Scale an HPLC Method: Column and Particle Size

To scale an HPLC method to a new column, keep column chemistry unchanged, hold the length-to-particle-size ratio (L/d_p) within −25% to +50%, scale flow rate with the square of internal diameter (under ⟨621⟩, also particle size) and scale injection volume and gradient time with column volume so the gradient volume, in column volumes, stays constant.^1,2,3,4

Which scaling relations keep an HPLC separation the same?

Scaling works only if the chemistry of the system does not change: the same mobile phase, column temperature and column chemistry.¹ Ideally the column keeps the same bonded phase and base silica.⁵ A change of stationary phase is no longer a method transfer but a new method that needs to be validated again, a task for developing an HPLC method.⁶ With chemistry fixed, isocratic k and α stay constant, so resolution is kept if the plate number N is kept.¹ Table 1 lists the relations.

**Table 1.** Scaling relations for column length L, internal diameter d_c and particle size d_p. Model: chemistry unchanged.¹
Quantity	Scales with	Purpose
Plate number N	L/d_p¹	keeps resolution
Flow rate F (constant linear velocity)	d_c²^3,6	keeps linear velocity
Flow rate F (⟨621⟩ equation)	d_c²/d_p²	also corrects for particle size
Injection volume	column volume, L × d_c²⁴	general rule; confirm empirically⁴
Gradient time of each segment	(L × d_c²)/F^2,4	keeps gradient volume in column volumes³
Pressure	L × F/(d_c² × d_p²)¹	checks the instrument limit
Dwell volume (in theory)	column volume⁷	keeps early-peak spacing⁴

t_G2 = t_G1 × (F₁/F₂) × [(L₂ × d_c2²)/(L₁ × d_c1²)]

Here t_G is the time of one gradient segment, F the flow rate, L the column length, d_c the internal diameter, and subscripts 1 and 2 denote original and new conditions; ⟨621⟩ applies this to every segment.² Flow and gradient time change together, because an uncompensated flow change alters the gradient retention factor k*.⁴

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How does the L/dp ratio preserve resolution when particle size changes?

The theoretical plate number is directly proportional to column length and inversely proportional to particle size, so holding L/d_p constant holds N approximately constant.¹ ⟨621⟩ accepts a new length or particle size if L/d_p stays within −25% to +50% of the prescribed ratio, for isocratic and gradient elution.² A modest loss of N costs little resolution, because resolution changes only with the square root of the plate number.⁸

Superficially porous particles typically give plate numbers corresponding to much smaller particles, so L/d_p can mislead for them.⁹ For that case there is an optional allowance: the plate number itself should stay within −25% to +50%.⁹

How do you scale an HPLC method from 150 × 4.6 mm, 5 µm to 100 × 2.1 mm?

Assume a gradient method on a 150 × 4.6 mm, 5 µm column (1.0 mL/min, 20 min gradient, 20 µL injection, 100 bar) moved to a 100 × 2.1 mm column of the same stationary phase. Table 2 collects the results.

Step 1: check L/dp

The original ratio is 150/5 = 30. A 100 mm column of 2.7 µm particles gives 100/2.7 = 37.0, a change of +23%, inside the −25% to +50% window.² This assumes a totally porous 2.7 µm column; for a superficially porous one, the plate-number allowance above and the ⟨621⟩ condition of equivalent selectivity and elution order apply.^9,2 The same length with 1.7 µm particles gives 100/1.7 = 58.8, or +96%, outside the window; 1.7 µm pairs instead with a 50 mm column (50/1.7 = 29.4, −2%).²

Step 2: scale the flow rate

F₂ = F₁ × [(d_c2² × d_p1)/(d_c1² × d_p2)]

Here d_c is the internal diameter and d_p the particle size of the original (1) and new (2) columns.² Holding linear velocity alone gives 1.0 × (2.1/4.6)² = 0.208 mL/min.⁷ Including the particle-size term gives 1.0 × (2.1² × 5)/(4.6² × 2.7) = 0.386 mL/min.² The particle-size term is there because smaller-particle columns need higher linear velocities for the same performance.²

