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RPM to Radians per Second

1 Revolutions per Minute (RPM) = 0.10472Radian per Second (rad/s)

By KAMP Inc. / UnitOwl · Last reviewed:

Result
0.10472 rad/s
1 RPM = 0.10472 rad/s
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How to Convert RPM to rad/s?

One revolution per minute (RPM) equals approximately 0.10472 radians per second (rad/s). To convert RPM to rad/s, multiply the RPM value by 2π/60 (approximately 0.10472). This conversion is essential for physics and engineering calculations involving rotational dynamics. While RPM is the practical measurement unit for rotating machinery, rad/s is required for physics equations involving torque, angular momentum, centripetal acceleration, and rotational kinetic energy. Every mechanical engineering student, robotics developer, and physics student needs this conversion to bridge between the workshop (RPM) and the equations on the whiteboard (rad/s). The distinction matters because spec sheets, tachometers, and machine labels rarely use rad/s, but nearly every serious rotational formula does. Converting early keeps motor power, inertia, flywheel, and control-system calculations in the units expected by physics and engineering equations. Without that step, torque-power, flywheel, and centripetal-force results are numerically wrong by a large factor. Converting once at the start prevents mistakes from propagating through the rest of the calculation. It also keeps simulation and control models dimensionally consistent. That is especially useful in motor and robotics spreadsheets.

How to Convert Revolutions per Minute to Radian per Second

  1. Start with your rotational speed in RPM.
  2. Multiply the RPM value by 2π/60 (≈ 0.10472) to get rad/s.
  3. The result is your angular velocity in radians per second.
  4. The formula combines two steps: RPM / 60 = revolutions per second, then x 2π = radians per second.
  5. For example, 60 RPM x 0.10472 = 6.283 rad/s (= 2π rad/s, exactly one revolution per second).

Real-World Examples

A motor runs at 1,800 RPM. What is the angular velocity for a torque calculation?
1,800 x 0.10472 = 188.5 rad/s. Power = torque x angular velocity, so you need rad/s for this formula.
A car wheel rotates at 900 RPM at highway speed.
900 x 0.10472 = 94.25 rad/s. Needed for calculating tire slip, centripetal force, or ABS dynamics.
A centrifuge runs at 12,000 RPM.
12,000 x 0.10472 = 1,256.6 rad/s. This angular velocity squared times radius gives the centripetal acceleration.
A gyroscope spins at 6,000 RPM.
6,000 x 0.10472 = 628.3 rad/s. Gyroscopic precession calculations require angular velocity in rad/s.
A turntable rotates at 33.3 RPM.
33.3 x 0.10472 = 3.49 rad/s. Slow consumer devices still use the same conversion and are a good sanity check for the formula.

Quick Reference

Revolutions per Minute (RPM)Radian per Second (rad/s)
10.10472
20.20944
50.523599
101.0472
252.61799
505.23599
10010.472

History of Revolutions per Minute and Radian per Second

The radian per second became the SI unit of angular velocity through the formalization of the radian as the standard angle unit. In physics, angular velocity in rad/s makes rotational equations mirror their linear counterparts: linear velocity v = rω (where ω is in rad/s), torque τ = Iα, and power P = τω. If RPM were used directly in these equations, additional conversion factors (involving 2π and 60) would clutter every formula. The elegance of rad/s in rotational physics is analogous to the elegance of radians over degrees in trigonometric calculus.

Common Mistakes to Avoid

  • Using RPM directly in physics formulas that require rad/s. The equation P = τω only works when ω is in rad/s. Using RPM gives a result that is off by a factor of 2π/60 (≈ 0.1047).
  • Forgetting the 2π factor. Dividing RPM by 60 gives revolutions per second (Hz), not rad/s. You must also multiply by 2π because one revolution is 2π radians.
  • Confusing rad/s with degrees per second. One revolution = 360° = 2π rad ≈ 6.283 rad. A motor at 60 RPM spins at 360°/s = 6.283 rad/s. Using 360 instead of 2π gives degrees/s, not rad/s.
  • Mixing rad/s with torque in non-SI units. If you use ω in rad/s with P = τω, torque should be in N·m to get power in watts.
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Frequently Asked Questions

Why do physics equations use rad/s instead of RPM?
Because rad/s makes the equations clean. Velocity = radius x ω (rad/s). Kinetic energy = 0.5 x I x ω². Power = torque x ω. Using RPM would require inserting 2π/60 conversion factors into every equation. Rad/s is to rotational physics what m/s is to linear physics.
How do I calculate motor power from torque and RPM?
Convert RPM to rad/s first: ω = RPM x 2π/60. Then Power (watts) = Torque (Nm) x ω (rad/s). Example: 10 Nm at 3,000 RPM: ω = 3,000 x 0.10472 = 314.2 rad/s. Power = 10 x 314.2 = 3,142 W (about 4.2 HP).
What is the angular velocity of Earth's rotation?
Earth rotates once per day (1,440 minutes), so: 1/1,440 RPM x 2π/60 = 7.27 x 10⁻⁵ rad/s. This tiny angular velocity still produces significant centripetal effects at the equator and is critical for satellite orbital mechanics.
What does 60 RPM equal in radians per second?
Exactly 2π rad/s, or about 6.283 rad/s. That is because 60 RPM equals one full revolution per second, and one revolution is 2π radians.
What is 3,000 RPM in rad/s?
3,000 RPM is about 314.16 rad/s because 3,000 x 2π/60 = 314.16. That is a common benchmark in motor power, flywheel, and robotics calculations.
Quick Tip

The quickest way to remember the conversion: 60 RPM = 2π rad/s ≈ 6.283 rad/s. This means 1 revolution per second equals 2π radians per second. From this benchmark: 600 RPM ≈ 62.83 rad/s, 6,000 RPM ≈ 628.3 rad/s. For motor power calculations, the most practical form is: Power (kW) = Torque (Nm) x RPM / 9,549.

Sources & References