Elara BennettDisclosure: This post contains affiliate links, which means we may earn a commission if you purchase through our links at no extra cost to you.
The conversion of 1 rps (revolutions per second) to radians results in approximately 6.2832 rad.
Since 1 revolution equals 2π radians, and 1 rps is one revolution per second, multiplying 1 by 2π gives us the radians per second, which is approximately 6.2832 rad.
Conversion Result
1 rps equals approximately 6.2832 radians.
Conversion Tool
Result in rad:
Conversion Formula
The formula to convert revolutions per second (rps) to radians is: radians = rps × 2π. This works because each revolution is equivalent to 2π radians, so multiplying rps by 2π gives the total radians per second. For example, 1 rps: 1 × 2π = 6.2832 radians, showing the direct proportionality between revolutions and radians.
Conversion Example
- Example 1: Convert 2 rps to radians:
- Multiply 2 by 2π.
- 2 × 2π = 4π ≈ 12.5664 rad.
- Example 2: Convert 0.5 rps:
- 0.5 × 2π = π ≈ 3.1416 rad.
- Example 3: Convert 10 rps:
- 10 × 2π = 20π ≈ 62.8320 rad.
Conversion Chart
| rps | Radians |
|---|---|
| -24.0 | -150.7965 |
| -20.0 | -125.6637 |
| -16.0 | -100.5309 |
| -12.0 | -75.3982 |
| -8.0 | -50.2655 |
| -4.0 | -25.1327 |
| 0.0 | 0.0 |
| 4.0 | 25.1327 |
| 8.0 | 50.2655 |
| 12.0 | 75.3982 |
| 16.0 | 100.5309 |
| 20.0 | 125.6637 |
| 24.0 | 150.7965 |
| 26.0 | 163.3628 |
This chart shows rps values from -24.0 to 26.0 and their equivalent radians, allowing quick reference for different speeds or rotations.
Related Conversion Questions
- How many radians are in 1.5 rps?
- What is the radian equivalent of 5 revolutions per second?
- Can I convert 0.1 rps to radians per second?
- How do I calculate radians for 10 rps?
- What is the radians value of half a revolution per second?
- Is 1 rps equal to 2π radians per second?
- How do I convert negative rps values to radians?
Conversion Definitions
rps
Revolutions per second (rps) measures how many complete turns an object makes every second. It is a unit of rotational speed, indicating the frequency of rotation, where one revolution equals 2π radians.
rad
Radian (rad) is a measure of angle based on the radius of a circle. One radian is the angle where the arc length equals the radius, with 2π radians representing a full circle’s rotation.
Conversion FAQs
Why is 1 rps equal to 2π radians?
This is because one revolution corresponds to an angle of 2π radians. Since rps measures revolutions per second, multiplying by 2π converts revolutions into radians, giving the total radians rotated per second.
How can I quickly convert rps to radians without a calculator?
You can memorize that 1 rps equals about 6.2832 radians, as it’s based on the constant 2π. For other values, multiply the rps by 2π or use the conversion tool to get precise results.
Are negative rps values meaningful in radians?
Yes, negative rps indicate rotation in the opposite direction. When converted, negative radians show the angle of rotation in the reverse direction, maintaining the same magnitude but with a negative sign.
Can I convert fractional rps values easily?
Absolutely, just multiply the fractional rps by 2π. For example, 0.75 rps: 0.75 × 2π ≈ 4.7124 radians, showing that even fractional speeds can be converted accurately using the same formula.
