Hertz to Megahertz Converter
Common Conversions
| Hz | MHz |
|---|---|
| 100 | 0.0001 |
| 500 | 0.0005 |
| 1000 | 0.001 |
| 5000 | 0.005 |
| 10000 | 0.01 |
| 100000 | 0.1 |
| 500000 | 0.5 |
| 1000000 | 1 |
| 10000000 | 10 |
| 1000000000 | 1000 |
Why this conversion matters in chemistry
NMR spectrometers are identified by their proton Larmor frequency in MHz — a 400 MHz instrument operates in a 9.4 T magnetic field, a 600 MHz one at 14.1 T. The spectrum's actual frequency axis runs in Hz on the raw data, but chemical shifts get reported as a field-independent ppm scale. The conversion is what makes that scale work: a 1000 Hz peak offset on a 400 MHz instrument is 2.5 ppm (1000 Hz ÷ 400 MHz, expressed in parts per million), which is the value a synthetic chemist actually reads off the spectrum. Dividing by 10⁶ is how absolute Hz frequency maps onto the field-independent ppm framework.
Formula
Where the factor comes from
Start with the unit rather than the prefix: the cycle in "cycles per second" is dimensionless, so hertz reduces to s⁻¹, and mega being 10⁶ by definition makes megahertz 10⁶ s⁻¹ — the older name megacycles per second says the same thing. The arithmetic is therefore free of measurement. What is measured is the MHz figure a magnet gets labeled with: it comes from ν = γB/2π, and the proton gyromagnetic ratio γ/2π is an experimental constant near 42.577 MHz/T. Run that through a 9.39 T field and roughly 400 MHz falls out, which is why the instrument wears that name. The label is empirical; the Hz-to-MHz step under it is not. A counter's MHz reading traces back through its reference oscillator to the defined cesium frequency, 9192631770 Hz, or 9192.63177 MHz.
Precision and significant figures
Chemistry rarely needs six decimal places in a frequency, and NMR is the exception that proves it. Writing a carrier as 400.132470 MHz is not padding: the sixth decimal is one hertz, and one hertz is a real linewidth. Digital resolution in a transformed spectrum is the reciprocal of the acquisition time, so a two-second acquisition resolves 0.5 Hz and justifies that many digits. Elsewhere in the MHz band — ultrasonic transducers, RF plasma sources — two or three significant figures exhaust what the hardware holds. Since the prefix is exact, the conversion never limits you: decide how many digits the measurement earned, then move the decimal six places without touching them.
Worked Examples
A 400 MHz NMR spectrometer's operating frequency for protons — the field-strength label that defines the instrument.
One million hertz — the conversion anchor and a useful per-unit reference.
About the spectral width covering aliphatic and olefinic protons on a 400 MHz instrument — 6 ppm × 400 Hz/ppm; a full ¹H window that includes aromatic and exchangeable signals runs closer to 4000 Hz.
Common mistakes
Nominal magnet label read as exact
A 400 MHz spectrometer does not observe protons at exactly 400.000000 MHz. The actual carrier depends on the shimmed field and the lock solvent, and commonly differs from the round number by more than a hundred kilohertz. Use the value the console reports for any ppm arithmetic; the nameplate is a model designation rather than a measurement.
Dividing twice on the way to ppm
Chemical shift in ppm is a peak offset in hertz divided by the carrier in megahertz — the factor of 10⁶ is already baked into "parts per million". Converting the offset to MHz first and then dividing gives an answer 10⁶ too small. Keep the offset in Hz, keep the carrier in MHz, and the ratio comes out in ppm directly.
Stacking prefix steps by mistake
Hz to kHz to MHz is two separate factors of 1000, and reading a value already displayed in kilohertz as though it were hertz costs a clean factor of a thousand. The error hides well because the result still looks like a plausible frequency for the experiment. Note the unit printed on the axis, not just the number under the cursor.