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
AvailableAssign ¹H peaks to atoms with shift, multiplicity, and structure.
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Frequently asked questions
What is the n+1 rule?
In first-order ¹H NMR, a nucleus with n equivalent neighbouring protons appears as n+1 lines. The intensities follow Pascal's Triangle (binomial coefficients).
What is J coupling?
J is the spin–spin coupling constant, measured in hertz. It equals the spacing between adjacent lines of a first-order multiplet and does not change with spectrometer field strength.
Why are intensities unequal?
For first-order multiplets they are unequal by design: Pascal ratios (1:1, 1:2:1, 1:3:3:1, …) reflect how many spin combinations produce each line.
Why doesn't every peak follow n+1?
Non-equivalent neighbours, second-order effects (Δδ ≈ J), exchange broadening, and overlapping signals produce patterns that are not simple n+1 multiplets.
What is a multiplet?
A multiplet (m) is a group of unresolved or complex lines. This simulator labels n ≥ 7 as multiplet while still showing the first-order envelope.
Does field strength affect splitting?
J in hertz is field-independent. The same multiplet spans fewer ppm at higher field (ppm = Hz / MHz), which often makes spectra look more first-order.
Why are some peaks broad?
Exchange (OH/NH), unresolved small couplings, viscosity, and shimming can broaden lines. Use the peak-width control to explore appearance.
What is first-order splitting?
When the chemical-shift difference (in Hz) is much larger than J, multiplets are symmetric with Pascal intensities — the regime this tool models.
What is a doublet of doublets?
Two different coupling constants to two non-equivalent neighbours give four lines. It is not the same as a Pascal quartet (1:3:3:1).
How do I measure J from a spectrum?
Convert the frequency difference between adjacent multiplet lines to hertz (or read Hz cursors in your processing software). Do not report J in ppm.
Are OH and NH counted in n?
Often no — exchangeable protons may not show stable coupling. Context (dry solvent, temperature, concentration) matters.
Is this tool AI-based?
No. All patterns are computed from the classical n+1 rule and Pascal's Triangle entirely in your browser.
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