1 RPS equals approximately 6.2832 radians
Converting 1 revolution per second (rps) to radians results in about 6.2832 radians. This is because one full rotation is 2π radians, so 1 rps means one complete turn per second.
Introduction
When you convert rps to radians, you are translating revolutions into radians, the standard unit of angular measurement. Since 1 revolution equals 2π radians, multiplying the rps value by 2π gives you the radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert revolutions per second (rps) to radians is: radians = rps * 2π. This is because each revolution encompasses 2π radians. Multiplying rps by 2π converts the number of revolutions into the total radians traversed per second.
For example, if you have 2 rps, then radians = 2 * 2π = 4π = approximately 12.5664 radians. This calculation ensures the conversion accurately reflects the angular distance in radians for any given rps value.
Conversion Example
- Example 1: Convert 3 rps:
- Multiply 3 by 2π: 3 * 2π = 6π
- 6π ≈ 18.8496 radians
- Example 2: Convert 0.5 rps:
- 0.5 * 2π = π
- π ≈ 3.1416 radians
- Example 3: Convert 10 rps:
- 10 * 2π = 20π
- 20π ≈ 62.8319 radians
Conversion Chart
| rps | Radians (approx.) |
|---|---|
| -24.0 | -150.7964 |
| -23.0 | -144.5134 |
| -22.0 | -138.2304 |
| -21.0 | -131.9474 |
| -20.0 | -125.6644 |
| -19.0 | -119.3814 |
| -18.0 | -113.0984 |
| -17.0 | -106.8154 |
| -16.0 | -100.5324 |
| -15.0 | -94.2494 |
| -14.0 | -87.9664 |
| -13.0 | -81.6834 |
| -12.0 | -75.4004 |
| -11.0 | -69.1174 |
| -10.0 | -62.8344 |
| -9.0 | -56.5514 |
| -8.0 | -50.2684 |
| -7.0 | -43.9854 |
| -6.0 | -37.7024 |
| -5.0 | -31.4194 |
| -4.0 | -25.1364 |
| -3.0 | -18.8534 |
| -2.0 | -12.5704 |
| -1.0 | -6.2874 |
| 0.0 | 0.0 |
| 1.0 | 6.2832 |
| 2.0 | 12.5664 |
| 3.0 | 18.8496 |
| 4.0 | 25.1328 |
| 5.0 | 31.4160 |
| 6.0 | 37.6992 |
| 7.0 | 43.9824 |
| 8.0 | 50.2656 |
| 9.0 | 56.5488 |
| 10.0 | 62.8320 |
| 20.0 | 125.6644 |
| 26.0 | 163.3628 |
Use this chart to quickly find the rad value corresponding to any rps value listed. Moving horizontally across the table from rps to radians can help you visualize the angular motion.
Related Conversion Questions
- How many radians are in 1.5 revolutions per second?
- What is the radian equivalent of 0.75 rps?
- How do I convert 5 rps to radians per second?
- What is the radians per second for 10 revolutions per second?
- Can I convert negative rps values to radians?
- What does 1 radian per second mean in terms of revolutions?
- How many radians do I get from 0.1 rps?
Conversion Definitions
rps
Revolutions per second (rps) measures how many full turns an object makes each second, representing the rotational speed. It is a frequency unit used in physics and engineering to describe circular motion rates.
rad
Radian (rad) is a unit of angular measurement that describes the angle created when the arc length equals the radius. It relates linear and angular distances, with 2π radians equating to a full circle of 360 degrees.
Conversion FAQs
What is the significance of multiplying rps by 2π?
Multiplying rps by 2π converts revolutions into radians because each revolution equals 2π radians. This operation translates the number of revolutions per second into the total radians traversed in one second, providing a standard angular measurement.
How can I convert radians back to revolutions per second?
To convert radians to rps, divide the radians value by 2π. This reverses the process, translating radians into the number of full revolutions per second, useful when you know the angular distance and want to find the rotational frequency.
Is there a difference between angular velocity in rad/sec and rps?
Yes, angular velocity in rad/sec measures how many radians an object rotates per second, while rps counts the number of revolutions per second. Rad/sec provides a finer, more precise measure of rotational speed and is often used in physics calculations.