NMR Coupling Pattern Calculator

Calculate the resulting first-order ¹H NMR multiplet from several groups of equivalent neighbouring protons (number n, coupling constant J) – including a short-hand name (e.g. "dt" for doublet of triplets) and a stick spectrum with relative intensities.

Enter coupling partners

This calculator assumes first-order coupling (J much smaller than the chemical-shift difference to the coupling partners). With J values of a similar magnitude to the shift difference (Δδ), roofing effects and more complex patterns occur that are not modelled here.

Hz
No group added? Then a simple singlet (no coupling) is calculated.

Explanation: first-order coupling patterns in NMR spectroscopy

What is a coupling pattern?

In ¹H NMR spectroscopy, a proton couples with magnetically non-equivalent neighbouring protons through chemical bonds. Each group of equivalent neighbouring protons splits the signal into multiple lines – the result is the signal's characteristic coupling pattern (multiplet).

If a proton couples simultaneously with several different groups of neighbours (with different coupling constants J), the individual splittings overlap into a more complex pattern, which can be predicted by successive convolution (the tree-diagram method).

n+1 rule

Number of lines = n + 1 (per group of equivalent neighbours)

The quantities at a glance

Number of equivalent neighbours (n)

The number of magnetically equivalent protons in this neighbouring group that couple with the proton under consideration (e.g. n=3 for a neighbouring CH₃ group).

Coupling constant (J)

The spacing between lines within a splitting pattern, in Hz. Typical values: ³J(H,H) in open-chain systems approx. 6–8 Hz, in alkenes (cis) approx. 6–12 Hz, (trans) approx. 12–18 Hz.

Pascal's triangle

The relative intensities within a single (n+1)-line system correspond to the binomial coefficients of the n-th row of Pascal's triangle (e.g. 1:3:3:1 for a quartet, n=3).

Worked example

A proton couples with one neighbouring proton (J₁ = 8 Hz) and another, chemically distinct neighbouring proton (J₂ = 4 Hz). What pattern results?

Given

Group 1: n=1, J=8 Hz; Group 2: n=1, J=4 Hz

Solution

Convolving the two doublets gives a doublet of doublets (dd) with 4 equally intense lines at offsets −6, −2, +2, and +6 Hz relative to the centre of the signal.

Tips and common mistakes

A common mistake is treating chemically distinct neighbouring groups that happen to have a similar J as a single group instead of entering them separately – the convolution automatically accounts for lines coinciding due to equal J (see the note in the result). A second mistake: the n+1 rule only applies to first-order coupling with magnetically equivalent neighbours, not to strong coupling (Δδ on the order of J).

The best approach

First identify all chemically distinct neighbouring groups individually (don't count all neighbours together if they have different J values), enter each group separately, and finally check the short-hand name against the pattern you expect from the spectrum.

Where are coupling patterns used?
  • Structure elucidation of organic molecules: reading off the number and arrangement of neighbouring protons from the spectrum
  • Distinguishing cis/trans or E/Z isomers based on characteristic coupling constants
  • Automated spectrum interpretation and structure-suggestion software in analytical chemistry

Frequently asked questions about NMR coupling patterns

First-order coupling occurs when the chemical-shift difference between coupling protons (in Hz) is much larger than the coupling constant J (rule of thumb: Δδ/J > 10). Only then do the simple n+1 rule and Pascal's-triangle intensity ratios apply; at smaller ratios, roofing effects and more complicated patterns occur that require higher-order treatment.

If a proton couples with two different neighbouring groups that happen to have the same coupling constant J, the theoretically more complex pattern simplifies to a simple (n₁+n₂+1) multiplet, since some lines overlap exactly. This is a well-known effect frequently observed in real spectra.

By convention, the group with the largest coupling constant is named first: "dt" means, for example, a doublet (from a group with n=1) that is further split by a smaller-J coupling into a triplet (n=2) – a total of (1+1)×(2+1) = 6 theoretical lines, unless some coincide.

For group sizes up to n=6 (i.e. up to a septet), common short names exist. Larger groups, or very complex patterns made up of many individual groups, are in practice usually just called an unresolved multiplet (m), even though the exact line structure can be calculated.