The conversion of 15000 rpm to radians per second results in approximately 1570.8 rad/s.
To convert rpm (revolutions per minute) to rad/s (radians per second), multiply rpm by 2π and then divide by 60, because there are 2π radians in one revolution and 60 seconds in a minute. So, the formula is: (rpm * 2π) / 60.
Conversion Result
Result in rad:
Conversion Formula
The formula to change rpm to rad/s is (rpm * 2π) / 60. Because each revolution is 2π radians, multiplying rpm by 2π converts revolutions to radians. Dividing by 60 adjusts from per minute to per second, giving the rad/s value. For example, 15000 rpm times 2π equals 94377.8 radians per minute, which divided by 60 gives 1572.963 rad/s.
Conversion Example
- Convert 1000 rpm to rad/s:
- Multiply 1000 by 2π: 1000 * 6.2832 = 6283.2 radians per minute.
- Divide by 60: 6283.2 / 60 = 104.72 rad/s.
- Result: 1000 rpm equals approximately 104.72 rad/s.
- Convert 500 rpm to rad/s:
- 500 * 2π = 3141.6 radians per minute.
- Divide by 60: 3141.6 / 60 = 52.36 rad/s.
- Result: 500 rpm is about 52.36 rad/s.
- Convert 200 rpm to rad/s:
- 200 * 2π = 1256.6 radians per minute.
- Divide by 60: 1256.6 / 60 = 20.94 rad/s.
- Result: 200 rpm equals roughly 20.94 rad/s.
Conversion Chart
| RPM | Radians per second (rad/s) |
|---|---|
| 14975.0 | 1570.6 |
| 14980.0 | 1571.0 |
| 14985.0 | 1571.4 |
| 14990.0 | 1571.8 |
| 14995.0 | 1572.2 |
| 15000.0 | 1572.6 |
| 15005.0 | 1573.0 |
| 15010.0 | 1573.4 |
| 15015.0 | 1573.8 |
| 15020.0 | 1574.2 |
| 15025.0 | 1574.6 |
This chart shows how different rpm values convert to radians per second. To read it, find your rpm value in the first column and follow across to see the corresponding rad/s in the second column.
Related Conversion Questions
- What is 15000 rpm in radians per second with a different conversion factor?
- How do I convert 15000 rpm to radians per second manually?
- What is the rad/sec equivalent of 15000 rpm in rotational speed?
- Is 15000 rpm faster than 2000 rad/sec?
- How many radians per second is 15000 rpm?
- Can I convert 15000 rpm to degrees per second instead?
- What is the angular velocity in rad/sec for 15000 rpm?
Conversion Definitions
rpm (revolutions per minute) measures how many full turns an object completes in one minute, used mainly for rotational speeds in engines and machinery.
rad (radian) is a unit for measuring angles, where one radian equals the angle created when the arc length equals the radius; there are 2π radians in a full circle, making it a natural measure for angular calculations.
Conversion FAQs
How accurate is the conversion from rpm to rad/sec?
The conversion is precise as it uses a fixed mathematical relationship based on the constant 2π. Minor discrepancies may occur due to rounding during calculation, but for most practical purposes, the result is accurate enough.
Can I convert any rpm value to rad/sec with the same formula?
Yes, the same formula applies regardless of the rpm value. Simply multiply the rpm number by 2π and divide by 60 to get the rad/sec equivalent, making it a universal conversion method for rotational speeds.
Why do we divide by 60 in the formula?
Because rpm measures revolutions per minute, dividing by 60 converts the measurement to revolutions per second, which is necessary for rad/sec. This step ensures the units align correctly for angular velocity calculations.
What is the significance of 2π in the conversion?
2π radians correspond to one full revolution. Using 2π ensures the conversion from revolutions to radians is accurate, linking the number of turns directly to the angular measure in radians.