Beer–Lambert Law
A = εcl for absorbance, concentration, molar absorptivity or path length, absorbance ↔ transmittance, and a calibration curve that reads unknown samples.
The quantity you solved for with the transmittance beside it, or a fitted calibration line with slope, intercept, R² and residuals, the concentration of a sample read off it, and dilution applied.
Example: A = 0.65 with ε 14 500 L/(mol·cm) in a 1 cm cell is 44.8 µM, transmitting 22.4 % of the light. Five standards fit A = 621.5·c with R² 0.9999, so a sample reading 0.310 AU is 499 µM.
Absorbance is linear
in concentration — for a while.
The law, the logarithm behind transmittance, and why a calibration curve beats a single ε.
A = εcl
Absorbance is the molar absorptivity times the concentration times the path length: dimensionless, because ε carries L/(mol·cm) against c in mol/L and l in cm. Solve it for any of the four. ε belongs to a substance *at one wavelength* in one solvent at one pH — quoting it without the wavelength is meaningless, and a shift in pH that changes the species changes ε with it.
Absorbance and transmittance
A = −log₁₀ T, where T is the fraction of light getting through, so A = 1 lets 10 % through, A = 2 lets 1 % and A = 3 only 0.1 %. That logarithm is why high absorbances are noisy: the detector is measuring a vanishing signal against its own dark current and any stray light in the instrument. Below about A = 0.1 the opposite problem appears — the reading is a small difference between two large numbers. Most work sits between 0.1 and 1.
Why calibrate
Rather than trust a published ε, measure standards of known concentration and fit a line. The page does least squares either through the origin (the physically correct form when the blank is right) or with an intercept, reporting the slope (= εl), R² and each residual, then reads an unknown sample off the line and applies a dilution factor. An R² below 0.99 or a clear intercept says something is wrong — a bad blank, a mis-made standard, or a range where the law has stopped being linear. Association, dissociation, fluorescence and scattering from particles all bend it, so a sample reading above the highest standard is flagged rather than extrapolated. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- A = ε·c·l; A = −log₁₀ T = 2 − log₁₀(%T); calibration by least squares through the origin or with an intercept, R² from the residual and total sums of squares; linearity typically fails above A ≈ 1–2
Last reviewed 22 September 2026. How results are checked: How we verify.