This Beer-Lambert calculator solves A = εbc in every direction — absorbance, molar absorptivity, path length or concentration — and converts absorbance to percent transmittance, the two languages spectrophotometers speak.
Light as a Measuring Tape
The law in one line: A = ε · b · c. Absorbance grows linearly with concentration and with path length, scaled by ε — how greedily the molecule drinks light at the chosen wavelength (ε ranges from ~10 for weak transitions to >100,000 for dyes; it's tabulated at λ-max). That linearity is why UV-Vis spectroscopy is analytical chemistry's concentration meter for anything colored — or made colorable. Concentrations connect to our Molarity Calculator and dilution workups. Part of our Chemistry Calculators collection.
Worked Example (Verified)
A = 0.450, ε = 25,000 L/mol·cm (a strongly absorbing analyte at its λ-max), 1 cm cuvette:
- c = 0.450 ÷ (25,000 × 1) = 1.8 × 10⁻⁵ mol/L = 18 µM — the widget's defaults: micromolar sensitivity is spectrophotometry's party trick
- Its transmittance: %T = 10^(−0.450) × 100 = 35.5% of the light survives the cuvette
- Double the concentration (36 µM) and A doubles to 0.900 (%T drops to 12.6%) — linear in A, logarithmic in light: check your intuition against both scales
Where the Law Bends
- High concentrations: above A ≈ 1–2, stray light and molecular interactions curve the line — dilute into the honest range (0.1–1.0 A) rather than trusting the extrapolation.
- ε belongs to one wavelength and one solvent/pH environment; measuring off λ-max or after a pH shift rewrites it.
- Scattering (turbid samples) fakes absorbance — the instrument can't tell absorbed light from deflected light.
- Standard curves (known concentrations → measured A → fit) remain the professional method; this calculator is the algebra they're built from.
Related Tools
- Dilution Calculator — bringing samples into range
- Molarity Calculator — preparing the standards
- Chemistry Calculators — the full collection
Frequently Asked Questions
What is the Beer-Lambert law formula?
A = εbc: absorbance equals molar absorptivity (L/mol·cm) × path length (cm) × concentration (mol/L). Absorbance itself is unitless, defined as −log₁₀(transmittance).
How do you calculate concentration from absorbance?
c = A ÷ (ε × b). With A = 0.450, ε = 25,000 and a 1 cm cuvette: c = 1.8×10⁻⁵ M. You need ε at your wavelength — from literature or from a standard of known concentration.
What is a good absorbance range?
Roughly 0.1–1.0 for accuracy: below it, noise dominates; above ~1.5–2, so little light reaches the detector that stray light and detector limits bend results. Dilution (or a shorter-path cuvette) fixes the top end.
How are absorbance and transmittance related?
A = −log₁₀(%T/100): A 0 = 100% T, A 1 = 10%, A 2 = 1%, A 3 = 0.1%. Old instruments read %T; modern work uses A because only A is linear in concentration.
Why does my standard curve curve?
Usually concentration range (the law's dilute-solution assumption fades), chemical changes in the analyte (dimerization, pH equilibria shifting the absorbing species), or instrument stray light. Each has a different cure — narrower range, buffered pH, or a better instrument.
Is this Beer-Lambert calculator free?
Yes — free, instant, no sign-up.