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Beer–Lambert Law Calculator
Solves the Beer–Lambert law A = ε·l·c for the selected quantity (absorbance, concentration, molar absorptivity or path length) from the other three, and reports the percent transmittance T = 100 × 10^(−A).
When to use
You have a spectrophotometer absorbance and need the concentration of the absorbing species from its molar absorptivity, the expected absorbance of a solution, or the molar absorptivity or cuvette path length from a calibration measurement.
Do not use when: Absorbance is above about 2, or the sample is concentrated, turbid or chemically interacting (the law is linear only for dilute, non-scattering solutions in monochromatic light); for concentration from a weighed mass use molarity.
Formula
A = molar_absorptivity_l_mol_cm × path_length_cm × concentration_mol_l; c = A / (ε × l); ε = A / (l × c); l = A / (ε × c); transmittance_percent = 100 × 10^(−A)
A is the decadic absorbance log10(I0/I) and ε the molar decadic absorption coefficient, so ε is in L·mol⁻¹·cm⁻¹ with l in cm and c in mol/L. Linearity assumes monochromatic light and a dilute (below about 0.01 mol/L), homogeneous, non-scattering sample; above A ≈ 1.5–2 stray light and detector limits make readings unreliable.
Inputs
| Parameter | Type | Unit | Required | Description |
|---|---|---|---|---|
mode | enum: concentration | absorbance | molar_absorptivity | path_length | default concentration | Quantity to solve for; the other three must be given (path_length_cm defaults to a 1 cm cuvette). | |
absorbance | number | no | Blank-corrected absorbance (optical density, base-10, dimensionless). Leave empty when solving for it. Range: ≥ 0, ≤ 10 | |
molar_absorptivity_l_mol_cm | number | L/(mol·cm) | no | Molar (decadic) absorption coefficient at the measurement wavelength, e.g. 6220 for NADH at 340 nm. Leave empty when solving for it. Range: > 0, ≤ 10000000 |
path_length_cm | number | cm | default 1 | Optical path length through the sample (inner cuvette width); standard cuvettes are 1 cm. Ignored when mode = path_length. Range: > 0, ≤ 1000 |
concentration_mol_l | number | mol/L | no | Molar concentration of the absorbing species. Leave empty when solving for it. Range: > 0, ≤ 100 |
Outputs
| Output | Type | Unit | Description |
|---|---|---|---|
absorbance | number | Base-10 absorbance, given or solved. | |
molar_absorptivity_l_mol_cm | number | L/(mol·cm) | Molar absorption coefficient, given or solved. |
path_length_cm | number | cm | Optical path length, given or solved. |
concentration_mol_l | number | mol/L | Molar concentration, given or solved. |
concentration_scientific | string | The concentration in scientific notation, mol/L. | |
concentration_umol_l | number | µmol/L | The same concentration in micromoles per litre (µM). |
transmittance_percent | number | % | 100 × 10^(−A): share of the incident light that passes through the sample. |
solved_for | string | Name of the output that was computed: absorbance, molar_absorptivity_l_mol_cm, path_length_cm or concentration_mol_l. |
Example
Absorbance of 1.0×10⁻⁴ M NADH at 340 nm (ε 6220, 1 cm cuvette): {"mode":"absorbance","molar_absorptivity_l_mol_cm":6220,"path_length_cm":1,"concentration_mol_l":0.0001} → {"absorbance":0.622,"transmittance_percent":23.88,"concentration_umol_l":100,"solved_for":"absorbance"}
Concentration from A = 0.500 with ε 6220 in a 1 cm cuvette: {"mode":"concentration","absorbance":0.5,"molar_absorptivity_l_mol_cm":6220} → {"concentration_mol_l":0.000080386,"concentration_scientific":"8.039e-5","concentration_umol_l":80.386,"transmittance_percent":31.62,"solved_for":"concentration_mol_l"}
GET https://tttkmbb.com/api/v1/calculate/beer-lambert?mode=absorbance&molar_absorptivity_l_mol_cm=6220&path_length_cm=1&concentration_mol_l=0.0001
Machine access
- API:
GET https://tttkmbb.com/api/v1/calculate/beer-lambert(query parameters) orPOSTwith a JSON body{"inputs": {...}} - Schema: https://tttkmbb.com/api/v1/calculators/beer-lambert · Markdown: https://tttkmbb.com/chemistry/beer-lambert.md · JSON definition: https://tttkmbb.com/chemistry/beer-lambert.json
- MCP: server
https://tttkmbb.com/mcp, toolrun_calculator with calculator_id="beer-lambert" - OpenAPI operationId:
calculate_beer_lambert_law - Freshness:
static. Authentication: none. Rate limit: fair use (see rate limits).
Sources
- Wikipedia – Beer–Lambert law (reference)
- IUPAC Gold Book – Beer–Lambert law (standard)
- LibreTexts – The Beer-Lambert Law (textbook)
FAQ
What if my ε is in mM⁻¹cm⁻¹ or the concentration in mg/L?
Multiply an ε in mM⁻¹·cm⁻¹ by 1000 to get L·mol⁻¹·cm⁻¹ (NADH: 6.22 mM⁻¹cm⁻¹ = 6220). For mass concentrations divide by the molar mass to get mol/L, or use a specific absorbance in L·g⁻¹·cm⁻¹ and read the result as g/L.
Why is absorbance above 2 unreliable?
At A = 2 only 1 % of the light reaches the detector, so stray light and detector noise dominate and the response flattens; dilute the sample or use a shorter path length to bring A into the 0.1–1 range.
Is absorbance the same as optical density?
In practice yes for clear solutions: both are log10(I0/I). Optical density also includes light lost by scattering, which is why turbid samples deviate from the Beer–Lambert law.
Related calculators
- Molarity Calculator — Prepare a standard of known molarity for the calibration.
- Dilution Calculator — Dilute a sample whose absorbance is outside the linear range.