Hertz to Megahertz

Chemical Shift Arrives in Hertz, Referenced to a Megahertz Carrier

A resonance is measured as a frequency offset from the reference, and the spectrometer reports that offset in hertz. Nobody quotes a shift that way, because the number is only true for one magnet: a peak sitting 3 630 Hz out on a 500 MHz instrument is 2 178 Hz out on a 300. The measurement becomes portable only when the hertz offset is divided by the frequency the instrument is named after — and that means putting it on the megahertz scale.

Conversion factor: 1 MHz = 1 000 000 Hz, so divide the hertz figure by a million. A residual CHCl₃ peak 3 630 Hz from TMS on a 500 MHz spectrometer is 0.003 63 MHz; divide that by 500 MHz and the result is 7.26 × 10⁻⁶ — the familiar 7.26 ppm of every chloroform spectrum.

Why the Two Scales Sit Side by Side

Field strength sets the carrier

Protons precess at about 42.577 MHz per tesla, so a 3 T scanner resonates them near 127 732 435 Hz and an 11.74 T magnet lands close to 500 MHz — which is where a spectrometer gets its name.

A part per million is hertz over megahertz

The two conversions cancel neatly: an offset in hertz divided by the carrier in megahertz gives ppm straight away. 3 630 ÷ 500 = 7.26, and the same molecule gives 7.26 on any instrument in the building.

Coupling refuses to scale

Splitting inside a multiplet comes from the bonds, not the magnet: a 7 Hz vicinal coupling is 7 Hz at 300 MHz and still 7 Hz at 900. That is precisely why J values are quoted in hertz and never converted to ppm.

Window width lives in both units

A proton window of 13 ppm spans 6 500 Hz — 0.006 5 MHz — on a 500 MHz instrument, but 11 700 Hz on a 900. Acquisition parameters are set in hertz, so the ppm range has to be turned back into a count of cycles.

Turning a Peak Offset into a ppm Value

The path from a raw peak position to a number worth putting in a table is short, and only the first step needs converting.

Enter the offset the spectrometer reported

Type the hertz figure into the left field — 3 630, 1 043, 6 500 — and the megahertz equivalent appears beside it. Spaces in a grouped number are ignored and a comma is accepted as the decimal point.

Divide by the instrument frequency

Take the megahertz result and divide it by the proton frequency of the magnet: 0.003 63 MHz ÷ 500 MHz = 7.26 × 10⁻⁶, which is 7.26 ppm. Use the console's actual carrier — 500.13 rather than a round 500 — when the report demands it.

Copy the plain number into the peak list

The copy button returns the digits alone, with no unit and no spacing, which is what a results table, a supporting-information block or a spreadsheet column expects. Ctrl + C inside a field does the same.

Reverse to size a window in hertz

Press the swap button (↔) to run MHz → Hz when planning acquisition: a spectral width written as 0.006 5 MHz is 6 500 Hz, the figure the parameter set actually wants.

The reference has to be stated: an offset only means a chemical shift against a declared zero — TMS for ¹H and ¹³C, or a solvent signal referenced to it — and against the transmitter offset the experiment used. A raw hertz number from a different console setting will not line up.

Field Strength and Proton Larmor Frequency

Multiplying the field in tesla by 42.577 MHz/T gives the frequency protons resonate at — as the raw count of cycles per second, and as the megahertz figure the magnet is known by.

Field	Where it is met	Proton frequency in hertz	On the megahertz scale
0.55 T	Low-field clinical scanner	23 417 613 Hz	23.42 MHz
1.5 T	Standard clinical scanner	63 866 218 Hz	63.87 MHz
3 T	Clinical and research imaging	127 732 435 Hz	127.73 MHz
7 T	Human research imaging	298 042 349 Hz	298.04 MHz
9.4 T	400 MHz spectrometer, preclinical imaging	400 228 298 Hz	400.23 MHz
11.74 T	500 MHz spectrometer	499 859 597 Hz	499.86 MHz
14.1 T	600 MHz spectrometer	600 342 446 Hz	600.34 MHz
23.5 T	Gigahertz-class research magnet	1 000 570 744 Hz	1 000.57 MHz

The names are rounded, as the table shows: an instrument called a 500 is really running just under 499.9 MHz before shimming and the transmitter offset are taken into account. That rounding never reaches the reported shifts, because the software divides by the carrier it actually used.

Handling the Numbers on This Page

Peak offsets and carriers together

Enter offsets one after another on the left and read megahertz on the right; nothing needs clearing, so a whole peak list can be worked through in one sitting.

Reverse for acquisition planning

Swapping runs MHz → Hz, the direction that turns a spectral width discussed in megahertz back into the cycles-per-second value the parameter set stores.

Values that drop into a results table

Copy returns the digits by themselves, which is the form a peak-list column or a supporting-information document is going to accept without editing.

Small offsets stay readable

A coupling of a few hertz is a vanishingly small number of megahertz; results carry up to eight decimals and switch to scientific notation below 0.000001 instead of rounding away to zero.

Chemical Shift and Field Strength Questions

Why is a shift reported in ppm rather than the hertz that was measured?

Because the hertz offset belongs to one magnet. The chloroform signal is 2 178 Hz from TMS at 300 MHz, 3 630 Hz at 500 MHz and 6 534 Hz at 900 MHz — three numbers for one molecule. Dividing by the carrier expressed in megahertz cancels the field out, leaving 7.26 in every case, so a spectrum recorded anywhere can be compared with a literature value.

What proton frequency goes with 1.5 T and 3 T?

Multiply by 42.577 MHz per tesla: 1.5 T gives 63 866 218 Hz, or 63.87 MHz, and 3 T gives 127 732 435 Hz, or 127.73 MHz. A 7 T research system sits at 298.04 MHz. That is the radio frequency the coils transmit and receive at, which is why hardware is built and tuned for one field and cannot simply be moved to another.

Why does a coupling constant stay the same in hertz at every field?

J-coupling is transmitted through the bonding electrons between two nuclei, so it does not depend on the external field at all. In ppm it therefore appears to shrink as the magnet gets stronger: 7 Hz is 0.023 ppm on a 300 MHz instrument but only 0.014 ppm on a 500. Shifts spread out with field while splittings stay put, and that widening gap is what makes crowded multiplets resolve at high field.

How wide does the spectral width need to be in hertz?

Choose the ppm range first, then multiply by the carrier in megahertz. A 13 ppm proton window is 6 500 Hz on a 500 MHz magnet and 11 700 Hz on a 900. Carbon is far worse: about 240 ppm of range against a ¹³C frequency near 125.7 MHz at 11.74 T works out around 30 200 Hz. The wider the window, the fewer hertz each data point covers for a given number of points.

Why does the console report 500.13 MHz instead of 500?

The instrument name is a rounded label for the magnet, while the console states the transmitter frequency it is genuinely using — a value that depends on the exact field after shimming and on where the offset has been placed within the region of interest. Nothing downstream suffers, because the shift calculation divides by that real carrier rather than by the nominal one.