# Equations

## by Pritesh Patel, PharmD

The equations used to calculate values are presented on this page. These equations are for adult patients and cannot be used for infants and pediatric patients. Click on an equation to display a larger image.

# Creatinine Clearance

• Cockroft-Gault estimation: $\text{Cl} = \frac{140 - \text{age}}{72\times \text{S}_{\text{cr}}}$, where Scr is serum creatinine; multiply by 0.85 for women; for age 65 and over, if Scr is < 1, round up to 1
• Jelliffe estimation: $\text{Cl} = \frac{98 - 0.8\times(\text{age} - 20)}{\text{S}_{\text{cr}}}$, multiply by 0.9 for women

Cl = creatining clearance; Scr = serum creatinine

# Iron Dextran Dosing

$\text{dose in mL }= 0.0422 \times [\text{desired Hb} - \text{patient's Hb}]\times\text{IBW} + (0.26 \times \text{IBW})$
• Hb = hemoglobin.
• The formula gives the dose in mL for iron dextran 50 mg elemental iron per mL.
• Multiply the dose in mL by 50 to get dose in mg of iron dextran.
• Use weight in kilograms. Ideal body weight is the same as lean body weight.

# Vancomycin Prospective Assessment

These equations are used to prospectively dose vancomycin. The equations are extrapolated from population averages.

• Elimination rate constant (ke in hr-1): $k_{e} = 0.00083 \times \text{Cl} + 0.0044$, where Cl is the renal clearance.
• Volume of distribution (Vd in L): $V_{d} = V _{d} \text{ factor} \times \text{BW}$, where BW is the actual body weight. The Vd factor is a range from 0.7 to 0.85. For a typical patient, use 0.75. For elderly, use a higher value such as 0.8 to 0.85.
• The steady-state peak is estimated using the equation: ${{C}_{sspeak}}=\frac{\text{Dose}\cdot (1-{{e}^{-{{k}_{e}}t'}})}{{{k}_{e}}\cdot {{V}_{d}}\cdot t'\cdot (1-{{e}^{-{{k}_{e}}T}})}$, where t' is the infusion time in hours.
• Once stead-state peak is obtained, steady-state trough can be estimated with: ${C}_{sstrough}={{C}_{sspeak}}\cdot {{e}^{-{{k}_{e}}(T-t')}}$, where T is the dosing interval in hours.

# Aminoglycoside Prospective Assessment

These equations are used to prospectively dose aminoglycosides (traditional dosing). The equations are extrapolated from population averages.

• Elimination rate constant (ke in hr-1): $k_{e} = 0.00285 \times \text{Cl} + 0.014$, where Cl is the renal clearance.
• Volume of distribution (Vd in L): $V_{d} = V _{d} \text{ factor} \times \text{BW}$, where BW is the IBW unless if actual body weight is less than IBW. Use adjusted BW for obese patient. The Vd factor is a range from 0.25 to 0.28.
• The steady-state peak is estimated using the equation: ${{C}_{sspeak}}=\frac{\text{Dose}\cdot (1-{{e}^{-{{k}_{e}}t'}})}{{{k}_{e}}\cdot {{V}_{d}}\cdot t'\cdot (1-{{e}^{-{{k}_{e}}T}})}$, where t' is the infusion time in hours.
• Once stead-state peak is obtained, steady-state trough can be estimated with: ${C}_{sstrough}={{C}_{sspeak}}\cdot {{e}^{-{{k}_{e}}(T-t')}}$, where T is the dosing interval in hours.

# Vancomycin Iteration Kinetics

It is not always necessary to obtain a vancomycin peak. A trough level can be obtained and this level can be used to obtain a theoretical peak using the iteration formula. Then, the actual trough and iterated peak can be used to find ke and Vd using actual assessment equations above.

• Calculate estimated Vd from prospective equations above.
• Estimated ke: ${{k}_{e}}=-\frac{\ln \left( {}^{\frac{\text{tr}\cdot {{V}_{d}}}{\text{dose}}}\!\!\diagup\!\!{}_{1+\frac{\text{tr}\cdot {{V}_{d}}}{\text{dose}}}\; \right)}{T}$, where T is the dosing interval.

# Weights

• $\text{IBW} = 50 + 2.3\times(\text{inches over 60})$ for men and $\text{IBW} = 45 + 2.3\times(\text{inches over 60})$ for women
• $\text{ABW} = \text{IBW} + 0.4\times(\text{actual W} - \text{IBW})$ if actual weight is 120% or greater than IBW

W = weight; IBW = ideal body weight; ABW = adjusted body weight

# Body-surface Area

$\text{BSA = }\sqrt{\frac{\text{height (in)} \times \text{weight (lb)}}{3131}}$
$\text{BSA = } \sqrt{\frac{\text{height (cm)} \times \text{weight (kg)}}{3600}}$

# Temperature Conversions

• Celcius to Fahrenheit: $\text{C} = \frac{5}{9}\times(\text{F} - 32)$
• Fahrenheit to Celcius: $\text{F} = \frac{9}{5}\times\text{C} + 32$

# Low Albumin Corrections

• Phenytoin (Dilantin): $\text{corrected phenytoin} = \frac{\text{lab phenytoin}}{0.2\times\text{albumin} + 0.1}$
• Calcium: corrected calcium = (normal albumin - patient's albumin)×0.8 + patient's measured calcium

The equation provided on this page are based on the principles and equations of pharmacokinetics and those found in popular reference books. The results from these calculations should not replace the clinical judgment of the practitioner. This site assumes no responsibility for injudicious interpretation of calculations.