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1 rps equals approximately 6.2832 radians per second
When converting 1 rps (revolutions per second) to radians, the result is about 6.2832 rad. This is because each revolution equals 2π radians, so 1 rps means one full turn every second, which corresponds to 2π radians.
Since 1 revolution (rev) is 2π radians, and rps (revolutions per second) measures how many turns happen each second, multiplying rps by 2π gives radians per second. Therefore, 1 rps equals 2π rad, approximately 6.2832 rad, indicating the angular displacement in radians per second.
Conversion Tool
Result in rad:
Conversion Formula
The conversion from rps to rad involves multiplying the number of revolutions per second by 2π, since each revolution equals 2π radians. This works because radians measure angles, and a full circle is 2π radians. For example, 1 rps times 2π gives 2π radians per second.
Mathematically, the formula is: radians per second = revolutions per second × 2π. So, if you have 3 rps, multiply 3 by 2π (approximately 6.2832) to get about 18.8496 rad/sec. This straightforward calculation converts revolutions into angular displacement in radians.
Conversion Example
- Convert 2 rps:
- Multiply 2 by 2π: 2 × 6.2832 = 12.5664 rad/sec
- Convert 0.5 rps:
- Multiply 0.5 by 2π: 0.5 × 6.2832 = 3.1416 rad/sec
- Convert 10 rps:
- Multiply 10 by 2π: 10 × 6.2832 = 62.832 rad/sec
- Convert 0.1 rps:
- Multiply 0.1 by 2π: 0.1 × 6.2832 = 0.6283 rad/sec
- Convert 5 rps:
- Multiply 5 by 2π: 5 × 6.2832 = 31.416 rad/sec
Conversion Chart
| Revolutions per second (rps) | Radians per second (rad/sec) |
|---|---|
| -24.0 | -150.796 |
| -23.0 | -144.513 |
| -22.0 | -138.229 |
| -21.0 | -131.946 |
| -20.0 | -125.663 |
| -19.0 | -119.379 |
| -18.0 | -113.096 |
| -17.0 | -106.813 |
| -16.0 | -100.529 |
| -15.0 | -94.246 |
| -14.0 | -87.963 |
| -13.0 | -81.679 |
| -12.0 | -75.396 |
| -11.0 | -69.113 |
| -10.0 | -62.832 |
| -9.0 | -56.548 |
| -8.0 | -50.265 |
| -7.0 | -43.982 |
| -6.0 | -37.699 |
| -5.0 | -31.416 |
| -4.0 | -25.132 |
| -3.0 | -18.849 |
| -2.0 | -12.566 |
| -1.0 | -6.283 |
| 0.0 | 0.0 |
| 1.0 | 6.283 |
| 2.0 | 12.566 |
| 3.0 | 18.849 |
| 4.0 | 25.132 |
| 5.0 | 31.416 |
| 6.0 | 37.699 |
| 7.0 | 43.982 |
| 8.0 | 50.265 |
| 9.0 | 56.548 |
| 10.0 | 62.832 |
| 20.0 | 125.664 |
| 30.0 | 188.496 |
| 40.0 | 251.328 |
| 50.0 | 314.159 |
| 60.0 | 376.991 |
| 70.0 | 439.823 |
| 80.0 | 502.655 |
| 90.0 | 565.487 |
| 100.0 | 628.318 |
| 200.0 | 1256.637 |
| 300.0 | 1884.955 |
| 400.0 | 2513.274 |
| 500.0 | 3141.592 |
| 600.0 | 3769.911 |
| 700.0 | 4398.229 |
| 800.0 | 5026.548 |
| 900.0 | 5654.866 |
| 1000.0 | 6283.184 |
Use this chart to quickly find radians per second for any rps value listed, whether positive or negative, by reading across the table, allowing for easy conversions without calculations.
Related Conversion Questions
- How many radians per second is 1 rps?
- What is the rad equivalent of 1 revolution per second?
- Convert 1 rps to radians for angular velocity calculations?
- How do I change 1 rps into radians per second?
- What is the rad value for 1 revolution per second?
- Since 1 rps equals how many radians per second?
- Is 1 rps equal to 2π radians per second?
Conversion Definitions
rps
Revolutions per second (rps) measures how many complete turns an object makes each second, indicating angular speed. It quantifies rotational frequency, with 1 rps meaning one full rotation every second, often used in engineering and physics contexts.
rad
Rad, short for radians, is a unit of angular measurement representing the ratio of arc length to radius. One radian equals the angle subtended at the circle’s center by an arc equal in length to the radius, with a full circle being 2π radians.
Conversion FAQs
Why is 1 rps equal to 2π radians?
This is because one revolution equals 2π radians. Therefore, if an object completes one turn per second, it covers 2π radians in that second, making the conversion straightforward by multiplying rps by 2π.
How do I convert 1 rps to radians manually?
Multiply 1 by 2π: 1 × 6.2832 = 6.2832 radians. This simple multiplication transforms revolutions into radians, providing the angular displacement in radians per second for 1 revolution per second.
Can this conversion apply to other rotation speeds?
Yes, the same formula applies universally: multiply the rps value by 2π to get radians per second. Whether the value is positive or negative, the calculation remains the same, indicating directionality if sign is considered.
