Chromatography Resolution Calculator – Read a Chromatogram and Know What to Change
Every HPLC or GC method lives or dies by its critical pair, the two neighbouring peaks that are hardest to pull apart. This chromatography resolution calculator takes the peak table you already have (retention time and width for each peak, plus the dead time) and returns the resolution Rs, plate count N, retention factor k and selectivity α for every adjacent pair. It draws the chromatogram those numbers describe and shows how far each of the three levers would have to move to reach Rs 1.5 or 2.0. Everything is calculated in your browser.
What Rs measures
Resolution compares the gap between two apexes with the width of the peaks. With half-height widths, as in the harmonised USP <621> and Ph. Eur. 2.2.46 text, it is:
Rs = 1.18 · (t_R,b − t_R,a) / (W₀.₅,a + W₀.₅,b)With baseline tangent widths the constant is 2 instead. The rule of thumb is simple: below Rs 1.0 the peaks overlap noticeably, 1.5 is baseline resolution for equal Gaussian peaks, and 2.0 leaves a margin for tailing, column ageing and unequal peak sizes. The reference thumbnails in the tool show what each level looks like, with the share of each peak that crosses into its neighbour: about 2.3 % at Rs 1.0 and 0.13 % at Rs 1.5.
Half-height or tangent widths, and why data systems disagree
The plate count is N = 5.54 (t_R / W₀.₅)² from the half-height width, or N = 16 (t_R / W_b)² from the tangent width. For a perfect Gaussian both give the same answer. Real peaks tail, and then the method matters: tangent widths, the 5σ method at 4.4 % height and statistical moments all weigh the tail more heavily than the half-height width does, so they report lower plate counts. Pick the width definition you actually measured, and compare plate counts only between reports that use the same one.
Retention factor and dead time
The retention factor k = (t_R − t₀) / t₀ tells you how much longer a compound stays on the column than the mobile phase does. You need the dead time t₀: the first baseline disturbance, an unretained marker such as uracil in reversed-phase LC, or methane in GC. If you have none, the calculator estimates t₀ from the column diameter, length, flow rate and total porosity.
The Purnell equation, term by term
Rs = (√N / 4) · ((α − 1) / α) · (k / (1 + k))The three factors are efficiency, selectivity and retention, using N and k of the later peak. The tool shows them multiplied out for your critical pair, for example 32.8 × 0.0685 × 0.646 = 1.45, next to the measured Rs. The two differ slightly because Purnell assumes both peaks share the later peak's width.
Why selectivity beats plates
Plates enter under a square root, so doubling the column length buys only 41 % more resolution, at twice the run time and pressure. Selectivity works far harder: at α = 1.074, raising α by just 0.01 does as much as multiplying N by about 1.27. The calculator prints that equivalence for your own pair. In LC the practical selectivity levers are the organic modifier, the pH near the analytes' pKa, the stationary-phase chemistry and the temperature; in GC they are the phase polarity and the temperature programme.
Why more retention buys little above k ≈ 10
The retention term k / (1 + k) is 0.50 at k = 1, 0.83 at k = 5 and 0.91 at k = 10, then creeps towards 1. Pushing k from 5 to 10 raises Rs by only 9 % but nearly doubles the run time. When the required k comes out impossibly high, the tool says so and gives the ceiling Rs that infinite retention would reach.
Gradient elution and peak capacity
In gradient or temperature-programmed runs peaks are compressed as they travel, so N and k from t_R and W lose their meaning. Resolution from widths is still valid, and the calculator adds the peak capacity n_c = 1 + t_G / W̄_b, roughly the largest number of peaks the gradient could separate at Rs 1.