The result of converting 15 rpm to radians is approximately 1.57 rad.
Since 1 revolution equals 2π radians, and rotations per minute (rpm) measures how many full turns are completed each minute, to convert rpm to radians per second, you multiply rpm by 2π and divide by 60. For 15 rpm, that gives us (15 * 2π) / 60, which simplifies to π/2 ≈ 1.57 radians.
Conversion Result
15 rpm converts to about 1.57 radians. This means that when an object spins at 15 rotations every minute, it covers approximately 1.57 radians each second.
Conversion Tool
Result in rad:
Conversion Formula
To convert rpm to radians, multiply rpm by 2π, then divide by 60. The formula is: radians = (rpm * 2π) / 60. This works because 1 revolution equals 2π radians, and there are 60 seconds in a minute, so the conversion accounts for the rotation rate per second.
For example, with 15 rpm:
- Multiply 15 by 2π: 15 * 6.2832 ≈ 94.248
- Divide by 60: 94.248 / 60 ≈ 1.57 rad
Conversion Example
- Convert 10 rpm to rad:
- 10 * 2π ≈ 62.832
- 62.832 / 60 ≈ 1.047 rad
- Convert 20 rpm to rad:
- 20 * 2π ≈ 125.664
- 125.664 / 60 ≈ 2.094 rad
- Convert 5 rpm to rad:
- 5 * 2π ≈ 31.416
- 31.416 / 60 ≈ 0.524 rad
- Convert 30 rpm to rad:
- 30 * 2π ≈ 188.496
- 188.496 / 60 ≈ 3.141 rad
Conversion Chart
| rpm | Radians (rad) |
|---|---|
| -10.0 | -1.0472 |
| -5.0 | -0.5236 |
| 0.0 | 0 |
| 5.0 | 0.5236 |
| 10.0 | 1.0472 |
| 15.0 | 1.57 |
| 20.0 | 2.0944 |
| 25.0 | 2.6180 |
| 30.0 | 3.1416 |
| 35.0 | 3.6652 |
| 40.0 | 4.1888 |
This chart helps you see the radian equivalents for different rpm values. To use it, find your rpm in the left column and read across to see the corresponding radian measure.
Related Conversion Questions
- How many radians are in 15 rpm?
- What is the radian equivalent of 15 revolutions per minute?
- Convert 15 rpm to radians per second.
- How do I change 15 rpm into radians?
- What is the radian measure for a 15 rpm rotation?
- At 15 rpm, how many radians are covered per second?
- Is 15 rpm equal to approximately 1.57 radians?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many complete turns an object makes in one minute, used to describe rotational speed, especially in engines and machinery, helping to gauge how fast something spins in a given amount of time.
rad
Radian (rad) is a unit of angular measure representing the angle at the center of a circle subtended by an arc equal in length to the radius, used in mathematics and physics to describe rotation and angular displacement.
Conversion FAQs
How accurate is the conversion from rpm to radians for small values like 15 rpm?
The conversion is highly accurate because it is based on precise mathematical relationships between rotations and radians, with no approximation errors besides rounding. For 15 rpm, the result is reliably about 1.57 radians per second.
Can I convert rpm to radians for any rotational speed using this formula?
Yes, the formula applies universally for any rpm value; simply multiply the rpm by 2π and divide by 60. This method ensures correct conversion regardless of how fast or slow the rotation is.
What is the significance of 2π in the conversion formula?
2π represents the number of radians in a full revolution around a circle. Since rpm measures full turns per minute, multiplying by 2π converts revolutions into radians, which are a more fundamental angular measure.
Why do we divide by 60 in the formula?
Dividing by 60 accounts for converting minutes to seconds because the rpm measures rotations per minute, but radians per second are often used in calculations requiring seconds, making the units compatible.