Quick answer: gradient volume is tG × F; divide by column volume for column volumes. A 20-minute gradient at 1.0 mL/min on a 4.6 × 150 mm column is 20 mL = 8.0 CV. To move it to another column: tG,new = tG,old × (Vnew/Vold) × (Fold/Fnew). The %B range never changes — only the time axis.
Why a gradient in minutes is not a method
"5% to 95% B over 20 minutes" describes what one pump did on one day. It says nothing transferable, because the same 20 minutes delivers a completely different amount of solvent through a 2.1 × 50 mm column than through a 4.6 × 250 mm one.
What the chromatography actually responds to is the volume of mobile phase swept through the bed while the composition changes, measured relative to the size of that bed:
In column volumes: CV = VG ÷ Vcolumn
Worked through on the standard analytical column — 4.6 × 150 mm, geometric volume 2.49 mL, 1.0 mL/min, 20-minute gradient:
- Gradient volume: 20 × 1.0 = 20 mL
- In column volumes: 20 ÷ 2.49 = 8.0 CV
- Against void volume (1.70 mL): 20 ÷ 1.70 = 11.8 CV
Those last two lines are the same gradient described two ways, and the 1.5× gap between them is why a method that specifies "12 column volumes" without saying which column volume is still ambiguous. The column volume calculator covers the two conventions in full; this page reports both.
Gradient steepness: k*
Column volumes tell you how long a gradient is. They do not tell you whether it is any good. For that there is k* — the average retention factor a compound experiences during the gradient, and the gradient equivalent of isocratic k.
tG = gradient time · F = flow rate · ΔΦ = change in B as a fraction
Vm = column void volume · S ≈ 5 for small molecules
| k* | What it means | What to do |
|---|---|---|
| < 1 | Very steep — peaks compressed, poor resolution | Lengthen the gradient substantially |
| 1 – 2 | Steep — fast, resolution likely limiting | Lengthen if peaks are not resolving |
| 2 – 10 | The useful working window | Fine. Optimise within it |
| ≈ 5 | Generally the best resolution-per-minute trade | The usual target |
| > 10 | Shallow — long run, more solvent, little extra separation | Shorten unless you need the resolution |
The S term matters more than people expect. S describes how sharply a compound's retention responds to solvent composition, and it scales with molecular size. For small molecules under about 1,000 Da, S ≈ 5. For peptides and proteins it is far larger — 20 to 100 — which is why biomolecule gradients have to be dramatically shallower to reach the same k*. Run a protein on a small-molecule gradient and everything elutes in one unresolved band.
Scaling a gradient onto a different column
The whole point of thinking in volumes is that transfer becomes arithmetic. Two rules:
2. Scale gradient time: tG,2 = tG,1 × (V₂/V₁) × (F₁/F₂)
The %B range stays exactly the same.
Worked through for the most common real transfer, HPLC to UHPLC:
| Parameter | Original | Scaled | How |
|---|---|---|---|
| Column | 4.6 × 150 mm, 5 µm | 2.1 × 50 mm, 1.7 µm | — |
| Column volume | 2.493 mL | 0.173 mL | π(d/2)²L |
| Flow rate | 1.00 mL/min | 0.61 mL/min | × (2.1/4.6)² × (5/1.7) |
| Gradient time | 20.0 min | 2.28 min | × (0.173/2.493) × (1.00/0.61) |
| Gradient volume | 20.0 mL | 1.39 mL | tG × F |
| Gradient in CV | 8.0 CV | 8.0 CV | Unchanged — that is the point |
| %B range | 5 → 95% | 5 → 95% | Never changes |
| Injection volume | 20 µL | 1.4 µL | × volume ratio |
| Solvent per gradient | 20.0 mL | 1.39 mL | — |
The run went from 20 minutes to 2.3, and solvent use fell by a factor of 14 — the same separation, a tenth of the time, and a fraction of the acetonitrile. The gradient in column volumes is identical at 8.0, which is the check that the transfer was done correctly.
Two things this table does not cover. First, dwell volume — the two instruments almost certainly differ, and on a 0.173 mL column that difference is proportionally large. Second, the pressure: 1.7 µm particles at 0.61 mL/min will run considerably higher than the original method, and you should check it against your system limit with the flow rate calculator before starting.
Equilibration between runs
After a gradient finishes, the column has to be returned to starting conditions before the next injection, or retention drifts run to run. The conventional figure is 10 column volumes of the starting mobile phase.
| Column | Column volume | 10 CV | Flow | Time |
|---|---|---|---|---|
| 2.1 × 50 mm | 0.173 mL | 1.73 mL | 0.40 mL/min | 4.3 min |
| 2.1 × 100 mm | 0.346 mL | 3.46 mL | 0.40 mL/min | 8.7 min |
| 3.0 × 100 mm | 0.707 mL | 7.07 mL | 0.60 mL/min | 11.8 min |
| 4.6 × 150 mm | 2.493 mL | 24.9 mL | 1.00 mL/min | 24.9 min |
| 4.6 × 250 mm | 4.155 mL | 41.6 mL | 1.00 mL/min | 41.5 min |
That 4.6 × 250 mm row is worth noticing: the equilibration takes twice as long as a typical gradient. On a long sequence, most of the instrument time is spent not separating anything. It is one of the strongest practical arguments for smaller columns.