Step 3: scale gradient time and injection volume

The column-volume ratio is (100 × 2.1²)/(150 × 4.6²) = 0.139. Each gradient segment becomes 20 × (1.0/0.386) × 0.139 = 7.2 min.² Scaling injection volume with column volume gives 20 × 0.139 = 2.8 µL, a starting point to confirm empirically.⁴

**Table 2.** Worked example: assumed gradient method scaled from 150 × 4.6 mm, 5 µm to 100 × 2.1 mm, 2.7 µm, same stationary phase. Model: Table 1 relations with the ⟨621⟩ flow equation.²
Parameter	Original	Scaled	Relation
L/d_p	30	37.0 (+23%)	within −25% to +50%²
Flow rate	1.0 mL/min	0.386 mL/min	⟨621⟩ equation²
Gradient time per segment	20 min	7.2 min	× 0.360²
Injection volume	20 µL	2.8 µL	× 0.139⁴
Estimated pressure	100 bar	423 bar	× 4.23¹

Figure 1 shows both columns with each scaled quantity.

Two HPLC column tiles for method scaling, 150 × 4.6 mm 5 µm and 100 × 2.1 mm 2.7 µm, with chips for L/dp, flow rate, gradient time, injection volume, column volume ratio and estimated pressure. — **Figure 1. Original and scaled columns for the worked example.** Two column tiles, 150 × 4.6 mm, 5 µm and 100 × 2.1 mm, 2.7 µm, with each scaled quantity in a chip, computed from the relations in Table 1 for an assumed gradient method (1.0 mL/min, 20 min gradient, 20 µL injection, 100 bar) and the same stationary phase. L/dp stays within the ⟨621⟩ window; flow follows the ⟨621⟩ equation; gradient time and injection volume scale with column volume.^2,4 Pressure is an estimate.¹ Column length and internal diameter (enlarged ×4) are drawn to scale; particle glyphs are to scale with each other. Schematic, not data.

What back pressure does a scaled HPLC method generate?

Pressure is directly related to column length and flow rate, and inversely related to column cross-sectional area and the square of particle size.¹ For the example the ratio is (100/150) × (4.6/2.1)² × (5/2.7)² × (0.386/1.0) = 4.23, so the assumed 100 bar becomes ≈423 bar.¹ Conventional LC systems can generate 400 bar, so 423 bar calls for a UHPLC instrument.¹ Figure 2 plots this estimate against particle size.

Plot of estimated HPLC back pressure against particle size for a scaled 100 × 2.1 mm column, rising from 123 bar at 5 µm to 423 bar at 2.7 µm and 1,068 bar at 1.7 µm, with a 400 bar reference line. — **Figure 2. Estimated back pressure versus particle size for the scaled column.** Computed curve for a 100 × 2.1 mm column at 0.386 mL/min, from pressure proportional to L × F/(d_c² × d_p²), anchored to an assumed 100 bar for the original 150 × 4.6 mm, 5 µm column at 1.0 mL/min: 123 bar at 5 µm, 423 bar at 2.7 µm and 1,068 bar at 1.7 µm.^1,5 On a 100 mm column, 1.7 µm gives L/d_p +96%, outside the ⟨621⟩ window.² The dashed line marks 400 bar, which conventional LC systems can generate.¹ Viscosity and temperature are held constant; observed pressure will likely deviate somewhat, for example because of very small tubing diameters.¹ Computed values, not measurements.

In Dolan’s simulated example, a fivefold flow increase on a 50 × 2.1 mm, 1.7 µm column raised pressure fivefold to 13,170 psi (≈910 bar).⁷ Observed pressure will likely deviate somewhat from the calculated value, for example because of the additional pressure generated by very small tubing diameters used for UHPLC.¹ If pressure runs higher than expected, check the root causes of high backpressure in HPLC.

