Perpendicular drop or tangent skim: how to integrate overlapping HPLC peaks

Two peaks come out close together. The data system draws a line between them, the numbers go into the report, and the analyst moves on to the next sample.

That line is a decision. It decides how much of the area belongs to each peak, and when one of the peaks is an impurity near its limit, it can decide the result. Most of the time the analyst did not choose it. The data system’s default did.

The software details below are for Empower. The chromatography is the same in any data system.

The four ways to split overlapping peaks

There are four common choices.

Perpendicular drop. Draw a baseline from before the peak group to after it. From the lowest point of the valley, drop a vertical line to that baseline. Each peak gets the area on its side of the line. This is the default in Empower, for both algorithms (Empower tips #318 and #319).

Tangent skim. Draw a straight line under the small peak, from the valley to where the small peak ends, so the small peak sits on top of the large peak’s tail. The large peak keeps the area under the line.

Exponential skim. The same idea, with a curved line that follows the shape of the large peak’s tail.

Valley-to-valley. Bring the baseline up to the valley between the peaks. The area under that raised baseline belongs to neither peak.

Perpendicular drop for peaks of similar size

John Dolan wrote the clearest practical account of this in his LC Troubleshooting column (LCGC North America, October 2009). For two partly resolved peaks of about the same size, his recommendation is the perpendicular drop to the baseline extended before and after the group (p. 892).

The reasoning is that errors cancel. The tail of the first peak hides under the second peak, and the front of the second peak hides under the first. If the two peaks are about the same size and both are symmetric, those two hidden pieces are about the same size too.

That “if” carries the whole method. When one peak tails or fronts, or when one peak is much larger than the other, the hidden pieces are no longer equal and the error stops cancelling.

A small peak on the tail of a large one: skim it

Now take a small peak sitting on the tail of a large one. A perpendicular drop here gives the small peak a piece of the large peak’s tail. The small peak is over-reported and the large peak is under-reported. The proper integration is to skim the small peak off the tail (Dolan, p. 894).

When there is no real valley at all, only a shoulder, a perpendicular drop “will grossly over-integrate the peak” (p. 892). A skim is the better choice there too.

Dolan’s rule of thumb (p. 896):

• the small peak is less than about 10% of the large peak’s height: skim
• the small peak is more than 10%: perpendicular drop

It is a rule of thumb from 2009, and other authors put the switch point elsewhere. A 2026 review of the literature lists about 10% from Dolan, about 5% from Meyer, and lower values from Bicking (Forssén and Fornstedt 2026, p. 2). So use 10% as a starting point, and test it on your own peaks during validation.

Tangent or exponential?

Analysts argue about this more than it deserves. Dolan’s view is that the shape of the skim line is of little practical interest. Whenever a skim is used, it is an estimate, and consistency of the integration method is more important than whether the skim is a tangent or a curve (pp. 894–896).

I agree with him. The bigger error is skimming one batch and dropping a perpendicular in the next.

Valley-to-valley is seldom right

Valley-to-valley looks tidy, because every peak sits on its own little baseline. But all the area under the raised baseline is thrown away, so both peaks are under-integrated, and a shoulder can be missed completely (Dolan, p. 892).

It is defensible in one situation: a known, repeatable baseline disturbance under the peaks, such as a small broad rise that appears in every gradient blank. Even then, the valleys should come down nearly to the true baseline. Dolan’s conclusion is that valley-to-valley “seldom is the best approach” (p. 894).

The 2026 simulation agrees. With valley-to-valley, the error was above 5% in 99.8% of the peak pairs tested (Forssén and Fornstedt, p. 6).

How accurate is the perpendicular drop? What the 2026 simulation shows

Forssén and Fornstedt simulated 40,000 chromatograms of two overlapping peaks, with resolution from 0.5 to 2.1 and the smaller peak from 0.1% to 50% of the total area, and integrated each one with six different rules (pp. 1, 5).

For the perpendicular drop:

• it read the minor peak low, in a systematic way, because the valley shifts toward the smaller peak (pp. 6, 8)
• the error on the minor peak stayed within 1% only when resolution was at least 1.1 and the minor peak was at least 30% of the total area (p. 6)
• for an 80:20 pair at resolution 0.95, the minor peak came out 5.04% low (p. 7)

Two cautions before you use these numbers. The simulated peaks were symmetric, of equal width and free of noise, and real impurity peaks on a tailing main peak are none of those. And the paper promotes a new method of its own, based on peak heights, which is not in any commercial data system I know of. Read it for the perpendicular drop and valley-to-valley results, which agree with the older literature.

