# Chromatography Calculator - Rf Value, Resolution, Plate Number, Van Deemter and Internal Standard

> Free chromatography calculator: drag a TLC plate for Rf, get k, selectivity, resolution, plate number and Purnell, simulate a chromatogram and plot Van Deemter.

- URL: https://qilingtools.com/en/chemistry/chromatography
- Category: Chemistry Tools (https://qilingtools.com/en/chemistry)
- Tags: [Chemistry](https://qilingtools.com/en/tags/chemistry)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

This calculator covers the everyday formulas of chromatography. For thin-layer and paper chromatography the retention factor is Rf = distance moved by the spot ÷ distance moved by the solvent front: drag the origin line, the solvent front and the spots in several lanes of an interactive TLC plate, read each Rf, and have sample spots matched automatically against reference lanes run on the same plate (default tolerance ±0.03). For column chromatography, HPLC and GC it computes the retention factor k = (tR − tM)/tM, selectivity α = k₂/k₁, resolution Rs = 2(tR2 − tR1)/(w1 + w2) or the half-height form 1.18(tR2 − tR1)/(w½1 + w½2), plate number N = 16(tR/w)² = 5.54(tR/w½)² and plate height H = L/N, and uses the Purnell equation Rs = (√N/4)((α−1)/α)(k/(1+k)) to find the plates and column length needed for Rs = 1.5. For example, with a dead time of 1.0 min, peaks at 4.0 and 4.6 min and baseline widths of 0.30 and 0.32 min give k₁ = 3, k₂ = 3.6, α = 1.2 and Rs = 1.94 (baseline resolved), and only about 2116 plates are needed for Rs = 1.5; a peak at 5.0 min with w = 0.25 min has N = 6400. The chromatogram simulator turns a pasted peak table (name, tR, width, area) into Gaussian peaks, labels the resolution and overlap of each adjacent pair and exports SVG. The Van Deemter tab plots H = A + B/u + C·u with u_opt = √(B/C) and H_min = A + 2√(BC), and can least-squares fit A, B and C to measured (u, H) data. Quantification covers the internal standard method (relative response factor from a standard, then sample concentration), area normalization with optional response factors, and the USP tailing and asymmetry factors.

## How to use

1. Choose a mode: TLC Rf, column & resolution, chromatogram, Van Deemter or quantification
2. Drag spots on the TLC plate, or enter retention times, peak widths, dead time and column length — or paste a peak table from your data system
3. Read Rf, k, α, Rs, N, H, required plates, the simulated chromatogram and quantitative results, then copy values or export SVG

## Features

- Interactive TLC plate: drag origin, solvent front and spots in up to six lanes
- Automatic Rf matching of sample spots against same-plate references
- Retention factor k, selectivity α and resolution Rs from baseline or half-height widths
- Plate number N, plate height H, Purnell equation and plates / column length needed for Rs = 1.5
- Gaussian chromatogram from a pasted peak table, pairwise resolution and overlap, SVG export
- Van Deemter curve with u_opt and H_min, plus least-squares fit of A, B and C
- Internal standard response factor and concentration, area normalization and corrected normalization
- USP tailing factor T and 10%-height asymmetry factor As, with step-by-step working

## FAQ

### How do I calculate an Rf value, and can I compare it with literature values?

Rf = distance from the origin to the centre of the spot ÷ distance from the origin to the solvent front, so it lies between 0 and 1. A spot that moved 3.2 cm with the solvent front at 7.5 cm has Rf = 0.427. Rf depends strongly on adsorbent activity, eluent composition, temperature, loading and chamber saturation, so it reproduces poorly between labs. Run the reference on the same plate as the sample, ideally with a co-spot, instead of relying on a literature value.

### What resolution counts as baseline separation?

Rs = 2(tR2 − tR1)/(w1 + w2), with w the baseline width from tangents; with half-height widths Rs = 1.18(tR2 − tR1)/(w½1 + w½2). For two equal Gaussian peaks Rs = 1.0 still leaves about 2% overlap, while Rs = 1.5 leaves about 0.1%, so Rs ≥ 1.5 is taken as baseline resolution. The chromatogram tab shows the overlap of every adjacent pair.

### How are the plate number and plate height calculated?

N = 16(tR/w)² or N = 5.54(tR/w½)²; for a Gaussian peak they agree, because w = 4σ and w½ = 2.355σ (5.54 = 8 ln 2). A peak at tR = 5.0 min with w = 0.25 min gives N = 16 × 20² = 6400. Plate height H = L/N, so a 15 cm column with N = 6400 has H ≈ 23 µm. Higher N and lower H mean a more efficient column.

### What do the Purnell and Van Deemter equations tell me?

The Purnell equation Rs = (√N/4)·((α−1)/α)·(k/(1+k)) splits resolution into efficiency, selectivity and retention terms. Improving α is usually the most effective, because Rs grows only with √N: doubling the column length raises Rs by about 41%. Rearranged, it gives the plates required, N = 16Rs²(α/(α−1))²((1+k)/k)². The Van Deemter equation H = A + B/u + C·u describes plate height versus mobile-phase velocity. Its minimum lies at u_opt = √(B/C), where H_min = A + 2√(BC).

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