Frequency & Rotation Converter

About Frequency & Rotation Converter — Hz, RPM & rad/s

The frequency and rotation converter translates between the units that describe the same cycling on one machine: hertz from electrical supply and vibration spectra, kilohertz and megahertz from electronics and ultrasonics, RPM from motor nameplates and pump curves, radians per second from every dynamics formula (ω in τ = P/ω, v = ωr, kinetic energy ½Iω²), and revolutions per day from slow rotating equipment and astronomy. Every conversion runs through the SI unit — the hertz, one cycle per second — using exact identities: a minute is 60 s, a day is 86,400 s, and a revolution is 2π radians (NIST SP 811 Appendix B).

The anchors worth memorizing: 3,600 RPM = 60 Hz and 3,000 RPM = 50 Hz — the two-pole synchronous speeds of the world's two grids — and 1 rad/s ≈ 9.5493 RPM. The 60 in RPM ↔ Hz and the 2π in Hz ↔ rad/s are the two constants most often dropped or double-applied in motor and vibration calculations; running everything through the hertz makes each factor appear exactly once.

How It Works

1. Enter the value, pick the unit it is currently in ("from"), and pick the unit you need ("to"). The headline shows the converted value; the table below it shows the same frequency in all six units at once, so you can lift whichever one the next document needs.
2. Every conversion is value × (hertz per from-unit) ÷ (hertz per to-unit). The factors are exact: RPM is 1/60 Hz, rev/day is 1/86,400 Hz, and rad/s is 1/(2π) Hz — the same 2π-radians-per-revolution identity NIST SP 811 publishes as r/min → rad/s = 0.1047198.
3. Displayed values are rounded to 6 significant digits. That is display rounding only — the underlying conversion is done in full double precision, which is why round-trips return your original number.
4. Watch the cycles-vs-radians trap: Hz counts full cycles per second, rad/s counts phase angle per second, and they differ by exactly 2π. A 60 Hz supply is 377 rad/s; feeding 60 into a formula that wants ω under-drives it by 6.28×. The all-units table keeps both visible so the factor can never silently vanish.

Worked Example

A vibration spec limits a fan to its running speed of 3,600 RPM and the FFT analyzer reads in Hz. Through the hertz: 3,600 rev/min ÷ 60 s/min = 60 Hz — the 1× running-speed line sits at exactly 60 Hz (and its angular frequency is 376.991 rad/s for the dynamics model). The same machine on a 50 Hz grid runs at 3,000 RPM, which is why imported equipment "loses" 17% of its speed: 50 ÷ 60 of every rated RPM.

RPM to Hz conversion chart (with rad/s)

Common motor and machine speeds converted to hertz and radians per second with the exact identities (1 RPM = 1/60 Hz; 1 rev = 2π rad), shown to 6 significant digits — exactly what the converter outputs for the same inputs.

Formulas

Conversion through the base unit

x = value × f_from ÷ f_to

Hertz per unit (the factor table)

RPM 1/60 · rad/s 1/(2π) · rev/day 1/86,400 · kHz 10³ · MHz 10⁶

The everyday anchors

RPM = Hz × 60; ω [rad/s] = 2π × Hz; 1 rad/s ≈ 9.5493 RPM; 3,600 RPM = 60 Hz; 3,000 RPM = 50 Hz

Standards & References

• NIST SP 811, Guide for the Use of the International System of Units, Appendix B.8 — revolution = 6.283185 rad (= 2π, exact); revolution per minute → rad/s 1.047198×10⁻¹ (= 2π/60); the Hz forms restate the same identities per second (1 r/min = 1/60 r/s)
• SI Brochure (9th ed.) — the hertz is one cycle per second; the radian per second is the coherent unit of angular frequency, distinct by the factor 2π
• Displayed to 6 significant digits; conversions computed in full double precision

Frequently Asked Questions