HPLC Gradient Calculator: Gradient Retention Factor k*, Steepness & Dwell Time

Check whether a gradient is too steep, and how long to hold and re-equilibrate.

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Column length mm

Column ID mm

Flow mL/min

Gradient time min

Start %B %

End %B %

Dwell volume mL

Analyte size (S value)

Example: 150 × 4.6 mm, 1 mL/min, 5–95% B in 20 min, 1.0 mL dwell volume.

Gradient k*–

Steepness–

%B per column volume–

Dwell time–

Re-equilibration–

tG for k* = 5–

k* = tG·F/(1.15·Vm·Δφ·S) · Vm ≈ 0.5·L·d² · tD = VD/F · re-equilibration ≈ (10·Vm + VD)/F

How it works

In gradient elution each compound effectively elutes with an average retention factor k*, set by the gradient time, flow, column volume and the %B range. Linear solvent strength theory (Snyder and Dolan) gives k* = tG·F/(1.15·Vm·Δφ·S), where S describes how strongly retention depends on solvent strength: about 4 for small molecules and much larger for peptides and proteins.

Keeping k* constant is the key to transferring a gradient between columns: if the column volume or flow changes, change the gradient time in proportion. The dwell volume (mixer to column head) adds a delay before the gradient reaches the column and differs between instruments, which is a common cause of failed method transfers.

Re-equilibration of about 10 column volumes plus the dwell volume is a conservative default; confirm with replicate injections that retention times are stable.