RPM and rad/s Conversion
Instantly convert between revolutions per minute (RPM) and radians per second (rad/s) with our free online Converter.
How to Convert Between RPM and rad/s
RPM to rad/s Formula
To convert RPM to radians per second, multiply the RPM value by 0.10472:
rad/s = RPM × 0.10472
This is based on 1 revolution = 2π radians and 1 minute = 60 seconds: (2π / 60) ≈ 0.10472.
Example: Convert 1200 RPM to rad/s:
rad/s = 1200 × 0.10472 = 125.664 rad/s
rad/s to RPM Formula
To convert rad/s to RPM, multiply the rad/s value by 9.549297:
RPM = rad/s × 9.549297
This is the inverse: (60 / 2π) ≈ 9.549297.
Example: Convert 50 rad/s to RPM:
RPM = 50 × 9.549297 = 477.46485 RPM
RPM to rad/s Conversion Table
Here’s a table of common RPM values converted to rad/s, rounded to four significant digits:
| Revolutions per Minute (RPM) | Radians per Second (rad/s) |
|---|---|
| 10 RPM | 1.047 rad/s |
| 60 RPM | 6.283 rad/s |
| 100 RPM | 10.47 rad/s |
| 500 RPM | 52.36 rad/s |
| 1000 RPM | 104.7 rad/s |
| 2000 RPM | 209.4 rad/s |
rad/s to RPM Conversion Table
Here’s a table converting common rad/s values to RPM:
| Radians per Second (rad/s) | Revolutions per Minute (RPM) |
|---|---|
| 1 rad/s | 9.549 RPM |
| 10 rad/s | 95.49 RPM |
| 20 rad/s | 190.99 RPM |
| 50 rad/s | 477.5 RPM |
| 100 rad/s | 954.9 RPM |
| 300 rad/s | 2864.8 RPM |
What Are Revolutions per Minute (RPM)?
RPM measures how many full rotations an object completes in one minute. It’s widely used in practical settings, like car engines (e.g., 3000 RPM) or machinery speeds.
What Are Radians per Second (rad/s)?
Rad/s measures angular velocity in radians per second, where 1 radian is about 57.3 degrees. It’s the SI unit for rotational speed, common in physics and engineering.
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Frequently Asked Questions (FAQs)
How do I convert RPM to rad/s?
Multiply RPM by 0.10472. For example, 1500 RPM × 0.10472 = 157.08 rad/s.
How do I convert rad/s to RPM?
Multiply rad/s by 9.549297. For instance, 25 rad/s × 9.549297 = 238.732425 RPM.
What is 1 RPM in rad/s?
One RPM equals 0.10472 rad/s, derived from 2π radians per revolution divided by 60 seconds.
What is 1 rad/s in RPM?
One radian per second equals 9.549297 RPM, based on 60 seconds per minute divided by 2π radians.
Why use 0.10472 and 9.549297 as conversion factors?
These factors come from the relationship between radians (2π per revolution) and time (60 seconds per minute): 2π / 60 ≈ 0.10472, and 60 / 2π ≈ 9.549297.
When should I use RPM versus rad/s?
Use RPM for practical speeds (e.g., motors, fans), and rad/s for scientific calculations (e.g., angular momentum, torque).
What’s a real-world example of RPM and rad/s?
A car engine at 2000 RPM equals about 209.44 rad/s, useful for both mechanics (RPM) and engineers (rad/s).
How many radians are in one revolution?
One revolution is 2π radians, approximately 6.283185 radians.
Is there a quick estimation trick for conversions?
For RPM to rad/s, divide by 10 (e.g., 100 RPM ≈ 10 rad/s, actual 10.47). For rad/s to RPM, multiply by 10 (e.g., 20 rad/s ≈ 200 RPM, actual 190.99).