The practical point: a resolution of 1.5 in your system suitability is also a requirement for accurate areas, and the smaller the impurity, the more resolution it needs.

Area or height?

For overlapping peaks, peak height can be the better measure. At the apex of each peak there is little overlap, while the area includes the overlap you know is there (Dolan, p. 898).

For small, noisy peaks the opposite holds. One noisy point can be taken as the apex, and area averages the noise across the whole peak.

Dolan’s advice is the practical one: during validation, run known samples, calculate the results both ways, and use whichever gives the more accurate and precise result (p. 898).

Setting it in Empower

In Empower, a skim is an integration event.

• Tangential Skim works with both ApexTrack and Traditional integration. It has a start time, a stop time and a value. The value is the height ratio of the main peak to the rider peak, measured at the valley. The skim is applied when the real ratio is equal to or greater than the value you enter (tip #318).
• Exponential Skim is offered with the Traditional algorithm, as an event with the same three settings. A negative value skims a rider off the front of the main peak instead of the tail (tip #319).
• Put the start and stop times inside the peak cluster.

Notice what the value means. A value of 10 means “skim when the main peak is at least 10 times taller than the rider at the valley.” That is close to Dolan’s 10% rule, written the other way round.

One more Empower point, which catches people. In ApexTrack, the Peak Width setting decides where the inflection points are, and the inflection points decide the tangent width. A wrong Peak Width gives a wrong plate count and a wrong resolution, with no change to the chromatogram itself (Waters, ApexTrack Integration: Theory and Application, 720000494EN, 2016, p. 20). Check it before you trust a resolution value close to its limit.

Manual integration, and the audit trail

Data systems integrate most peaks well, and none integrates every peak correctly. Dolan’s own estimate, from reviewing thousands of chromatograms near the lower limit of quantification, was that fewer than a dozen needed no manual integration at all (p. 898). His recommendation is to inspect every chromatogram and correct the integration when it is wrong.

Manual integration is allowed in a regulated lab. What is required is the record. FDA’s data integrity guidance says the audit trail for an HPLC run should include the integration parameters used and the details of any reprocessing, with a justification for it (FDA, Data Integrity and Compliance With Drug CGMP, Questions and Answers, 2018, Q1c). It also expects data to be saved after each step, including peak integration, and not only at the end of the sequence (Q12).

So the question an auditor will ask is simple. Was the integration changed to correct an error, and does the record show why? Or was it changed until the result passed?

Writing the rule into the method answers that question before it is asked: which peaks get a skim, the height ratio that triggers it, and what happens to a shoulder.

The separation is the real fix

Dolan’s favourite line on the subject, loosely quoted from Dyson’s book on integration, is that chromatography always trumps integration (p. 898). You can choose the best rule for a partly resolved peak, and it is still an estimate of the result you would get if the peaks were baseline resolved.

If an impurity close to its limit sits on the tail of the main peak, the integration rule is a short-term answer. The longer one is in the method: selectivity, the gradient, the column.

Sources

• Dolan JW. Integration problems. LC Troubleshooting, LCGC North America 2009; 27(10):892–898. PDF via the LC Troubleshooting Bible.
• Forssén P, Fornstedt T. Accuracy of methods for integrating overlapping chromatographic peaks: a systematic evaluation. J Chromatogr A 2026; 1787:467393. doi:10.1016/j.chroma.2026.467393. A simulation study with idealised peaks; see the cautions above.
• Waters Empower Tips #318 and #319, Neil Lander, Waters Corporation.
• Waters. ApexTrack Integration: Theory and Application. 720000494EN, November 2016.
• US FDA. Data Integrity and Compliance With Drug CGMP: Questions and Answers. Guidance for industry, December 2018.

If your lab argues about integration every time a batch is reviewed, that is a sign the rule is not written down. Send me the peak pair and the limit on LinkedIn and I will tell you how I would write the rule. The validation-readiness checklist covers the other questions to settle before a method reaches routine use.