# ¹H NMR Spectrum Simulator - Splitting Patterns, n+1 Rule & Chemical Shift Table

> Simulate ¹H NMR spectra at 60–600 MHz from shifts, integrals and J values: splitting trees, multiplicity (t, q, dd, dt), journal peak lists and a shift table.

- URL: https://qilingtools.com/en/math/nmr
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Chemistry](https://qilingtools.com/en/tags/chemistry)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

In a ¹H NMR spectrum each set of chemically equivalent protons gives one signal: its position is the chemical shift δ in ppm, its area is proportional to the number of protons, and spin–spin coupling to n equivalent neighbouring protons splits it into n+1 lines with Pascal’s-triangle intensities. Ethanol is the classic example: the CH₃ is split by the two CH₂ protons into a triplet (1:2:1) at δ 1.22, the CH₂ is split by the three methyl protons into a quartet (1:3:3:1) at δ 3.69, both with J = 7.0 Hz, and the OH is a broad singlet because it exchanges quickly. This simulator builds a first-order spectrum from your own signals — enter δ, the number of H and one or more couplings (number of neighbours n and J in Hz) — and draws it with Lorentzian lines and an integral curve at 60, 90, 300, 400 or 600 MHz. For each signal it shows a splitting tree, names the multiplicity (s, d, t, q, quint, sext, sept, dd, dt, td, ddd or m) and writes the peak list in journal format, e.g. “δ 1.22 (t, J = 7.0 Hz, 3H)”. It also checks Δν/J for every coupled pair, warns about second-order effects when the ratio drops below 5 and applies a roofing approximation (exact solution for an isolated AB pair); switching the field shows J staying fixed while multiplets shrink on the ppm axis. Twelve example molecules — ethanol, ethyl acetate, isopropanol, toluene, propanoic acid, 1-bromopropane, butanone, diethyl ether, acetaldehyde, isobutanol, vinyl acetate and ethylbenzene — come with typical CDCl₃ data and colour-coded assignments on the structure. A chemical shift range table, a table of typical coupling constants and an n+1 rule explainer are included, and spectra export as PNG or SVG.

## How to use

1. Pick an example molecule, or clear it and add your own signals: chemical shift δ, number of H, and for each coupling the number of neighbours and J
2. Set the spectrometer frequency and linewidth, toggle the second-order approximation and integral curve, and click a peak label to zoom into a multiplet
3. Read the splitting tree, multiplicity and peak list, then copy the journal-format text or export the spectrum as PNG / SVG

## Features

- n+1 rule and multi-step splitting by several coupling constants with Pascal’s-triangle intensities
- 60 / 90 / 300 / 400 / 600 MHz spectrometer frequency and adjustable Lorentzian linewidth
- Integral curve with proton counts under each signal
- Splitting tree diagram showing each J and number of neighbours
- Automatic multiplicity: s, d, t, q, quint, sext, sept, dd, dt, td, ddd, m
- Journal-style peak list ready to copy: δ 1.22 (t, J = 7.0 Hz, 3H)
- Δν/J second-order check, roofing approximation and exact AB quartet
- 12 example molecules with colour-coded assignments, plus chemical shift and coupling-constant tables

## FAQ

### What is the n+1 rule in NMR?

A proton (or set of equivalent protons) coupled to n equivalent neighbouring protons appears as n+1 lines whose intensities follow row n of Pascal’s triangle: a doublet 1:1 for n = 1, a triplet 1:2:1 for n = 2, a quartet 1:3:3:1 for n = 3 and a septet 1:6:15:20:15:6:1 for n = 6. Coupling is usually through three bonds (H–C–C–H), and equivalent protons do not split each other.

### How do I predict splitting with two different neighbours?

When the coupling constants differ, split step by step: first by the larger J, then split each line by the smaller J, giving (n₁+1)(n₂+1) lines. The =CH–O proton of vinyl acetate couples to a trans proton (J ≈ 14 Hz) and a cis proton (J ≈ 6 Hz), so it is a doublet of doublets (dd). If the two J values are nearly equal the lines overlap and the signal looks like coupling to n₁+n₂ protons — the middle CH₂ of 1-bromopropane appears as a sextet.

### Why are high-field NMR spectra easier to interpret?

J is measured in Hz and does not depend on the magnetic field, while the shift difference in Hz equals Δδ times the spectrometer frequency. A 21 Hz wide quartet covers 0.35 ppm at 60 MHz but only 0.035 ppm at 600 MHz. A larger Δν/J means less overlap and a more first-order spectrum; below about Δν/J = 5 the multiplets lean toward each other (roofing) and second-order patterns appear.

### Why are OH, NH and COOH peaks broad singlets that move around?

These protons exchange rapidly with traces of water or with each other, faster than the coupling timescale, so their coupling to neighbouring C–H is usually not seen and the peak is broadened. Their shifts depend strongly on hydrogen bonding and change with concentration, temperature and solvent: alcohol OH roughly 1–5 ppm, carboxylic acid OH about 10–13 ppm. Shaking the sample with a drop of D₂O makes them disappear, a standard way to identify them.

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