Beer–Lambert law for absorbance and concentration
The Beer–Lambert law relates a sample’s absorbance to the concentration of an absorbing species, optical path length, and molar absorptivity at a selected wavelength.
The linear model is widely used in UV–visible spectrophotometry. Reliable work requires blank correction, appropriate wavelength selection, compatible units, and a concentration range where the instrument and sample obey the linear relationship.
How to use the Beer–Lambert law calculator
- Select the unknown: Choose absorbance, molar absorptivity, path length, or concentration.
- Enter three values: Provide the remaining values using L, mol, and cm compatible units.
- Calculate: Generate the missing value from A = εbc.
- Check linearity: Confirm the result lies within the validated calibration and instrument range.
Formula and variables
Absorbance equals molar absorptivity multiplied by optical path length and molar concentration.
A = εbc- A — Absorbance
- Base-10 logarithmic attenuation measure (dimensionless (AU))
- ε — Molar absorptivity
- Wavelength-dependent absorption coefficient (L/(mol·cm))
- b — Path length
- Distance light travels through the sample (cm)
- c — Concentration
- Amount concentration of absorbing species (mol/L)
Concentration from absorbance
A sample has absorbance 0.75 in a 1 cm cuvette and ε = 15,000 L/(mol·cm).
- A
- 0.75
- ε
- 15,000 L/(mol·cm)
- b
- 1 cm
- c = A/(εb)
- c = 0.75/(15,000 × 1)
- c = 5.0 × 10⁻⁵ mol/L
Result: The estimated concentration is 0.00005 mol/L, or 50 µmol/L.
The value is valid only if the sample and instrument behave linearly under the measurement conditions.
Understanding your results
Assessing the result
Absorbance should be blank-corrected and compared with a calibration or validated linear range.
- Unexpected absorbance can indicate scattering, contamination, saturation, or an incorrect blank.
- Molar absorptivity is specific to wavelength, chemical form, solvent, and conditions.
Assumptions
- Monochromatic light and a homogeneous, non-scattering sample.
- Independent absorbers and a sufficiently dilute solution.
- Compatible mol/L, centimetre, and L/(mol·cm) units.
Limitations
- High concentrations, chemical equilibria, stray light, fluorescence, and scattering can cause deviations.
- The calculator does not perform blank subtraction or calibration regression.
Common mistakes
- Using millimetres for path length without conversion.
- Treating absorbance as a percentage.
- Using ε measured at a different wavelength.
- Ignoring dilution performed before measurement.
Practical use cases
Quantitative spectrophotometry
Estimate analyte concentration when molar absorptivity and path length are known.
Method development
Check expected absorbance and select appropriate dilution or path length.
Frequently asked questions
Does absorbance have units?
Absorbance is dimensionless, though instruments commonly label it AU for absorbance units.
Can I use milligrams per millilitre for concentration?
Not directly with molar absorptivity in L/(mol·cm); convert mass concentration using molar mass or use a coefficient defined for those units.
Why does Beer–Lambert law fail at high absorbance?
Instrument stray light, detector limits, chemical interactions, and non-ideal solution behavior can make the response nonlinear.
Sources and review
- Beer–Lambert law — IUPAC Compendium of Chemical Terminology. Accessed 2026-07-13.
- NIST/SEMATECH e-Handbook of Statistical Methods: Calibration — National Institute of Standards and Technology. Accessed 2026-07-13.
Reviewed 2026-07-13.