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;  w_0.5 = Peak width measured at half height.

Two popular formulas are:

Tangent: USP (United States Pharmacopeia / ASTM)

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 (W_0.5). Less accurate for peaks which are poorly resolved or tail.

   N = 5.54 (tr / w_0.5)²

 

• Other formulas, not included, for calculating Plate numbers include: Half Width, Variance Method, Area / Height & Exponential Modified Gaussian (EMG).
• Caution. HPLC column "Plate" values should not be used for a final determination of efficiency unless you are comparing all results on the same exact HPLC system, which is setup and run under identical conditions each time. Since the result is based on many possible variables, including how your HPLC system is plumbed (dwell volume & tubing ID), the peak's Kprime and symmetry, the detector used, sampling rate, integration quality, flow cell volume, flow rate, actual column used (to name a few), it can easily be manipulated to be very large or small.