What is the n+1 rule?
For first-order ¹H spectra, a proton with n equivalent neighbouring protons is split into n+1 lines. Zero neighbours → singlet; one → doublet; two → triplet.
Jaconir NMR LabNMR Splitting
NMR Splitting
Pattern Simulator
Visualize proton NMR splitting patterns, Pascal's Triangle and J-coupling in real time.
SingletDoubletTripletQuartetQuintetSextetMultiplet
¹H splitting spectrum
Singlet · J = 0.0 Hz · 400 MHz
Width 0.0 Hz (0.000 ppm)
Workspace
Adjust neighbours and J — the spectrum updates instantly.
¹H splitting spectrum
Triplet · J = 7.0 Hz · 400 MHz
Width 14.0 Hz (0.035 ppm)
Pattern
Triplet
Number of peaks
3
Intensity ratio
1:2:1
Pascal row
2
J coupling
7.0 Hz
Expected appearance
Triplet
Pascal's Triangle
Row n = intensities for n neighbouring protons (n+1 peaks)
1
11
121
1331
14641
15101051
1615201561
Why is this a Triplet?
2 neighbouring equivalent protons split the signal into 3 equally spaced peaks according to the n+1 rule. Relative intensities follow Pascal's Triangle (1:2:1).
Common examples
Challenge Me
Identify the splitting
Pattern · neighbouring protons · Pascal ratio · approximate J
¹H splitting spectrum
Identify the pattern
Learn & understand
Visual concepts behind first-order proton splitting
Why do peaks split?
Neighbouring nuclear spins create tiny additional magnetic fields. The observed nucleus experiences slightly different fields depending on neighbour spin states — hence multiple resonances.
What is J coupling?
J is the coupling constant in hertz — the spacing between adjacent lines of a multiplet. It is field-independent (Hz stay the same at 300 or 800 MHz; ppm spacing shrinks at higher field).
Equivalent protons
Only chemically equivalent neighbours are counted together in the simple n+1 rule. Non-equivalent neighbours produce more complex patterns (dd, td, …).
Pascal's Triangle
Relative line intensities of first-order multiplets are the binomial coefficients from Pascal's Triangle: 1 · 1:1 · 1:2:1 · 1:3:3:1 · …
First-order splitting
First-order means Δδ ≫ J (chemical-shift difference much larger than coupling). Lines are equally spaced and intensities match Pascal ratios.
Second-order effects
When Δδ approaches J, multiplets distort (roofing). Intensities skew and the simple n+1 picture fails — use simulation software for analysis.
Common mistakes
Counting OH as a fixed neighbour, ignoring exchange, treating aromatic multiplets as first-order, and confusing Hz with ppm are the most frequent student errors.
Advanced topics
Continue your NMR workflow
A path from impurity check → prediction → assignment
- 1
NMR Impurity Solver
CompletedIdentify common solvent impurities before assigning compound peaks.
- 2
NMR Chemical Shift Predictor
CompletedPredict unknown proton environments after removing solvent impurities.
- 3
NMR Splitting Pattern Simulator
You are hereUnderstand why peaks split into doublets, triplets and multiplets.
- 4
Peak Assignment Assistant
Coming soonAssign peaks to molecular structures.
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