Also, 2.1 mm columns are highly prone to extra-column dispersion and suit modern low-dispersion systems.⁵ With a shorter column, extra-column volumes need critical evaluation because peaks elute in a smaller volume.⁶

What does USP ⟨621⟩ allow when column dimensions change?

The Stage 4 harmonized text of USP General Chapter ⟨621⟩ sets these requirements:²

L/d_p within −25% to +50% of the prescribed ratio, for isocratic and gradient elution.²
Flow rate scaled by the diameter and particle-size equation; for isocratic methods a further ±50% change is allowed after that adjustment.²
Gradient time of every segment scaled to column volume and flow.²
The initial isocratic step adapted for dwell-volume differences.²
Changes from totally porous to superficially porous particles are acceptable provided that system suitability criteria are fulfilled and selectivity and elution order are equivalent.²

These allowances apply only to monograph methods published in the USP.⁹ Older editions were narrower: in USP 40, column-dimension, particle-size and flow changes were allowed only for isocratic methods.⁹ Ph. Eur. 2.2.46 incorporates the same harmonized text, signed off by the Pharmacopoeial Discussion Group on 28 September 2021 and implemented from 1 January 2023.¹⁰ Additional verification tests may be required when a pharmacopoeial procedure is adjusted.¹⁰ For validated or compendial methods, the applicable procedure and regulatory framework take precedence over the general rules of thumb given here.

How does dwell volume affect a scaled gradient method?

Dwell volume, also called gradient delay volume, is the system volume between the point where the solvents are first mixed and the head of the column.^3,11 Its primary effect is an offset in retention time, with a secondary effect on selectivity.¹¹ Petersson and co-workers observed a complete elution reversal of two analytes between a binary high-pressure system (202 µL) and a quaternary low-pressure system (990 µL).¹² Early-eluting peaks are the most affected.^4,11

Dolan gives typical dwell volumes of 1.5–3.5 mL for conventional LC and 0.3–1.5 mL for UHPLC.⁷ Petersson and co-workers give ≈130–700 µL for UHPLC and ≈1000 µL for standard LC.¹² In a peer-reviewed study of gradient transfer, injected volume, flow rate, isocratic step duration and gradient slope all had to be adapted, and dwell volume was reduced together with column dead volume.¹³

Because dwell volume is seldom adjustable, compensate in the program: add an initial isocratic hold when moving to a lower-dwell system, or delay the injection when moving to a higher-dwell system.^4,12,11 As best practice, list the system dwell volume in the method description and state in the SOP the dwell-volume range for which the method is valid.^11,12 The HPLC method transfer guide covers how to measure and compensate it.

In what order should HPLC method scaling steps be checked?

Table 3 orders the steps, and Figure 3 draws the same sequence.

**Table 3.** Scaling workflow; the ⟨621⟩ conditions are requirements for monograph methods only.⁹
Step	Action	Pass condition
1. Compute	L/d_p, flow, gradient time, injection volume and pressure (Table 1)^2,4	pressure compatible with the instrument¹³
2. Check ⟨621⟩	compare with the allowed adjustments²	L/d_p within −25% to +50%²
3. Adjust dwell volume	isocratic hold or delayed injection¹¹	early-peak spacing unchanged¹¹
4. Verify system suitability	run the suitability test; document before-and-after performance⁸	criteria met (with equivalent selectivity and elution order for totally porous to superficially porous particle changes)²; calibration redetermined⁶

Workflow for HPLC method scaling in four steps: compute scaled conditions (sketch of the 150 × 4.6 mm and 100 × 2.1 mm columns), check USP ⟨621⟩ limits (L/dp window bar with +23% inside and +96% outside), adjust for dwell volume by isocratic hold or delayed injection (gradient program sketches), verify system suitability (matching original and scaled peak traces). — **Figure 3. Workflow for scaling an HPLC method.** Four sequential steps matching Table 3 row for row: compute the scaled conditions, check them against ⟨621⟩, compensate dwell volume with an isocratic hold or a delayed injection, then verify system suitability.^2,11,8 The ⟨621⟩ check is a requirement for monograph methods only.⁹ The column sketches and the step 2 markers (+23% at 2.7 µm and +96% at 1.7 µm, for a 100 mm column) come from the worked example (150 × 4.6 mm, 5 µm original). Schematic, not data.

