Frequency & RPM Converter
Hz ↔ rpm ↔ rad/s, period and wavelength — and the rim speed of a wheel or cutter.
Type a conversion in plain words — “1500 rpm to rad/s”, “50 Hz to ms”, “100 MHz in m”, “532 nm to THz” — or use the boxes below.
Exact · Hz = rpm ÷ 60 · 1 rpm ≈ 0.01666666667 Hz
- Revolution per minute: 1/60 rev/s; motor nameplates also write r/min or min⁻¹
- Hertz: SI unit of frequency: one cycle per second (s⁻¹), used for periodic phenomena
Surface speed from a diameter
Each turn moves the rim of a wheel, pulley, drum or cutter one circumference (π × d), so its surface speed is v = π × d × n. The rotation is the one above, in whatever unit you typed it.
For a vehicle wheel use the tyre’s rolling diameter: a loaded tyre turns on a slightly smaller circle than its size.
Type a diameter to see the rim speed.
The rpm for a surface speed
Tooling charts give a cutting speed for each material; n = v ÷ (π × d) turns it into spindle rpm for the diameter above. Use the figure your tool maker gives.
Type a surface speed and a diameter.
3000 rpm in every unit
Select a unit to convert to it. Values marked ≈ are rounded; all others are exact.
| Unit | Value | Copy |
|---|---|---|
| Frequency | ||
| to | 50 | |
| 0.05 | ||
| 0.00005 | ||
| 5 × 10⁻⁸ | ||
| 5 × 10⁻¹¹ | ||
| 3,000 | ||
| Rotation | ||
| 50 | ||
| from | 3000 | |
| ≈ 314.1592654 | ||
| 18,000 | ||
| Period (time for one cycle) | ||
| 0.02 | ||
| 20 | ||
| 20,000 | ||
| 2,00,00,000 | ||
| Wavelength in vacuum (radio, light) | ||
| 5,995.84916 | ||
| 59,95,849.16 | ||
| 59,95,84,916 | ||
| 5,99,58,49,160 | ||
| 59,95,84,91,60,000 | ||
| 5.99584916 × 10¹⁵ | ||
Convert a list of values
Up to 1,000 lines. Fractions (3/4), mixed numbers (1 1/2) and grouped digits (1,250) are fine.
| Value | Result |
|---|
About the Frequency & RPM Converter
Convert frequency and rotational speed in one place: hertz to terahertz, cycles per minute, revolutions per minute (rpm) and per second, radians per second and degrees per second — together with the period of one cycle and the wavelength in vacuum. Type in either box and the table underneath shows the value in every unit. A revolution per second is one hertz, so 3,000 rpm is exactly 50 Hz, a period of 20 ms.
The arithmetic uses exact fractions. Only the radian per second involves π (ω = 2π × n), so those results are marked ≈. Wavelengths use the exact speed of light, c = 299,792,458 m/s, so 100 MHz is exactly 2.99792458 m. Under the converter, Surface speed from a diameter turns the rotation into the speed at the rim of a wheel, pulley or cutter (v = π × d × n) in m/s, km/h, m/min, ft/min and mph, and works out the rpm for a cutting speed.
How to use it
- Type a number in From and pick its unit, then pick the unit you want in To — or type
1500 rpm to rad/s,50 Hz to msor100 MHz in min Quick convert and press Enter. - Read the result, its formula, the period and the wavelength under it, and every unit in the table. Values marked ≈ are rounded; choose a Precision for fewer digits.
- For a wheel, pulley or cutter, type its Diameter under Surface speed from a diameter to see the rim speed. To go the other way, type a cutting speed under The rpm for a surface speed and press Convert this rpm above.
- Copy the result or a link, download the table as CSV, or open Convert a list of values for a column of readings.
Examples
3,000 rpm to Hz
50 Hz (period 20 ms)
1 rev/s = 1 Hz, so divide rpm by 60. An induction motor runs a little below its synchronous speed.
1,500 rpm to rad/s
≈ 157.08 rad/s
1,500 ÷ 60 × 2π = 50π rad/s.
60 Hz to ms
≈ 16.667 ms
T = 1 ÷ f; 50 Hz is exactly 20 ms.
100 MHz to m
2.99792458 m (exact)
λ = c ÷ f = 299,792,458 ÷ 100,000,000.
2.4 GHz to cm
≈ 12.49 cm
532 nm to THz
≈ 563.52 THz
3,000 rpm, 100 mm diameter
≈ 15.708 m/s = 56.55 km/h = 942.5 m/min
π × 0.1 m × 50 rev/s.
100 m/min with a 10 mm cutter
≈ 3,183 rpm
n = v ÷ (π × d) = 1.6667 m/s ÷ (π × 0.01 m) = 53.05 rev/s.
Common uses
- Motor and pump nameplates: rpm to Hz and rad/s, and the period of one turn.
- Electronics and radio: kHz, MHz and GHz to the period and the wavelength of a signal or antenna band.
