Engineering
Beer-Lambert Law formula: Absorbance (2 - LOG10(%T)) & Molar Concentration
Convert UV-Vis % Transmittance into Optical Absorbance A = 2 - LOG10(%T) and calculate unknown analyte concentration c = A / (ε · l).
Spectrophotometry essentials: % Transmittance is logarithmic, Concentration is linear in A!
Enter percent transmittance as a number greater than 0 and at most 100: 25 means 25%, not the spreadsheet percentage value 0.25. Absorbance is -LOG10(T) for fractional transmittance T, equivalently 2-LOG10(percent T). Zero transmittance has no finite absorbance.
Under Beer-Lambert conditions A=epsilon*l*c. Use a calibrated molar absorptivity for the analyte, wavelength, solvent and conditions, in L/(mol cm), with path length in cm. The example epsilon=12000 is illustrative. Concentration in mol/L multiplied by one million gives micromolar.
This assumes a suitable linear absorbance range, blank correction and negligible scattering/interference. Instrument limitations and chemical equilibria can break linearity. Do not use a generic coefficient for an unidentified sample.
| % Transmittance (%T) | Optical Absorbance A = 2 - LOG10(%T) | Concentration (µM, ε=12,000, l=1 cm) |
|---|---|---|
| 100% T (Solvent Blank) | 0.0000 AU | 0.00 µM |
| 25% T (Sample) | 0.6021 AU | 50.17 µM |
| 10% T (Concentrated) | 1.0000 AU | 83.33 µM |
Optical Absorbance from % Transmittance and Beer-Lambert Concentration (µM)
2 - LOG10(A2) is algebraically identical to -LOG10(A2 / 100) when %T is entered on the 0–100 scale (e.g., 25 for 25% T).
=IF(OR(NOT(ISNUMBER(A2)),A2<=0,A2>100),"Invalid transmittance",ROUND(2-LOG10(A2),4))Solve unknown sample concentration in micromolar (µM) from %T, ε (B2), and path l (C2)
Multiplies Molarity mol/L by 1,000,000 (10⁶) to report convenient micromolar (µM) assay units.
=IF(OR(COUNT(A2:C2)<>3,A2<=0,A2>100,B2<=0,C2<=0),"Invalid inputs",ROUND((2-LOG10(A2))/(B2*C2)*1000000,2))Try the example
Use the original values or change them to test your understanding.