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RPM to Rad/s
Use this free RPM to rad/s converter to change angular velocity between revolutions per minute, radians per second, degrees per second, revolutions per second, and hertz. Enter a value, pick the unit you have and the unit you want, and the result updates instantly — in both directions, with all five units available on either side.
How it works
Angular velocity measures how fast something spins. RPM counts complete turns per minute, which is the number printed on most motor nameplates, fans, drills, and car tachometers. Radians per second counts the same spin in radians — the natural angle unit of mathematics and physics — where one full turn is 2π radians, about 6.2832. Because a minute holds 60 seconds, the bridge between the two is simple: one RPM equals 2π ÷ 60 radians per second, or about 0.10472 rad/s.
Degrees per second is the third common way to state the same spin. One full turn is 360 degrees, so one RPM equals 6 degrees per second. Revolutions per second is RPM divided by 60, and hertz is the same number again: one cycle per second is one revolution per second when the motion is a steady spin. That is why 60 RPM, 1 rev/s, and 1 Hz all describe exactly the same speed, and why this converter can show all five values at once.
To convert in any direction, the tool first changes your input into radians per second, then divides by the target unit's factor. Going from rad/s back to RPM means multiplying by 60 ÷ 2π, about 9.5493. Going from degrees per second to RPM means dividing by 6. Every pair of units passes through the same radians-per-second middle step, so no combination is a guess and every result is consistent with every other one.
Watch the units when you read a motor datasheet. A small cooling fan might be rated at 1,500 RPM, a washing-machine spin cycle at 1,200 RPM, and a hard drive at 7,200 RPM. In radians per second those are about 157, 126, and 754 rad/s. A robot arm joint, on the other hand, might be specified as 2 rad/s — only about 19 RPM — because slow, precise motion is easier to describe in radians. Mixing the two without converting is a common mistake that makes a design look ten times faster or slower than it really is.
The converter accepts decimals and negative values, since a negative sign simply means spinning in the opposite direction. It is meant for steady speeds; if a motor is speeding up or slowing down, the number you enter is its speed at that instant, not an average over the whole run.
Worked example
A ceiling fan spins at 300 RPM. What is that in radians per second, degrees per second, and hertz?
Step 1: Convert to rad/s — 300 × 2π ÷ 60 = 300 × 0.10472 = 31.416 rad/s.
Step 2: Convert to degrees per second — 300 × 6 = 1,800 deg/s.
Step 3: Convert to revolutions per second — 300 ÷ 60 = 5 rev/s, which is also 5 Hz.
Step 4: Check by going back — 31.416 × 9.5493 = 300 RPM, so the round trip closes.
Try it in the converter: enter 300, choose RPM on the left and rad/s on the right, and you will see 31.416 rad/s with the same supporting values underneath.
Quick reference
| RPM | rad/s | deg/s | rev/s (Hz) |
|---|---|---|---|
| 1 | 0.10472 | 6 | 0.0167 |
| 60 | 6.2832 | 360 | 1 |
| 300 | 31.416 | 1,800 | 5 |
| 1,500 | 157.08 | 9,000 | 25 |
| 3,000 | 314.16 | 18,000 | 50 |
| 7,200 | 753.98 | 43,200 | 120 |
FAQ
How many rad/s is 1 RPM?
One revolution per minute equals about 0.10472 radians per second. Multiply the RPM value by 2π ÷ 60 (0.10472) to get rad/s. So 60 RPM is 6.283 rad/s, which is exactly one revolution per second.
What is the difference between RPM and Hz?
RPM counts revolutions per minute and Hz counts cycles per second, and one revolution is one cycle. Divide RPM by 60 to get Hz: 3,000 RPM is 50 Hz. The converter treats rev/s and Hz as the same value.
How do I convert rad/s back to RPM?
Multiply rad/s by 60 ÷ 2π, which is about 9.5493. For example, 10 rad/s × 9.5493 = 95.49 RPM. This converter does that step for you when you choose rad/s on the left and RPM on the right.
Why do motors use both RPM and rad/s?
RPM is the familiar workshop number on nameplates and speed controls, while rad/s is the natural unit for physics formulas such as angular velocity, torque, and power, where power equals torque times angular velocity. Converting between them keeps both worlds consistent.