The result of converting 1 rps to radians is approximately 6.2832 rad.
Since 1 revolution per second (rps) means one full turn every second, and one turn is 2π radians, multiplying rps by 2π gives radians per second. Therefore, 1 rps equals 2π radians, which is about 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 per second (rad/sec) is: radians/sec = rps * 2π. This works because each revolution contains 2π radians, so multiplying the number of revolutions per second by 2π gives the radians per second. For example, 1 rps equals 1 * 2π = 6.2832 rad/sec.
Conversion Example
- Example 1: Convert 2 rps to rad/sec.
- Step 1: Write the formula: radians/sec = rps * 2π.
- Step 2: Substitute 2 for rps: 2 * 2π.
- Step 3: Calculate: 2 * 6.2832 = 12.5664 rad/sec.
- Answer: 2 rps equals 12.5664 radians per second.
- Example 2: Convert 0.5 rps to rad/sec.
- Step 1: Write the formula: radians/sec = rps * 2π.
- Step 2: Substitute 0.5 for rps: 0.5 * 2π.
- Step 3: Calculate: 0.5 * 6.2832 = 3.1416 rad/sec.
- Answer: 0.5 rps equals 3.1416 radians per second.
- Example 3: Convert -1 rps to rad/sec.
- Step 1: Write the formula: radians/sec = rps * 2π.
- Step 2: Substitute -1 for rps: -1 * 2π.
- Step 3: Calculate: -1 * 6.2832 = -6.2832 rad/sec.
- Answer: -1 rps equals -6.2832 radians per second.
Conversion Chart
This chart shows selected rps values and their radian equivalents. For example, -24.0 rps equals -150.7964 rad, and 26.0 rps equals 163.3624 rad. Use the table to easily find the conversion for specific rps values without calculating manually.
| rps | radians |
|---|---|
| -24.0 | -150.7964 |
| -23.0 | -144.4610 |
| -22.0 | -138.1256 |
| -21.0 | -131.7902 |
| -20.0 | -125.4548 |
| -19.0 | -119.1194 |
| -18.0 | -112.7840 |
| -17.0 | -106.4486 |
| -16.0 | -100.1132 |
| -15.0 | -93.7778 |
| -14.0 | -87.4424 |
| -13.0 | -81.1070 |
| -12.0 | -74.7716 |
| -11.0 | -68.4362 |
| -10.0 | -62.1008 |
| -9.0 | -55.7654 |
| -8.0 | -49.4300 |
| -7.0 | -43.0946 |
| -6.0 | -36.7592 |
| -5.0 | -30.4238 |
| -4.0 | -24.0884 |
| -3.0 | -17.7530 |
| -2.0 | -11.4176 |
| -1.0 | -5.0822 |
| 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 |
| 26.0 | 163.3624 |
Related Conversion Questions
- How many radians are in 1.5 revolutions per second?
- What is the radian equivalent of 0.75 rps?
- Convert 10 rps to radians per second?
- How do I calculate radians from revolutions per second?
- What is the formula to change rps to radians?
- Is 1 rps equal to 2π radians?
- How many radians in 5 revolutions per second?
Conversion Definitions
rps: Revolutions per second (rps) measures how many times an object completes a full circle in one second. It is used in rotational speed, indicating the frequency of rotations or turns per second.
rad: Radians (rad) are units of angular measure. One radian is the angle created when the arc length equals the radius of a circle. A full circle contains 2π radians, linking linear and angular measurements.
Conversion FAQs
Why is 1 rps equal to 2π radians?
Because each revolution corresponds to 2π radians, multiplying revolutions per second by 2π gives radians per second. This conversion stems from the circle’s total angle in radians per full turn.
Can I convert rps to radians per minute directly?
Yes, by first converting rps to rad/sec using the formula, then multiplying the result by 60 to get radians per minute. It’s a two-step process but straightforward once you understand the conversion factor.
What is the significance of radians in rotational measurements?
Radians provide a natural way to measure angles based on the circle’s radius, making calculations in physics and engineering more convenient, especially when dealing with arc lengths, angular velocity, and rotational dynamics.
Does the conversion work for negative rps values?
Yes, negative rps indicates rotation in the opposite direction, and multiplying by 2π gives the corresponding negative radians per second, maintaining the sign and meaning of rotational direction.
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