{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"beer-lambert"},"result":{"entity_type":"calculator","id":"beer-lambert","calculator_id":"beer-lambert","canonical_url":"https://tttkmbb.com/chemistry/beer-lambert","name":"Beer–Lambert Law Calculator","title":"Beer–Lambert Law Calculator – Absorbance, Concentration, Molar Absorptivity or Path Length (A = εlc)","category":"chemistry","category_name":"Chemistry","tool_name":"calculate_beer_lambert_law","featured_mcp_tool":false,"description":"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).","use_when":"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.","inputs":[{"name":"mode","label":"Solve for","type":"enum","required":false,"default":"concentration","values":[{"value":"concentration","label":"Concentration c","aliases":["c","concentration_mol_l"]},{"value":"absorbance","label":"Absorbance A","aliases":["a"]},{"value":"molar_absorptivity","label":"Molar absorptivity ε","aliases":["epsilon","extinction_coefficient","molar_absorptivity_l_mol_cm"]},{"value":"path_length","label":"Path length l","aliases":["l","path_length_cm"]}],"description":"Quantity to solve for; the other three must be given (path_length_cm defaults to a 1 cm cuvette).","example":"concentration"},{"name":"absorbance","label":"Absorbance A","type":"number","required":false,"min":0,"max":10,"description":"Blank-corrected absorbance (optical density, base-10, dimensionless). Leave empty when solving for it.","example":0.622},{"name":"molar_absorptivity_l_mol_cm","label":"Molar absorptivity ε","type":"number","unit":"L/(mol·cm)","required":false,"max":10000000,"exclusive_min":0,"description":"Molar (decadic) absorption coefficient at the measurement wavelength, e.g. 6220 for NADH at 340 nm. Leave empty when solving for it.","example":6220},{"name":"path_length_cm","label":"Path length l","type":"number","unit":"cm","required":false,"default":1,"max":1000,"exclusive_min":0,"description":"Optical path length through the sample (inner cuvette width); standard cuvettes are 1 cm. Ignored when mode = path_length.","example":1},{"name":"concentration_mol_l","label":"Concentration c","type":"number","unit":"mol/L","required":false,"max":100,"exclusive_min":0,"description":"Molar concentration of the absorbing species. Leave empty when solving for it."}],"outputs":[{"name":"absorbance","label":"Absorbance A","type":"number","decimals":4,"description":"Base-10 absorbance, given or solved."},{"name":"molar_absorptivity_l_mol_cm","label":"Molar absorptivity ε","type":"number","unit":"L/(mol·cm)","decimals":3,"description":"Molar absorption coefficient, given or solved."},{"name":"path_length_cm","label":"Path length l","type":"number","unit":"cm","decimals":4,"description":"Optical path length, given or solved."},{"name":"concentration_mol_l","label":"Concentration c","type":"number","unit":"mol/L","decimals":10,"description":"Molar concentration, given or solved."},{"name":"concentration_scientific","label":"Concentration (scientific)","type":"string","decimals":4,"description":"The concentration in scientific notation, mol/L."},{"name":"concentration_umol_l","label":"Concentration","type":"number","unit":"µmol/L","decimals":4,"description":"The same concentration in micromoles per litre (µM)."},{"name":"transmittance_percent","label":"Transmittance","type":"number","unit":"%","decimals":2,"description":"100 × 10^(−A): share of the incident light that passes through the sample."},{"name":"solved_for","label":"Solved for","type":"string","decimals":4,"description":"Name of the output that was computed: absorbance, molar_absorptivity_l_mol_cm, path_length_cm or concentration_mol_l."}],"input_schema":{"type":"object","properties":{"mode":{"description":"Quantity to solve for; the other three must be given (path_length_cm defaults to a 1 cm cuvette).","type":"string","enum":["concentration","absorbance","molar_absorptivity","path_length"],"default":"concentration","examples":["concentration"]},"absorbance":{"description":"Blank-corrected absorbance (optical density, base-10, dimensionless). Leave empty when solving for it.","type":"number","minimum":0,"maximum":10,"examples":[0.622]},"molar_absorptivity_l_mol_cm":{"description":"Molar (decadic) absorption coefficient at the measurement wavelength, e.g. 6220 for NADH at 340 