Plate Number Calculator Formula
Understand the math behind the plate number calculator. Each variable explained with a worked example.
Formulas Used
Theoretical Plates (N)
plates = 16 * pow(tr / w, 2)Plate Height (HETP)
hetp = col_length / (16 * pow(tr / w, 2))Plate Height
hetp_um = col_length * 10000 / (16 * pow(tr / w, 2))Variables
| Variable | Description | Default |
|---|---|---|
tr | Retention Time (tR)(min) | 10 |
w | Peak Width at Base (w)(min) | 0.25 |
col_length | Column Length (L)(cm) | 25 |
How It Works
Theoretical Plate Number
The plate count N measures column efficiency. Higher N means sharper peaks and better separation potential.
Formula
N = 16 × (tR / w)²
HETP = L / N
where w is the peak width at the base (4-sigma). Modern HPLC columns typically give N = 10,000-20,000 per 25 cm column. UHPLC with sub-2-um particles can achieve 30,000+ plates.
Worked Example
A peak at 10 min with 0.25 min base width on a 25 cm column.
- 01N = 16 × (10 / 0.25)² = 16 × 40² = 16 × 1600 = 25,600 plates
- 02HETP = 25 / 25600 = 0.000977 cm = 9.8 um
Frequently Asked Questions
What is a good plate count?
For a 25 cm HPLC column: N > 10,000 is acceptable, > 15,000 is good, > 20,000 is excellent. For GC capillary columns: N can exceed 100,000 due to much longer columns.
Why does plate height matter?
HETP measures efficiency per unit length. Smaller particles give lower HETP (higher efficiency). A 5 um particle column has HETP ~10 um at optimum flow, while a 1.7 um column achieves ~3.5 um.
What causes low plate count?
Extra-column band broadening (dead volume in tubing and fittings), column deterioration, voids at column head, temperature gradients, and operating far from the optimum flow rate.
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