1500 rpm equals approximately 157.08 radians per second
Converting 1500 rpm to radians involves understanding that rpm stands for revolutions per minute, and radians measure angles. The result shows how many radians are covered in one second for 1500 rpm.
Conversion begins with knowing the basic formula: 1 revolution equals 2π radians, and there are 60 seconds in a minute. So, to convert rpm to rad/sec, multiply by 2π and divide by 60.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rpm to rad/sec is based on the fact that each revolution is 2π radians. To convert rpm to rad/sec, multiply the rpm value by 2π and then divide by 60 seconds. This converts revolutions per minute to radians per second, the SI unit for angular velocity.
For example, converting 1500 rpm:
- Start with rpm: 1500
- Multiply by 2π: 1500 × 6.2832 ≈ 9424.78
- Divide by 60: 9424.78 / 60 ≈ 157.08 rad/sec
Conversion Example
Convert 2000 rpm to rad/sec:
- Multiply rpm by 2π: 2000 × 6.2832 ≈ 12566.37
- Divide by 60: 12566.37 / 60 ≈ 209.44 rad/sec
Convert 1200 rpm to rad/sec:
- Multiply rpm by 2π: 1200 × 6.2832 ≈ 7539.84
- Divide by 60: 7539.84 / 60 ≈ 125.66 rad/sec
Convert 500 rpm to rad/sec:
- Multiply rpm by 2π: 500 × 6.2832 ≈ 3141.59
- Divide by 60: 3141.59 / 60 ≈ 52.36 rad/sec
Conversion Chart
| RPM | Radians per second (rad/sec) |
|---|---|
| 1475.0 | 154.73 |
| 1476.0 | 154.86 |
| 1477.0 | 154.99 |
| 1478.0 | 155.12 |
| 1479.0 | 155.25 |
| 1480.0 | 155.38 |
| 1481.0 | 155.51 |
| 1482.0 | 155.64 |
| 1483.0 | 155.77 |
| 1484.0 | 155.90 |
| 1485.0 | 156.03 |
| 1486.0 | 156.16 |
| 1487.0 | 156.29 |
| 1488.0 | 156.42 |
| 1489.0 | 156.55 |
| 1490.0 | 156.68 |
| 1491.0 | 156.81 |
| 1492.0 | 156.94 |
| 1493.0 | 157.07 |
| 1494.0 | 157.20 |
| 1495.0 | 157.33 |
| 1496.0 | 157.46 |
| 1497.0 | 157.59 |
| 1498.0 | 157.72 |
| 1499.0 | 157.85 |
| 1500.0 | 157.08 |
| 1501.0 | 157.21 |
| 1502.0 | 157.34 |
| 1503.0 | 157.47 |
| 1504.0 | 157.60 |
| 1505.0 | 157.73 |
| 1506.0 | 157.86 |
| 1507.0 | 157.99 |
| 1508.0 | 158.12 |
| 1509.0 | 158.25 |
| 1510.0 | 158.38 |
| 1511.0 | 158.51 |
| 1512.0 | 158.64 |
| 1513.0 | 158.77 |
| 1514.0 | 158.90 |
| 1515.0 | 159.03 |
| 1516.0 | 159.16 |
| 1517.0 | 159.29 |
| 1518.0 | 159.42 |
| 1519.0 | 159.55 |
| 1520.0 | 159.68 |
| 1521.0 | 159.81 |
| 1522.0 | 159.94 |
| 1523.0 | 160.07 |
| 1524.0 | 160.20 |
| 1525.0 | 160.33 |
Use this chart to quickly see the rad/sec values for RPMs between 1475 and 1525. Read the RPM column, then look across to see the corresponding radians per second.
Related Conversion Questions
- How many radians per second is 1500 rpm?
- What is the rad/sec equivalent of 1500 rpm?
- Convert 1500 rpm to radians, what is the exact number?
- In terms of radians per second, what does 1500 rpm translate to?
- How do I convert 1500 revolutions per minute to radians per second?
- Is 1500 rpm equal to approximately 157.08 rad/sec?
- What is the radians per second for 1500 rpm?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns or cycles an object completes in one minute, used to describe rotational speed in mechanical systems and engines, indicating how fast a shaft or wheel spins around its axis.
rad
Radians (rad) are units of angular measure representing the angle created when the arc length equals the radius, with 2π radians equaling a full circle, used in mathematics and physics to quantify rotation and angular displacement.
Conversion FAQs
How accurate is the conversion from rpm to radians per second?
The conversion is precise as it relies on the fundamental relationship between revolutions and radians, multiplying rpm by 2π and dividing by 60 ensures an exact measure of angular velocity in rad/sec, assuming the rpm value is accurate.
Can I convert rpm to radians per second for any rotational speed?
Yes, the formula applies universally for converting any rpm value to radians per second, regardless of the magnitude, because it is based on fixed mathematical relationships between revolutions, radians, and seconds.
Why is the conversion factor 2π divided by 60?
Because one revolution equals 2π radians and there are 60 seconds in a minute, dividing by 60 converts revolutions per minute into radians per second, aligning units for standard SI measurement of angular velocity.
What are some real-world uses of converting rpm to rad/sec?
This conversion is used in engineering, physics, and automotive industries to analyze rotational speeds of engines, turbines, or gears, providing standardized units for calculations involving angular acceleration, torque, and dynamics.