Chemistry Calculations

Statistics & Quality Control

Mean/Average (unit)

The mean is the average of a series of numbers. Report to the same units and decimal places as the data.

$$\overline{x}=\frac{x_1+x_2+\mathrm{...}+x_n}{n}$$

Sample Standard Deviation (same unit as data)

Use standard deviation when the mean of two methods is the same. Report as +1 decimal place more than the data.

$$s=\sqrt{\frac{\Sigma (x-\overline{x}{)}^2}{n-1}}$$where x = data and $\overline{x}=\text{Mean}$

Coefficient of Variation (%)

Use coefficient of variation when the mean of two methods is different. Report to 1 decimal place.

$$CV=\frac{SD}{Mean}\ast 100$$

Percent Error (%)

Report to 1 decimal place.

$$\mathrm{\%}\mathrm{E}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}=\frac{Actual-Theoretical}{Theoretical}\ast 100\mathrm{\%}$$

Westgard Rules

There are 4 reject rules and 2 warning rules:

• 1-3s (one control value exceeds the mean ±3 SD)
• 2-2s (two consecutive control values exceed the mean ±2 SD)
• R-4s (when one value exceeds the mean +2 SD and another value exceeds -2 SD within the same run so that the values are 4 SD different from each other)
• 4-1s (four consecutive control values exceed the mean ±1 SD)

Warning Rules:

• 1-2s (one control value exceeds the mean ±2 SD)
• R10x (ten consecutive values fall on one side of the mean)

Specificity Calculation (%)

$$Specificity=\frac{\text{True Negatives}}{\text{True Negatives }+\text{ False positives}}$$

Sensitivity Calculation (%)

$$Sensitivity=\frac{\text{True Positives}}{\text{True Positives }+\text{ False negatives}}$$

Blood pH & Respiration

Blood pH Calculations (unitless)

$$pH=6.1+log\frac{[HC{O}^{-}]}{0.03\ast P_{CO2}}$$

dCO₂ = dissolved CO₂

PCO₂ = partial pressure CO₂

[HCO^-] = concentration of bicarbonate

Kidney Function Testing

Creatinine Clearance (mL/s)

Creatinine clearance is (U*V)/S and the corrected creatinine clearance uses BSA to correct for size/muscle mass.

$$CC=\frac{U\ast V}{S}\ast \frac{1.73}{BSA}$$

$$CC=\frac{\text{[Urine Creatinine]}\ast \text{Urine flow}]}{\text{[Serum creatinine]}}\ast \frac{1.73}{\text{Body surface area}}$$

Convert mmol/L to mmol/day:

$$\text{24h excretion}=\frac{\text{24h urine volume }\ast \text{ [Analyte]}}{1000}$$

U = urine creatinine (μmol/L)

S = serum creatinine (μmol/L)

V = urine flow rate (mL/s) - this is the 24h volume (mL) divided by 86 400 seconds per 24h

BSA = body surface area (m²) - calculate using height and weight on nomogram

Creatinine (mmol/d)

Used as measure of creatinine levels from 24h urine.

$$Creatinine=\frac{V\ast c}{1000}$$

$$=\frac{\text{Urine volume }\ast [Creatinine]}{1000}$$

eGFR Estimated Glomerular Filtration Rate

Complicated calculation using standardized serum creatinine and many correction factors for age and gender.

Electrolytes & Osmolality

Osmolal Gap (Osm/kg)

Calculates difference between expected osmolality vs actual osmolality. High osmolar gap may be due to presence of volatile or osmotically active compounds like ethanol, methanol, etc.

$$\text{Calculated Osmolality}=2\ast [N{a}^{2+}]+[Urea]+[Glucose]$$

From this, the osmolar gap can be calculated:

$$\text{Osmolar Gap}=\text{Measured Osmolality}-\text{Calculated Osmolality}$$

Dilutions & Concentrations

Calculating Dilutions Using Dilution Factors and Total Volume

You can determine the amount of solute required for a dilution with a given dilution factor and final (total) volume.

$$DF=\frac{V_{total}}{V_{solute}}$$

$$V_{solute}=\frac{V_{total}}{DF}$$

DF = dilution factor (e.g., in a 1:250 dilution, the DF is 250)

You can then determine the amount of diluent/solvent needed from the calculated volume of solute required.

$$V_{diluent}=V_{total}-V_{solute}$$