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 (%)

The specificity is the probability that a given person who does not have a condition (i.e., is healthy) would actually test negative.

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

Sensitivity Calculation (%)

The sensitivity is the probability that a given person who has a condition (e.g., disease) would actually test positive.

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

Negative Predictive Value (%)

The negative predictive value (NPV) is a measure of how often someone who tests negative for a disease will not have the disease.

$$\text{Negative Predictive Value}=\frac{\text{True Negatives}}{\text{True Negatives }+\text{ False negatives}}$$

Positive Preductive Value (%)

The positive predictive value (PPV) is a measure of how often someone who tests positive for a disease will actually have the disease.

$$\text{Positive Predictive Value}=\frac{\text{True Positives}}{\text{True Positives }+\text{ False positives}}$$

Blood pH & Respiration

Blood pH Calculations (unitless)

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

OR

$$pH=6.1+log\frac{[HC{O}^{-}]}{dC{O}_2}$$

dCO₂ = dissolved CO₂ (mmol/L)

PCO₂ = partial pressure CO₂ (mmHg)

[HCO^-] = concentration of bicarbonate (mmol/L)

Conversion Between PCO₂ (mmHg) and dCO₂ (mmol/L)

$$dC{O}_2=PC{O}_2\ast 0.03$$

Calculation of HCO₃^- (mmol/L)

Used when TCO₂ is measured via a wet or dry methodology.

$$[HC{O}_3^{-}]=T_{C{O}_2}-1.2\text{ mmol/L}$$

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:

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

Freezing Point Depression (°C)

Calculates the freezing temperature based on osmolality.

$$\text{Osmolality (mmol/kg)}=\frac{\text{FP Depression}}{1.86\text{°C}}\ast 100$$

Anion Gap - North America (mmol/L)

The anion gap estimates the difference in cations vs. anions in blood. It can be used to help investigate acid-base disturbances and issues with electrolyte measurement. Potassium (K⁺) ions are not included in this calculation in North America.

$$\text{Anion gap}=(N{a}^{+})-(C{l}^{-}+HC{O}_3^{-})$$

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.

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

Absorbance & Measurement

Determining Unknown Concentration by Absorbance

$$[Unknown]=\frac{Ab{s}_u\ast [Standard]}{Ab{s}_s}$$