The changes should be documented, along with a comparison of method performance before and after the change.⁸ For validated or compendial methods, the applicable procedure and regulatory framework take precedence over the general rules of thumb given here.

Frequently asked questions

Why does the injection volume shrink when the column gets narrower?

As a general rule, injection volume is adjusted in proportion to column volume, which scales with length times the square of internal diameter.⁴ Moving from 150 × 4.6 mm to 100 × 2.1 mm cuts column volume to 0.139 of the original, so a 20 µL injection becomes about 2.8 µL. Dolan suggests testing the calculated volume against injections at half and twice that volume before fixing the new value.⁴

Can a 2.7 µm superficially porous column replace a 5 µm totally porous column?

The L/d_p rule can mislead here, because superficially porous particles typically give plate numbers corresponding to much smaller particles.⁹ An optional allowance therefore lets the plate number itself stay within −25% to +50% of the original.⁹ For a compendial method the change is acceptable only if system suitability criteria are fulfilled and selectivity and elution order are equivalent.²

Does Ph. Eur. 2.2.46 follow the same adjustment rules as USP ⟨621⟩?

For the harmonized provisions, yes. Ph. Eur. 2.2.46 incorporates the harmonization text signed off by the Pharmacopoeial Discussion Group on 28 September 2021, with implementation from 1 January 2023.¹⁰ The revised chapter describes harmonized conditions for adjusting mobile phase composition, flow rate and injection volume in isocratic elution.¹⁰ EDQM also notes that additional verification tests may be required when a pharmacopoeial procedure is adjusted.¹⁰

Do ⟨621⟩ allowable adjustments apply to in-house methods?

No. ⟨621⟩ applies only to monograph methods published in the USP, not to methods developed and validated in a laboratory, taken from the literature or inherited.⁹ Its rules can serve as the basis of a laboratory SOP for method adjustment, but they are then the laboratory’s guidelines rather than the USP’s.⁹ They do not give permission to change other methods without complying with the applicable regulations.⁹

Why do early-eluting peaks change most after a gradient is scaled?

During the dwell time the sample sees an isocratic hold at the starting composition before the gradient reaches the column.¹¹ Analytes that are not highly retained at the column inlet start to migrate during that hold, so a different dwell volume changes their spacing, while fully retained analytes are all affected to the same extent.¹² Early peaks are therefore the ones to check after a transfer.¹¹

The takeaway

Scaling an HPLC method is arithmetic on a fixed chemistry: keep L/d_p within −25% to +50%, scale flow with the square of internal diameter (and, under ⟨621⟩, inversely with particle size), scale injection volume and every gradient segment with column volume and check the estimated pressure against the instrument.^2,3,4,1 Then compensate dwell volume with an isocratic hold or a delayed injection and confirm system suitability.^11,8

