Frequency Converters 8
Frequency is the only quantity on this site where every conversion is an exact power of ten — the kilohertz is 1,000 hertz, the megahertz is a million, the gigahertz is a billion, by definition. The one exception is the rotation-to-frequency pair: 1 RPM = 1/60 Hz, because a hertz is one cycle per second and a revolution per minute is one cycle per 60 seconds. That single factor of 60 is the only non-power-of-ten in the whole family, and it's the one that trips up motor engineers and audio folks alike.
Why Frequency Conversion Feels So Easy (and Where It Bites)
The hertz — cycles per second — was named in 1930 by the IEC in honor of Heinrich Hertz, who proved the existence of radio waves in 1887. The SI adopted it as the unit of frequency in 1960, and its SI-prefixed derivatives (kHz, MHz, GHz) are exact powers of ten by construction. This makes most frequency conversion trivial: moving between Hz, kHz, MHz, and GHz is decimal-point shifting, not multiplication by a constant. A 2.4 GHz Wi-Fi channel is 2,400,000,000 Hz. A 440 Hz tuning note is 0.44 kHz. Both are exact.
The trap is the crossover between cycles-per-second and revolutions-per-minute. A motor spinning at 3,600 RPM is not spinning at 3,600 Hz — it's spinning at 60 Hz, because each revolution is one cycle and each minute holds 60 seconds. A 60 Hz AC power line drives a 4-pole motor at exactly 1,800 RPM (synchronous speed). The Hz to RPM and RPM to Hz converters exist for this crossover, and the factor of 60 is exact — 1 RPM = 1/60 Hz. If you're converting audio frequencies (Hz to kHz), the frequency conversions in this hub are your pages. If you're converting motor speeds, the RPM pages are the ones that matter, and they link naturally to the time and speed families.
What's on this page
Eight converters covering the frequency range from a heartbeat (1.2 Hz) to a 5 GHz Wi-Fi band — plus the RPM crossover that links frequency to rotating machinery. Every conversion here is exact: no measured constants, no rounding, no approximation. The kHz/MHz/GHz steps are powers of ten; the Hz↔RPM pair uses the exact factor of 60. If you're converting signal frequencies, the data storage hub has the related data-rate converters (Mbps, Gbps) for network speeds. If you're converting motor speeds, the speed hub covers the linear velocities those rotations produce.
Deep dive: read the Frequency Conversion Guide — the 440-Hz standard, the 50/60 Hz grid divide, and why the hertz is the easiest unit on this site except for the RPM crossover.
Exact conversion factors
Frequency conversions are decimal at every step except one: the hertz to RPM conversion, which depends on the number of seconds in a minute. The table gives both, with the angular form that equations usually need.
| From | To | Exact factor | Basis |
|---|---|---|---|
| 1 kilohertz | hertz | 1,000 | Exact, SI decimal prefix |
| 1 megahertz | hertz | 1,000,000 | Exact |
| 1 gigahertz | hertz | 1,000,000,000 | Exact |
| 1 gigahertz | megahertz | 1,000 | Exact, both prefixes are decimal |
| 1 hertz | revolutions per minute | 60 | Exact, 60 seconds in a minute |
| 1 revolution per minute | hertz | 0.0166666666667 | Exact reciprocal, 0.0166666666667 |
| 1 revolution per minute | radians per second | 0.10471975512 | Derived, 0.10471975512 |
| 1 hertz | radians per second | 6.28318530718 | Exact, one full cycle in radians |
| 1 megahertz | kilohertz | 1,000 | Exact |
| 1 revolution per second | hertz | 1 | Exact by definition |
Defining values and exact constants
- One hertz is one cycle per second, so frequency and period are reciprocals. A 50 Hz supply has a period of 20 ms, and a 60 Hz supply has a period of 16.67 ms.
- SI prefixes on the hertz are strictly decimal. One gigahertz is 10 to the ninth hertz, not 2 to the thirtieth, which is why clock speeds use the same numbers as radio bands.
- One revolution per minute is 1/60 Hz exactly. A 3,000 RPM shaft turns at 50 Hz, which is what lets a synchronous motor lock to the mains frequency.
- One RPM is 0.10471975512 rad/s. Multiply by 2π and divide by 60 whenever an equation needs angular velocity rather than frequency.
- Audible sound spans roughly 20 Hz to 20 kHz, FM broadcast 88 to 108 MHz, and Wi-Fi at 2.4 and 5 GHz. Each band sits a thousandfold above the previous one.
Frequently asked questions
How do you convert RPM to Hz?
Divide by 60. A 1,500 RPM shaft is 25 Hz. The factor is exact, because there are exactly 60 seconds in a minute and no rounding enters the calculation.
Is a hertz the same as a cycle per second?
Yes. The hertz replaced the phrase cycles per second in 1960 and names exactly the same quantity. Older radio documentation may still write kc for kilohertz.
Why is one gigahertz not 1,024 megahertz?
Because SI prefixes are decimal. One gigahertz is 10 to the ninth hertz and one megahertz is 10 to the sixth, so the ratio is exactly 1,000. The 1,024 factor belongs to binary data units such as the kibibyte.
How many radians per second is one RPM?
0.10471975512. One revolution is 2π radians and one minute is 60 seconds, so the conversion is 2π divided by 60, the same route as RPM to hertz with π inserted.