Two caveats. Ion-pairing reagents and HILIC methods equilibrate far more slowly — 30 CV or more is common, and under-equilibration is a leading cause of drifting retention in HILIC. And the system dwell volume must also be flushed back, so the true requirement is column equilibration plus dwell volume.
Common mistakes & pro tips
- Changing flow rate without rescaling gradient time. Doubling the flow on a fixed 20-minute gradient doubles the gradient volume and halves k* — that changes selectivity, not just speed. Peaks can swap order.
- Not stating which column volume you mean. Geometric and void differ by ~1.5×. Write it down in the method.
- Using small-molecule assumptions for peptides. S is five to twenty times larger for biomolecules; the same gradient is far steeper than it looks.
- Ignoring dwell volume on transfer. Scaling the gradient perfectly and then not correcting the delay still shifts every early peak.
- Skimping on equilibration to save time. The first injections in a sequence drift, and the first is often a standard.
- Pro tip — record k*, not just gradient time. It is the one number that survives a change of column, flow rate or instrument.
- Pro tip — check the CV figure before and after transfer. If it is not identical, the scaling is wrong. It is a two-second sanity check that catches most transfer errors.
How to use this calculator
- Analyse a gradient — enter the column, flow, gradient time and %B range to get the gradient volume, column volumes, k* and a steepness verdict.
- Scale to a new column — enter both columns and both flow rates to get the new gradient time, with the CV figure shown for both so you can confirm they match.
- Set the porosity to match your packing — it changes the void volume that k* depends on.
- Set S to 5 for small molecules, or higher for peptides and proteins.
Frequently asked questions
How do you express a gradient in column volumes?
Multiply the gradient time by the flow rate to get the gradient volume, then divide by the column volume. A 20-minute gradient at 1.0 mL/min delivers 20 mL of mobile phase; on a 4.6 × 150 mm column with a geometric volume of 2.49 mL that is 8.0 column volumes. Expressing a gradient this way is what makes it transferable between column sizes.
How do you scale a gradient to a different column?
New gradient time = old gradient time × (new column volume ÷ old column volume) × (old flow rate ÷ new flow rate). Scaling a 20-minute gradient from a 4.6 × 150 mm column at 1.0 mL/min to a 2.1 × 50 mm column at 0.61 mL/min gives 20 × 0.0694 × 1.64, which is about 2.3 minutes. The percentage range of solvent B never changes.
What is k* in gradient elution?
k* is the average retention factor a compound experiences during a gradient, and it is the gradient equivalent of the retention factor k in an isocratic method. It is calculated as gradient time × flow rate, divided by 1.15 × the change in solvent fraction × the column void volume × the solvent strength parameter S. A value around 5 is generally optimal; below about 2 the gradient is too steep and resolution suffers, above about 10 the run is longer than it needs to be.
How many column volumes should a gradient run over?
Analytical reversed-phase gradients commonly run over 10 to 20 column volumes. Fewer than about 5 gives a steep gradient with compressed peaks and poor resolution; more than about 30 usually buys very little extra separation for a lot of extra time and solvent. Be explicit about whether "column volume" means the geometric volume or the void volume, because the two differ by roughly a factor of 1.5.
How long should I equilibrate between gradient runs?
Ten column volumes of the starting mobile phase is the usual figure for reversed phase, which on a 4.6 × 150 mm column at 1 mL/min is about 25 minutes. Ion-pairing and HILIC methods often need considerably more, sometimes 30 column volumes or beyond, before retention is reproducible. Remember that the system dwell volume also has to be flushed back to starting conditions, so the true requirement is the column equilibration plus the dwell volume.
Why do my retention times shift when I change the flow rate?
Because in gradient elution the gradient is defined in time, not in volume. Changing the flow rate while keeping the gradient time fixed changes the gradient volume, which changes the steepness k* and therefore changes selectivity, not just speed. If you want to change the flow rate without changing the separation, you must scale the gradient time inversely so that the gradient volume stays constant.
References & further reading
- Snyder, L. R. & Dolan, J. W., High-Performance Gradient Elution: The Practical Application of the Linear-Solvent-Strength Model — the origin of k* and the S parameter.
- Dolan, J. W., "Gradient Elution" series, LCGC — practical treatment of scaling, dwell volume and equilibration.
- Snyder, Kirkland & Dolan, Introduction to Modern Liquid Chromatography, 3rd ed.
- USP General Chapter <621> — permitted gradient adjustments during method transfer.
k* uses the linear-solvent-strength model with typical S values; real behaviour varies by analyte and stationary phase. Treat the figures as method-development guidance rather than prediction. See our accuracy policy.