2π converts revolutions into radians, which is necessary when measuring angular velocity in radians/sec.
Can this conversion be used for other units like degrees?
This specific formula is for radians, but if you want degrees, multiply rpm by 360 and divide by 60, resulting in degrees per second. Radians are more common in higher mathematics and physics because of their natural relation to circle measures.
What happens if I input a negative rpm value?
Negative rpm indicates rotation in the opposite direction. When converted to radians/sec, the sign remains, so negative values show opposite rotational directions, useful in applications needing directional control or analysis of rotational movement.
