NMR Reference and Calculators

Dipolar Couplings

The static dipolar couping constants are calculated as follows1:

\( D_{ij} = - \frac{\mu_0 \gamma_i \gamma_j \hbar}{4 \pi r_{ij}^3} \) in rad/s

Isotopes Distance (Å) Dipolar Coupling (Hz)



The nuclear Overhauser effect (NOE) rates are calculated as follows:1

\( \sigma_{ij} = \frac{1}{10} \left( \frac{\mu_0 \gamma_i \gamma_j \hbar^2}{4 \pi r_{ij}^3} \right) \tau_c \) in s-1

Isotopes Distance (Å) τc (ns) σi,j (s-1) R2 (s-1)



The chemical shift tensors are defined as follows:2,3

Spin δ (ppm)a ηb δiso (ppm)e β (deg)c Δδ / Δσ (ppm)d δ11 / σzz (ppm)e δ22 / σxx (ppm)e δ33 / σyy (ppm)e
13C' (ave carbonyl) 38
15N (ave backbone) 19
1HN (ave backbone) 8

  1. Reduced chemical shift anisotropy: \( \delta = \delta_{zz} - \delta_{iso} \)
  2. Asymmetry: \( \eta = (\delta_{yy} - \delta_{xx}) / \delta\)
  3. Azimuthal angle: The angle between the tensor principal component and bonds in the molecule.
  4. Chemical shift anisotropy: \( \Delta\delta = \delta_{zz} - (\delta_{xx} + \delta_{yy}) / 2\) and the relationship between the chemical shift (\( \delta \)) and chemical shielding (\( \sigma \)) through the following relationship: \( \delta = - \sigma \)
  5. Isotropic chemical shift: \( \delta_{iso} = (\delta_{xx} + \delta_{yy} +\delta_{zz}) /3 \) where in the Haeberlen covention \( |\delta_{zz} - \delta_{iso}| \ge |\delta_{xx} - \delta_{iso}| \ge |\delta_{xx} - \delta_{iso}| \) and in the Mehring convention \( \delta_{11} \ge \delta_{22} \ge \delta_{11}\)
  6. Chemical shielding anisotropy: \( \Delta \sigma = \sigma_{33} - (\sigma_{22} + \sigma_{11})/2 \)



The 3JHN-HA couplings in proteins can be calculated from the backbone φ angle as follows:4

\( ^3J_{HNHA} = A \cos^2(\phi - 60) + B \cos(\phi - 60) + C \) in Hz where A=6.51, B=-1.76 and C=1.60

φ (deg) 3JHNHA (Hz)


Pulse Widths

The following are pulse calculations for a null at ν1 (ppm) when the pulse is applied at ν2

ν0H (MHz) Channel ν1 (ppm) ν2 (ppm) p90 (μs) 0.5·p180 / p180 (μs)



  1. Cavanagh J, Fairbrother W, Palmer A, Skelton N. Protein NMR Spectroscopy: Principles and Practice. 2nd ed. Burlington, MA: Academic Press; 2007.
  2. Cornilescu G, Bax A. J Am Chem Soc. 2000 Oct;122(41):10143–10154.
  3. Saitô H, Ando I, Ramamoorthy A. Prog Nucl Magn Reson Spectrosc. 2010 Aug;57(2):181–228.
  4. Vuister G, Bax A. J Am Chem Soc. 1993;115:7772–7777.

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