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Rotational Speed Calculator

Convert between RPM, rad/s, Hz, and deg/s instantly for any rotating shaft or motor.

Angular velocity
157.0796 rad/s
ω = 2π × N ÷ 60, where N is the speed in RPM. At 1,500 rpm the shaft completes 25 full revolutions every second.
RPM
1,500
rad/s
157.0796
rev/s (Hz)
25
deg/s
9,000

How it works

  1. 1Choose your input unit — RPM, rad/s, or Hz (rev/s) — using the tab selector at the top.
  2. 2Enter the rotational speed value in the field provided.
  3. 3All four equivalent units (RPM, rad/s, rev/s, deg/s) are shown instantly using ω = 2πN/60.

Use cases

  • Motor and pump engineers checking angular velocity against specification sheets.
  • Robotics and servo designers converting encoder feedback (rad/s) to readable RPM.
  • Students verifying rotational quantities when working through dynamics or vibration problems.

Frequently asked questions

How is rad/s related to RPM?

The formula is ω (rad/s) = 2π × N / 60, where N is the speed in RPM. For example, 1500 rpm gives ω = 2π × 1500 / 60 ≈ 157.08 rad/s.

What is Hz (rev/s) for a rotating shaft?

Revolutions per second (Hz) is RPM divided by 60. A 3000 rpm motor therefore spins at 3000 / 60 = 50 Hz. This unit matches SI frequency and is common in vibration analysis.

How many degrees per second is 1500 rpm?

One revolution is 360°, and 1500 rpm = 25 rev/s = 25 × 360 = 9000 deg/s. The shortcut formula is deg/s = rpm × 6.

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