Translator for HPLC HINTS and TIPS for Chromatographers

Saturday, June 2, 2018

Number of theoretical plates (N), Calculation Formulas

Number of theoretical plates (N):

Often used to quantify the efficiency (performance) of a column (HPLC or GC). "Plates" are expressed per meter of column length and should be calculated based on a retained peak with ideal peak shape or symmetry. 

   N = Plates; tr = Retention Time of Peak; w = Peak width;  w0.5 = Peak width measured at half height.

Two popular formulas are:

Tangent: USP (United States Pharmacopeia)

Best for Gaussian peaks. Peak width is often determined at 13.4% of the peak height (w). Inaccurate for peaks which are non-Gaussian, poorly resolved or tail.

   N = 16 (tr / w)2

Half Peak Height: (European Pharmacopeia)

For peaks which are less Gaussian in appearance, using a slightly different formula with the peak width measurement made at the half-height (W0.5). Less accurate for peaks which are poorly resolved or tail.

   N = 5.54 (tr / w0.5)2

  • Other formulas, not included, for calculating Plate numbers include: Area / Height & Exponential Modified Gaussian (EMG).

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