Proton NMR integration: peak areas and proton ratios
Use integrated peak areas to determine the relative numbers of each proton environment.
Section 37 · Analytical techniques
What does integration tell you in proton NMR?
The integrated area of a proton NMR signal tells you the relative number of hydrogen atoms in that chemical environment. Compare the areas as a ratio, then use the molecular formula to work out the actual numbers of protons.
| Step | Example |
|---|---|
| Read the integrated areas | Three signals have areas 6 : 4 : 2. |
| Simplify the ratio | Divide every area by 2 to get 3 : 2 : 1. |
| Check the molecular formula | If these signals account for all 12 hydrogens, multiply the ratio by 2: the counts are 6, 4 and 2. |
Little memory hook: area tells you how many; splitting helps you find the neighbours. Use the whole multiplet's area, not the height of one line.
Syllabus reference: Cambridge Chemistry 9701 syllabus, 2028–2030 · section 37.4
Keep going: explanation and practice ↓A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 37. Use the supplied spectra, shift table and chromatography conditions. Interpret peaks as evidence and state when a short trace cannot uniquely identify a substance. Written practice is self-checked
Before you begin
- Recognise functional groups, molecular structures, polarity, intermolecular interactions and the distinction between equivalent and different chemical environments.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does a proton NMR integral measure?
What you will learn
- Interpret integral ratios
- Convert ratios to integer proton counts
- Distinguish area from peak height and signal count
Areas give relative proton numbers
In a proton NMR spectrum, the integrated area of a signal is proportional to the number of protons in that environment. Compare areas as a ratio, then scale to the simplest whole-number ratio consistent with the formula.
For example, areas 6:4:2 simplify to 3:2:1. The ratios tell how many protons contribute to each environment relative to one another, not their absolute number until the molecular formula or other information sets the scale.
Do not use peak height as integration
A narrow tall peak can have less total area than a broader lower peak. Use the integral trace or relative peak areas supplied, not visual height alone.
Equivalent protons contribute to the same signal. If a signal is split into several lines, integrate the complete multiplet rather than counting each line as a separate proton environment.
Pause and explain
What is the simplest whole-number ratio for areas 4:6:2?
Worked example
Three proton NMR signals have relative areas 6:4:2. Simplify the proton ratio.
Show the worked solution
- Find a common divisor.
- Divide each area by 2.
- Keep the order of the signals.
Answer The relative proton ratio is 3:2:1.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Simplify an integral ratio of 9:6:3 and state what it represents.
Give me a hint
Divide all areas by their greatest common factor.
Compare my reasoning
- The common factor is 3.
- The simplified ratio is 3:2:1.
- Relate it to relative proton counts.
3:2:1 relative protons in the three signal environments.
Look for these in your work
- Ratio simplified
- Signal order retained
- Meaning stated
A multiplet contains four lines with an integral covering all four. Should it be counted as four proton environments?
Give me a hint
Distinguish splitting lines from the integrated signal.
Compare my reasoning
- The lines form one signal multiplet for one proton environment.
- Integrate the whole multiplet.
- The area gives the relative proton count for that environment.
No. The four lines are one split signal; its total integrated area represents one proton environment's relative proton number.
Look for these in your work
- Multiplet recognized
- Environment distinguished
- Area interpreted
A student estimates proton counts by comparing peak heights, but one signal is broad. What measurement should they use instead?
Give me a hint
Broadness changes height without necessarily changing total integrated area.
Compare my reasoning
- Use integrated areas or the integral trace.
- Compare the area under each complete signal.
- Simplify the resulting ratio.
Use integrated peak areas, because peak height depends on width and is not a reliable proton-count measure.
Look for these in your work
- Correct quantity selected
- Full signal considered
- Reason stated
Common mistakes
- Treating area as peak height
- Counting each line in a multiplet as a new environment
- Assuming relative areas directly give absolute proton counts
- Forgetting to simplify the ratio
What can you explain now?
What does a proton NMR integral measure?
Compare with the explanation
Relative numbers of protons in signal environments
Area is proportional to the number of contributing protons.
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Make it stick
How do integrated areas translate into relative proton numbers?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.