Chromatography calculations These are the equations which is used to calculate various things during chromatography including column volume, media requirements for column, resolution etc Total or Empty column volume Ve = π * r2 * L or 1/4 π * d2 * L Ve = empty column volume r = column radius L = length of the column (or packed bed) D = column diameter If r (or d) and L are expressed in mm, Ve will be in µL. If in cm, then Ve in mL. Volumetric Flow Rate (VFR) Calculation from Linear Flow Rate (LFR) This can be useful because the chromatographic media has certain flow rate specification at which it can be operated, for example a chromatographic media specification says use 150 cm/hr flow rate so while setting up the flow rate in peristaltic pump or in other automated system like AKTA volumetric flow rate need to be calculated, using the equation below it can be calculated. VFR (ml/min) = LFR(cm/hr) / 60 * πr2 we need 150cm/hr and the column used has a diameter of 0.5cm or 0.25cm as radius so, VFR = 150/60 * 3.14 * (0.25)2 ; Volumetric flow rate will be ~ 0.5 ml/min Linear Flow Rate (LFR) Calculation from Volumetric Flow Rate (VFR) LFR(cm/hr) = VFR(ml/min) * 60 / πr2 Similarly we need 1ml/min and the column used has a diameter of 0.5cm or 0.25cm as radius so, LFR(cm/hr) = 1 * 60 / ( 3.14 * (0.25)2 ) Linear flow rate will be ~ 300 cm/hr Bed Volume Bed volume (L) = Bed height (cm) * Column cross-sectional area (cm2) / 1000 cross-sectional area = π * r2 Packed Bed Volume Packed bed volume (L) = Column bed height (cm) * cross-sectional area (cm2) * x10-3 cross-sectional area = π * r2 Settled chromatography medium volume Settled chromatography medium volume (L) = Packed bed volume (L) * compression factor compression factor can be obtained from the chromatographic media specification sheet. Slurry volume Slurry volume (L) = Settled chromatography medium volume (L) / (slurry concentration (%) * x 10-2) The chromatography medium volume for HIC, IEX, Affinity, Reverse Phase The chromatography medium volume is calculated from the formula: The chromatography medium volume (L) = (Quantity to be bound (g) * (1+ safety margin (%) / 100)) / (Dynamic binding capacity (g/L) The chromatography medium volume for Gel Filtration Chromatography The chromatography medium volume (L) = Sample volume to be processed (L) / (Sample volume in percent of total column volume (%) / 100) Resolution (Rs) Chromatographic peak resolution can be calculated using the following equation Rs = (tR1 – tR2) / 0.5(W1 + W2) Rs – Resolution tR1 – Retention time of the first peak tR2 – Retention time of the second peak w1 – Width of first peak w2 – width of second peak Sources & References GE Life Sciences - Chromatography medium volume calculators Tosoh Bioscience LLC: The Chemistry of Innovation - Technical Support – Basic Chromatographic Calculations Got something to say about this post? Leave a comment...your comments are valuable for improving the posts.