Chromatography Calculators
Column Volume / Dead Volume Calculator
From column ID, length and porosity ε, calculates the mobile phase volume in the column, VM(the dead volume), used to estimate dead time tM, equilibration and flush volumes. The geometric column volume Vcol。
Formula VM = π·(ID/2)²·L·ε | Vcol = π·(ID/2)²·L — ε is the "accessible porosity". Reference values: fully porous C18 ≈ 0.65, core-shell ≈ 0.55 (the solid core is inaccessible), bare silica or wide-pore media ≈ 0.70. Converting packing density to ε is explained below.
Media Quantity Calculator
Estimates how much medium is needed to pack one column from the column dimensions and bed density, with the result in kg. Applies to preparative columns, industrial DAC columns and self-packed columns.
Formula Media quantity m = Vcol × ρbed | Vcol = π·(ID/2)²·L — the value required here is thebed (packing) density, not the skeletal true density. Reference values: fully porous silica 0.35–0.55 g/mL (0.50 for most ODS), higher for core-shell, PS/DVB polymer media roughly 0.30–0.40. Gel media such as agarose or dextran ship as slurries and are measured by settled volume, so this formula does not apply. Conversion between density and porosity is explained below.
Analytical → Preparative Flow Rate Scale-Up
Calculates the flow rate the preparative column needs to keep linear velocity constant.
Formula F2 = F1 × (d2/d1)² — constant linear velocity scale-up (column length unchanged). Sample load scales by the same (d2/d1)² factor; if the column length changes, keep the flow rate and extend the gradient time in proportion to the column volume.
Theoretical Plate Number N
Measures column efficiency; a key system suitability criterion (N ≥ 2000 required).
Formula N = 5.545 × (tR / W½)² — half-height method (5.545 = 8·ln2), consistent with the general chromatography chapter of the USP. W½ and tR must use the same time units.
Resolution Rs
Measures how well two adjacent peaks are separated; Rs ≥ 1.5 is baseline resolution.
Formula Rs = 2·(tR2 − tR1) / (W1 + W2) — tangent method (W is the baseline peak width). If only half-height widths are available, use Rs = 1.18·(tR2 − tR1) / (W½,1 + W½,2)。
Porosity ε and Packing Density Are Different Quantities
These two are often confused, but they differ in meaning, units and use. Calculating VM requires porosity, not packing density.
| Quantity | Definition | Unit | Typical value |
|---|---|---|---|
| Interstitial porosity εe | Fraction of column volume in the voids between particles | Dimensionless | 0.36–0.42 (random close packing of spherical particles) |
| Total (accessible) porosity εt | Interstitial voids plus the part of the particle pore volume the mobile phase can occupy | Dimensionless | Fully porous C18 0.60–0.70; core-shell 0.50–0.60; bare silica around 0.70 |
| Bed (packing) density ρbed | Mass of dry medium packed per unit column volume | g/mL | Fully porous silica 0.35–0.55; higher for core-shell |
| Particle density ρp | Density of a single particle including its pores, ρp = 1 / (1/ρs + Vp) | g/mL | About 0.74 at a pore volume of 0.9 mL/g |
| Skeletal (true) density ρs | Bulk density of amorphous silica | g/cm³ | About 2.2 |
Conversion εe = 1 − ρbed / ρp · εt = 1 − ρbed / ρs
Why measured values are lower ε calculated from densityt often reaches 0.75–0.80, but the V measured with an unretained markerM gives only 0.60–0.70 of the column volume. The difference has three sources: the bonded phase (the C18 carbon layer, for example) itself occupies part of the pore volume; some micropores are inaccessible to both mobile phase and marker; and the solid core of core-shell media takes no part at all. The ε used in the calculator should therefore be taken on ameasured basis, not back-calculated as a theoretical value from packing density.
Worked example At a pore volume of 0.9 mL/g, ρs = 2.2 g/cm³ → ρp ≈ 0.74 g/mL; if εe = 0.40, then ρbed ≈ 0.44 g/mL and the theoretical εt ≈ 0.80, whereas the measured value on the same C18 column is usually around 0.65.