References

Dolan JW. LC method scaling, part I: isocratic separations. LCGC Europe. 2014;27(2). https://www.chromatographyonline.com/view/lc-method-scaling-part-i-isocratic-separations-0 — N proportional to L/dp; linear velocity and cross-sectional area; pressure proportional to L and F and inversely to column cross-section and dp²; chemistry must not change.
United States Pharmacopeial Convention. USP General Chapter ⟨621⟩ Chromatography, Stage 4 harmonized text (official 1 December 2022). https://www.usp.org/sites/default/files/usp/document/harmonization/gen-chapter/harmonization-november-2021-m99380.pdf (accessed 2026-10-17) — allowable adjustments for isocratic and gradient LC: L/dp window, flow-rate, gradient-time and injection-volume equations, ±50% flow, dwell-volume correction, system suitability conditions.
Dolan JW. Method adjustment for gradient elution. LCGC North America. 2017;35(8). https://www.chromatographyonline.com/view/method-adjustment-gradient-elution-0 — gradient scaling at constant gradient volume in column volumes, flow with square of diameter, three-step procedure and dwell-volume scaling.
Dolan JW. LC method scaling, part II: gradient separations. LCGC North America. 2014;32(3). https://www.chromatographyonline.com/view/lc-method-scaling-part-ii-gradient-separations-0 — gradient k* depends on tG·F/Vm; each segment scaled separately; injection volume scaled with column volume and verified empirically; dwell volume affects early peaks.
Edge T, James M, Soliven A. Applying sustainability concepts to modern liquid chromatography. LCGC International. 2024:20–25. https://doi.org/10.56530/lcgc.int.gw3787f6 — pressure scales with the square of particle size at fixed length; flow scaled for constant linear velocity and injection volume scaled; shorter columns of smaller particles give the same efficiency; same stationary phase chemistry; extra-column dispersion with 2.1 mm columns.
Guillarme D, Veuthey JL, Meyer VR. Method transfer in HPLC. LCGC Europe. 2008;21(6). https://www.chromatographyonline.com/view/method-transfer-hplc-0 — flow scaling with diameter squared, pressure consequences of smaller particles and higher flow, extra-column volume, and stationary-phase change as a new method.
Dolan JW. Be careful of the flow rate. LCGC North America. 2015;33(4). https://www.chromatographyonline.com/view/be-careful-flow-rate — worked 150 × 4.6 mm, 5 µm → 50 × 2.1 mm, 1.7 µm example: flow factor, simulated pressures and typical dwell volumes.
Dolan JW, Osmani F. Evaluation of an LC Method. LCGC Europe. 2012;25(11). https://www.chromatographyonline.com/view/evaluation-lc-method-1 — practitioner case: resolution scales with √N, small flow changes barely affect N, compendial adjustments require passing system suitability and documentation.
Dolan JW. Method adjustment the USP way. LCGC Asia Pacific. 2017;20(2). https://www.chromatographyonline.com/view/method-adjustment-usp-way — scope of USP ⟨621⟩ adjustments (monograph methods only), L/dp −25% to +50%, flow-rate equation, SPP caveat and the optional plate-number allowance.
European Directorate for the Quality of Medicines & HealthCare. General chapter 2.2.46. Chromatographic separation techniques now published in Ph. Eur. 11th Edition. https://www.edqm.eu/en/-/general-chapter-2.2.46.-chromatographic-separation-techniques-now-published-in-ph.-eur.-11th-edition (accessed 2026-10-17) — Ph. Eur. 2.2.46 harmonized with USP ⟨621⟩ (PDG sign-off 28 September 2021; implementation 1 January 2023); verification tests after adjustment.
Dolan JW. Gradient elution, part IV: dwell-volume problems. LCGC Europe. 2013;26(6). https://www.chromatographyonline.com/view/gradient-elution-part-iv-dwell-volume-problems — definition and consequences of dwell volume; compensation by isocratic hold or delayed injection; record dwell volume in the method.
Petersson P, Euerby MR, Field J, Vitiello B. Understanding how dwell volume can affect selectivity in reversed-phase gradient chromatography. LCGC Europe. 2019;32(6). https://www.chromatographyonline.com/view/understanding-how-dwell-volume-can-affect-selectivity-reversed-phase-gradient-chromatography — dwell-volume differences change gradient selectivity; isocratic hold vs delayed injection; typical UHPLC vs HPLC dwell volumes; SOPs should state the valid dwell-volume range.
Guillarme D, Nguyen DTT, Rudaz S, Veuthey JL. Method transfer for fast liquid chromatography in pharmaceutical analysis: application to short columns packed with small particle. Part II: gradient experiments. European Journal of Pharmaceutics and Biopharmaceutics. 2008;68(2):430–440. https://doi.org/10.1016/j.ejpb.2007.06.018 — gradient transfer requires adapting injected volume, flow, isocratic step and gradient slope; dwell volume affects selectivity; small particles raise back pressure.

HPLC Column Dimensions and Particle Size: How to Scale a Method Correctly