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.
tr = 10w = 0.25col_length = 25
- 01N = 16 × (10 / 0.25)² = 16 × 40² = 16 × 1600 = 25,600 plates
- 02HETP = 25 / 25600 = 0.000977 cm = 9.8 um
Ready to run the numbers?
Open Plate Number Calculator