Converting 30 rpm to radians results in approximately 3.14 radians.
Table of Contents
Since 1 revolution equals 2π radians, and 1 minute contains 30 revolutions per minute (rpm), multiplying rpm by 2π and dividing by 60 converts revolutions per minute to radians per second. Therefore, 30 rpm equals 30 × 2π / 60, which simplifies to π/1, or about 3.14 radians.
Conversion Result
Result in rad:
Conversion Formula
The formula to convert rpm to radians per second is: radians/sec = rpm × (2π) / 60. This works because each revolution is 2π radians, and there are 60 seconds in a minute. By multiplying rpm by 2π, you get radians per minute, then dividing by 60 gives radians per second. For example, 30 rpm: 30 × (2π) / 60 = π radians/sec, about 3.14.
Conversion Example
- Convert 45 rpm to rad/sec:
- Multiply 45 by 2π: 45 × 6.2832 ≈ 282.743
- Divide by 60: 282.743 / 60 ≈ 4.712 rad/sec
- Convert 15 rpm to rad/sec:
- 15 × 6.2832 ≈ 94.248
- Divide by 60: 94.248 / 60 ≈ 1.57 rad/sec
- Convert 60 rpm to rad/sec:
- 60 × 6.2832 ≈ 376.992
- Divide by 60: 376.992 / 60 ≈ 6.283 rad/sec
- Convert 10 rpm to rad/sec:
- 10 × 6.2832 ≈ 62.832
- Divide by 60: 62.832 / 60 ≈ 1.047 rad/sec
- Convert 75 rpm to rad/sec:
- 75 × 6.2832 ≈ 471.238
- Divide by 60: 471.238 / 60 ≈ 7.854 rad/sec
Conversion Chart
| rpm | Radians/sec |
|---|---|
| 5.0 | 0.524 |
| 10.0 | 1.047 |
| 15.0 | 1.57 |
| 20.0 | 2.094 |
| 25.0 | 2.618 |
| 30.0 | 3.142 |
| 35.0 | 3.665 |
| 40.0 | 4.189 |
| 45.0 | 4.712 |
| 50.0 | 5.236 |
| 55.0 | 5.76 |
Use this chart to quickly find the rad/sec equivalent for any rpm value listed, or interpolate for values in between.
Related Conversion Questions
- How many radians per second is 30 rpm?
- What is the radian measure equivalent of 30 revolutions per minute?
- Convert 30 rpm to angular velocity in radians per second?
- How do I change 30 rpm into radians per second manually?
- What is the radian value for 30 rpm in physics calculations?
- How to express 30 revolutions per minute in radians per second?
- Is 30 rpm equal to about 3.14 radians per second?
Conversion Definitions
rpm
Revolutions per minute (rpm) measures how many full turns an object makes in one minute. It is a rotational speed commonly used in engines, motors, and spinning devices, indicating the rate of rotation without considering the size of the object.
rad
Radian (rad) is a measure of angle based on arc length, where one radian equals the angle at the center of a circle subtending an arc equal in length to the radius. It provides a direct measure of rotational angle, used in mathematics and physics for precise calculations.
Conversion FAQs
How do I convert rpm to radians per second manually?
Multiply the rpm value by 2π to get radians per minute, then divide by 60 to convert to radians per second. For example, for 30 rpm: 30 × 2π ≈ 188.5; then 188.5 / 60 ≈ 3.14 rad/sec, the angular velocity.
Why is the factor 2π used in the conversion?
Because one full revolution equals 2π radians, using 2π converts revolutions into radians. This factor accounts for the complete circle measurement, making the conversion from revolutions to radians straightforward and accurate.
Can I convert rpm to degrees per second instead?
Yes, multiply rpm by 360 and divide by 60. Since 1 revolution is 360 degrees, rpm times 6 gives degrees per second, as 360/60 = 6. For 30 rpm, that would be 30 × 6 = 180 degrees/sec.
What is the importance of radian in angular calculations?
Radians provide a natural way to relate angles to arc lengths and rotational motion, simplifying formulas in physics and mathematics. They allow for direct and consistent calculations of angular velocity, acceleration, and other rotational properties.