NMR Chemical Shift Converter – ppm, Hz and MHz for Any Nucleus and Field
Every NMR spectrum mixes two kinds of numbers. Chemical shifts are reported in parts per million, while coupling constants, linewidths and the spectrometer itself are described in hertz and megahertz. This NMR chemical shift converter moves between the two for ¹H, ¹³C, ¹⁵N, ¹⁹F, ³¹P and a dozen other nuclei at any field strength, measures J from a peak list, predicts how an AB pattern changes with the magnet, and re-references spectra to the solvent signal.
Why shifts are in ppm and couplings in Hz
The shielding that produces a chemical shift is proportional to the applied field, so a peak moves twice as many hertz on a magnet twice as strong. Dividing by the spectrometer frequency removes that dependence and gives a number, δ, that is the same on every instrument. A J coupling is transmitted through the bonding electrons and does not depend on the field at all. That is why a doublet that spans 0.13 ppm at 60 MHz spans only 0.013 ppm at 600 MHz, while J stays at 8 Hz.
The δ definition and a worked ppm to Hz example
IUPAC defines δ = (ν − ν_ref) / ν_ref × 10⁶, where ν_ref is the frequency of the 0-ppm reference for the observed nucleus in the same magnet. Once that frequency, SF, is known the conversion is exact: Δν (Hz) = δ (ppm) × SF (MHz). On a 400 MHz spectrometer the CHCl₃ signal at 7.26 ppm lies 7.26 × 400 = 2904 Hz above TMS. The CDCl₃ carbon at 77.16 ppm on the same magnet is 77.16 × 100.58 = 7760.8 Hz from TMS, because ¹³C is observed at 100.58 MHz, not at 400 MHz.
The IUPAC unified scale Ξ
The 2001 IUPAC recommendations tabulate, for each nucleus, the ratio Ξ of its 0-ppm frequency to the ¹H frequency of TMS in the same field. The calculator uses SF_X = SF_H × Ξ / 100 for every nucleus, so one table defines where 0 ppm falls on any magnet: 25.145020 % for ¹³C, 40.480742 % for ³¹P and 94.094011 % for ¹⁹F. If you copy the exact SF from your acquisition parameters, the tool uses it instead.
Why higher fields simplify spectra
Two coupled protons form an AB system. When their shift difference in Hz, Δν, is large compared with J, you see two clean doublets (AX). When Δν/J is small, the inner lines grow, the outer lines fade and the doublets lean towards each other: the roof effect. Because Δν scales with the field and J does not, the same molecule that gives a tangled second-order pattern at 60 MHz can look first-order at 600 MHz. The stacked spectra in the coupling tab show this directly, and the analysis mode recovers J and the true shifts from four measured AB lines.
Referencing to residual solvent signals
Most organic spectra are calibrated on the residual protio signal of the deuterated solvent. Accepted values include 7.26 ppm for CHCl₃ in CDCl₃, 2.50 ppm for DMSO-d₆ and 77.16 ppm for the CDCl₃ carbon. If the solvent peak appears at the wrong position, the same offset is added to every peak. The HDO signal of D₂O moves with temperature, so DSS is the better reference for aqueous samples.
The ¹⁵N reference split
Chemists reference ¹⁵N to nitromethane, the IUPAC primary standard, while protein NMR uses liquid ammonia, about 380 ppm lower. The change of reference is a ratio of frequencies, not a fixed offset: the familiar 380.44 ppm is exact only at δ = 0 and drifts by about 0.1 ppm across the amide region. The re-reference tab shows the exact value next to the constant-offset approximation.
The historical τ scale
Older literature uses the τ scale introduced by Tiers in 1958, τ = 10 − δ, on which TMS sits at 10 and shifts increase upfield. It is shown as an extra column for ¹H so old values can be compared with modern δ values.