- Optics: the frequency of light from its wavelength in nm.
- Machining: spindle rpm for a cutting speed in m/min or SFM, and the cutting speed at a given rpm.
- Wheels, rollers, belts and pulleys: the speed at the rim from the shaft speed.
- Gyroscopes, servos and turntables quoted in °/s or rpm.
Hertz, rpm and rad/s
The SI Brochure gives the hertz (Hz = s⁻¹) as the SI unit of frequency, to be used for periodic phenomena, and the radian per second as the unit of angular velocity. Their numbers differ by a factor of 2π — confusing them gives a result 6.28 times too big or too small — so the brochure recommends always writing Hz or rad/s, never a bare s⁻¹. It also notes that “cycle/s” (cps) and “revolution/s” (rev/s), which some countries use instead of Hz, are not SI units.
- rev/s = Hz (one turn per second is one cycle per second)
- Hz = rpm ÷ 60 — 1,500 rpm = 25 Hz
- rad/s = rpm × 2π ÷ 60 ≈ rpm × 0.10472 (NIST SP 811, Appendix B.8 gives 1 rpm = 0.1047198 rad/s)
- °/s = rpm × 6 — 360 °/s is one turn a second
Period and wavelength
The period is the time one cycle (or one turn) takes: T = 1 ÷ f. At 50 Hz it is 20 ms, at 60 Hz 16.67 ms, at 1 GHz 1 ns.
The wavelength in vacuum is the distance an electromagnetic wave — radio, microwaves, light — travels in one period: λ = c ÷ f, with c = 299,792,458 m/s exactly (an SI defining constant). Handy forms: λ in metres = 299.792458 ÷ f in MHz, and λ in nm = 299,792.458 ÷ f in THz. In air the wavelength is very slightly shorter, and in glass, water or a cable it is noticeably shorter, because waves travel more slowly there.
Sound is a different kind of wave and is far slower, so these wavelengths do not apply to it: a sound’s wavelength is the speed of sound ÷ f, about 0.77 m for 440 Hz at the 340.294 m/s of the standard atmosphere at sea level. For the same reason the line under the result gives a wavelength only when you convert a frequency, a period or a wavelength, not a rotation such as rpm.
Surface speed of wheels, pulleys and cutters
In one turn a point on the rim travels one circumference, π × d. So the surface speed is v = π × d × n, with d the diameter and n the revolutions per second. In workshop units:
- cutting speed in m/min = π × D in mm × rpm ÷ 1,000
- surface feet per minute (SFM) = π × D in inches × rpm ÷ 12
- and back: rpm = 1,000 × m/min ÷ (π × D in mm), or 12 × SFM ÷ (π × D in inches)
The same formula gives the speed of a vehicle from wheel rpm, if the wheel does not slip, and the speed of a belt from the pulley that drives it.
Limitations
- Results in rad/s involve π and are rounded (shown with ≈); every other conversion is exact until it is rounded for display.
- Wavelengths are those of electromagnetic waves (radio, light) in vacuum. In air, cables, optical fibre or water they are shorter, and a sound wave of the same frequency is almost a million times shorter.
- Frequency, period and wavelength must be greater than 0: at 0 Hz nothing repeats.
- Surface speed assumes a true circle turning without slip. For a cutting speed or a feed rate, use your tool maker’s data for the material and the Speeds and Feeds Calculator.
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Frequently asked questions
How do I convert rpm to Hz?
Divide by 60: Hz = rpm ÷ 60. One revolution per second is one hertz, so 3,000 rpm is 50 Hz and 1,800 rpm is 30 Hz.
How do I convert rpm to rad/s?
Multiply by 2π and divide by 60: rad/s = rpm × 0.10472. 1,500 rpm is about 157.08 rad/s; 1 rad/s is about 9.549 rpm.
Are Hz and rad/s the same thing?
No. Both have the dimension of 1/s, but a frequency in Hz counts cycles per second while an angular velocity in rad/s counts radians per second, and one cycle is 2π radians. So 1 Hz corresponds to 2π ≈ 6.283 rad/s.
What is the period of 50 Hz and 60 Hz?
20 ms for 50 Hz and 16.67 ms for 60 Hz: the period is 1 ÷ f.
How do I get the wavelength from the frequency?
Divide the speed of light by the frequency: λ = c ÷ f, with c = 299,792,458 m/s. 100 MHz gives 2.998 m, 2.4 GHz about 12.49 cm, and 5 GHz about 6 cm.
How do I work out surface speed from rpm?
Multiply the circumference by the revolutions per second: v = π × d × rpm ÷ 60. A 100 mm wheel at 3,000 rpm has a rim speed of about 15.7 m/s (56.5 km/h).
Is rpm an SI unit?
No. The SI unit of angular velocity is the radian per second, and the SI Brochure counts the “revolution” among the words that are not SI units. Still, rpm — also written r/min — is the usual unit on motors, engines and machine tools, and it converts exactly: 1 rpm = 1/60 rev/s.