Convert between RPM, frequency (Hz), angular velocity (rad/s), and period. Calculate tip speed, centripetal acceleration, and vibration frequency.
The RPM to Frequency Calculator converts between revolutions per minute (RPM), frequency in Hertz (Hz), angular velocity in radians per second (rad/s), and period in seconds. Enter any one value and instantly get all others, plus derived quantities like tip speed and centripetal acceleration. It is a convenient way to move between the units different teams use for the same rotating system.
Understanding rotational-to-linear conversions is essential across mechanical engineering, electrical motor selection, CNC machining, vibration analysis, and physics. A motor spinning at 3,600 RPM produces a 60 Hz frequency — matching the AC power frequency in North America. The same motor with a 4-inch pulley produces a tip speed of 3,770 ft/min.
Enter RPM, frequency, or angular velocity along with an optional radius to get comprehensive results including linear tip speed, centripetal acceleration (in g-forces), and period. Compare common rotational speeds in the reference table. It is useful whenever a rotational speed needs to be translated into a real linear speed, force, or vibration frequency.
Use this calculator when you need to convert between RPM, frequency, angular velocity, and tip speed without doing the unit algebra yourself. It is useful for motors, pulleys, fans, vibration checks, and rotating machinery design, especially when safety or resonance depends on the answer. That makes it handy whenever mechanical and electrical specs need to line up.
Frequency (Hz) = RPM / 60. Angular Velocity (ω) = 2π × RPM / 60 rad/s. Period (T) = 60 / RPM seconds. Tip Speed = ω × r. Centripetal Acceleration = ω² × r. g-Force = Centripetal Acceleration / 9.81.
Result: 60 Hz, 376.99 rad/s, tip speed 37.7 m/s
3600 RPM ÷ 60 = 60 Hz. ω = 2π × 60 = 376.99 rad/s. Tip speed = 376.99 × 0.1 = 37.7 m/s. Centripetal acceleration = 376.99² × 0.1 = 14,212 m/s² = 1,449 g.
AC induction motors have discrete synchronous speeds determined by pole count and power frequency. In 60 Hz regions: 2-pole = 3,600, 4-pole = 1,800, 6-pole = 1,200, 8-pole = 900 RPM. Actual speed is 3-5% lower due to slip.
Variable Frequency Drives (VFDs) allow continuous speed adjustment by changing the frequency supplied to the motor. A VFD at 30 Hz drives a 4-pole motor at ~900 RPM instead of 1,800.
Vibration frequency is directly tied to RPM. The fundamental frequency = RPM/60 Hz. Bearing defect frequencies (BPFO, BPFI, BSF, FTF) are multiples of shaft RPM. Spectrum analysis identifies which component is failing by matching vibration peaks to calculated frequencies.
Rotating machinery generates enormous centripetal forces. A 100g mass at 10 cm radius spinning at 30,000 RPM experiences 98,700 g — nearly 100,000 times its weight. This drives material selection, safety factors, and containment requirements for high-speed rotors, turbines, and centrifuges.
Divide RPM by 60. Example: 1,800 RPM ÷ 60 = 30 Hz. This is because RPM counts revolutions per minute and Hz counts cycles per second (60 seconds per minute).
Angular velocity (ω) measures rotation rate in radians per second. One full revolution = 2π radians. So ω = 2π × frequency = 2π × RPM / 60 rad/s.
Idle: 600-1,000 RPM. Highway cruising: 2,000-3,000 RPM. Redline: 5,500-9,000 RPM (varies by engine). Most time is spent in the 1,500-3,500 RPM range.
3,600 RPM = 60 Hz, which matches the AC power frequency in North America. A 2-pole AC motor runs at synchronous speed of 3,600 RPM (actually ~3,450 due to slip). 4-pole: 1,800 RPM. 6-pole: 1,200 RPM.
Tip speed is directly proportional to radius. Doubling the radius doubles the tip speed at the same RPM. This matters for grinding wheels, rotors, fans, and turbines where tip speed determines cutting ability, stress, and efficiency.
Grinding wheels: typically 5,000-16,500 ft/min. Saw blades: 8,000-15,000 ft/min. Centrifuges: material-dependent, but carbon steel rotors fail around 400-600 m/s tip speed.