nm. Leave empty when solving for it. Unit: L/(mol·cm).","type":"number","maximum":10000000,"exclusiveMinimum":0,"examples":[6220],"x-unit":"L/(mol·cm)"},"path_length_cm":{"description":"Optical path length through the sample (inner cuvette width); standard cuvettes are 1 cm. Ignored when mode = path_length. Unit: cm.","type":"number","maximum":1000,"exclusiveMinimum":0,"default":1,"examples":[1],"x-unit":"cm"},"concentration_mol_l":{"description":"Molar concentration of the absorbing species. Leave empty when solving for it. Unit: mol/L.","type":"number","maximum":100,"exclusiveMinimum":0,"x-unit":"mol/L"}},"additionalProperties":false},"output_schema":{"type":"object","properties":{"absorbance":{"description":"Base-10 absorbance, given or solved.","type":"number"},"molar_absorptivity_l_mol_cm":{"description":"Molar absorption coefficient, given or solved. Unit: L/(mol·cm).","type":"number","x-unit":"L/(mol·cm)"},"path_length_cm":{"description":"Optical path length, given or solved. Unit: cm.","type":"number","x-unit":"cm"},"concentration_mol_l":{"description":"Molar concentration, given or solved. Unit: mol/L.","type":"number","x-unit":"mol/L"},"concentration_scientific":{"description":"The concentration in scientific notation, mol/L.","type":"string"},"concentration_umol_l":{"description":"The same concentration in micromoles per litre (µM). Unit: µmol/L.","type":"number","x-unit":"µmol/L"},"transmittance_percent":{"description":"100 × 10^(−A): share of the incident light that passes through the sample. Unit: %.","type":"number","x-unit":"%"},"solved_for":{"description":"Name of the output that was computed: absorbance, molar_absorptivity_l_mol_cm, path_length_cm or concentration_mol_l.","type":"string"}}},"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)","method":"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.","sources":[{"name":"Wikipedia – Beer–Lambert law","url":"https://en.wikipedia.org/wiki/Beer%E2%80%93Lambert_law","type":"reference","retrieved_at":"2026-09-24"},{"name":"IUPAC Gold Book – Beer–Lambert law","url":"https://goldbook.iupac.org/terms/view/B00626","type":"standard","retrieved_at":"2026-09-24"},{"name":"LibreTexts – The Beer-Lambert Law","url":"https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Spectroscopy/Electronic_Spectroscopy/Electronic_Spectroscopy_Basics/The_Beer-Lambert_Law","type":"textbook","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Absorbance of 1.0×10⁻⁴ M NADH at 340 nm (ε 6220, 1 cm cuvette)","inputs":{"mode":"absorbance","molar_absorptivity_l_mol_cm":6220,"path_length_cm":1,"concentration_mol_l":0.0001},"expected":{"absorbance":0.622,"transmittance_percent":23.88,"concentration_umol_l":100,"solved_for":"absorbance"},"url":"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"},{"name":"Concentration from A = 0.500 with ε 6220 in a 1 cm cuvette","inputs":{"mode":"concentration","absorbance":0.5,"molar_absorptivity_l_mol_cm":6220},"expected":{"concentration_mol_l":0.000080386,"concentration_scientific":"8.039e-5","concentration_umol_l":80.386,"transmittance_percent":31.62,"solved_for":"concentration_mol_l"},"url":"https://tttkmbb.com/api/v1/calculate/beer-lambert?mode=concentration&absorbance=0.5&molar_absorptivity_l_mol_cm=6220"}],"faq":[{"q":"What if my ε is in mM⁻¹cm⁻¹ or the concentration in mg/L?","a":"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."},{"q":"Why is absorbance above 2 unreliable?","a":"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."},{"q":"Is absorbance the same as optical density?","a":"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."}],"tags":["beer-lambert law","absorbance","molar absorptivity","extinction coefficient","spectrophotometer concentration","transmittance"],"related":[{"calculator_id":"molarity","reason":"Prepare a standard of known molarity for the calibration."},{"calculator_id":"dilution","reason":"Dilute a sample whose absorbance is outside the linear range."}],"links":{"html":"https://tttkmbb.com/chemistry/beer-lambert","markdown":"https://tttkmbb.com/chemistry/beer-lambert.md","json":"https://tttkmbb.com/chemistry/beer-lambert.json","api":"https://tttkmbb.com/api/v1/calculate/beer-lambert","schema":"https://tttkmbb.com/api/v1/calculators/beer-lambert","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:45:09Z"}