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Beer-Lambert Law Calculator

Chemistry

Calculate absorbance, concentration, or molar absorptivity using Beer-Lambert Law: A = ε × l × c. Solve for any variable from the other two.

6,220 M⁻¹cm⁻¹
M⁻¹cm⁻¹
1 cm
cm
0.1 mM
mM
0.622

Calculated Value

0.622
Transmittance (%T)
23.88
Absorbance (A)
0.622
Concentration
0.1

This calculator computes your Calculated Value, Transmittance (%T), Absorbance (A), Concentration from the values you enter.

Inputs
Solve ForMolar Absorptivity (ε)Path Length (l)Concentration (c)Absorbance (A)
Outputs
Calculated ValueTransmittance (%T)Absorbance (A)Concentration

What is a Beer-Lambert Law?

The Beer-Lambert Law Calculator solves for any one of the three variables in A = ε × l × c — absorbance (A), molar absorptivity (ε), or concentration (c) — given the other two. Select what you want to calculate, enter the known values, and get the result along with transmittance (%T).

Beer-Lambert Law is the quantitative foundation of UV-Vis spectrophotometry: absorbance is proportional to concentration (at fixed path length and extinction coefficient). This relationship enables quantitative determination of analyte concentration from a simple absorbance measurement. It is applied in every biochemistry, analytical chemistry, clinical, and industrial laboratory — from measuring DNA at 260 nm to running enzyme assays at 340 nm to determining blood glucose in hospital analysers.

The Beer-Lambert Law is the physical basis for calibration curves — the Calibration Curve Calculator builds the empirical A vs C plot when ε is unknown. For measuring DNA/RNA concentration after extraction and resuspension, the Resuspension Calculator uses these concentrations to compute buffer volumes. For enzymatic assays where NADH absorbance tracks substrate consumption, the Enzyme Activity Calculator converts this to enzyme Units.

How to use this Beer-Lambert Law calculator

  1. Select Solve For: Absorbance (A), Concentration (c), or Molar Absorptivity (ε).
  2. Enter the known values — leave the solve-for field unchanged.
  3. For solving A: enter ε (M⁻¹cm⁻¹), path length l (cm), and c (mM).
  4. For solving c: enter ε, l, and measured absorbance A.
  5. For solving ε: enter l, c (mM), and measured A.
  6. Check Transmittance — if %T < 5% (A > 1.3), dilute the sample before measurement.

Formula & Methodology

Beer-Lambert Law:

A = ε × l × c    where A = absorbance (dimensionless, log₁₀ scale)          ε = molar absorptivity (M⁻¹cm⁻¹)          l = path length (cm)          c = molar concentration (M)  Rearranged:   c (M) = A / (ε × l)     [solve for concentration]   ε = A / (l × c)          [solve for molar absorptivity]  Transmittance: T (%) = 10^(−A) × 100

Worked example — NADH consumption in LDH (lactate dehydrogenase) assay:

NADH (ε₃₄₀ = 6220 M⁻¹cm⁻¹, 1 cm cuvette) is oxidised to NAD⁺ (non-absorbing at 340 nm). Measured absorbance at time 0: A = 0.850; after 5 min: A = 0.540. ΔA = 0.310.

ΔA = ε × l × Δc → Δc = ΔA / (ε × l) = 0.310 / (6220 × 1) = 4.98 × 10⁻⁵ M = 0.0498 mM

For 1 mL assay: substrate consumed = 0.0498 mM × 1 mL = 0.0498 μmol = 49.8 nmol NADH in 5 min.

Activity = 49.8 nmol / 5 min / 1000 = 0.00996 μmol/min = 0.00996 U

For serum LDH clinical assay: normal range is 140–280 U/L. LDH isoenzymes (LDH1–5) have different tissue distributions — elevated total LDH in acute myocardial infarction (heart attack) was the classic diagnostic marker before troponin assays became standard at AIIMS, Apollo, and Fortis cardiology departments.

Frequently Asked Questions

Beer-Lambert Law (also Beer's Law or Beer-Lambert-Bouguer Law) states that the absorbance of a solution is directly proportional to the concentration of the absorbing species and the path length of light through the solution: A = ε × l × c, where A = absorbance (dimensionless), ε = molar absorptivity or extinction coefficient (M⁻¹cm⁻¹), l = path length (cm), c = molar concentration (M). It is the quantitative foundation of UV-Vis spectrophotometry — the most widely used analytical technique in chemistry, biochemistry, and pharmaceutical analysis worldwide.
Molar absorptivity ε (M⁻¹cm⁻¹) is the intrinsic property of a substance at a specific wavelength — how strongly it absorbs light per unit concentration. Representative values: NADH at 340 nm: ε = 6220 M⁻¹cm⁻¹ (used in enzyme assays). DNA at 260 nm: ε ≈ 10,000 M⁻¹cm⁻¹ per base. Haemoglobin (oxygenated) at 415 nm (Soret band): ε ≈ 125,000 M⁻¹cm⁻¹. Para-nitrophenol at 405 nm: ε ≈ 18,700 M⁻¹cm⁻¹. Tryptophan at 280 nm: ε ≈ 5500 M⁻¹cm⁻¹. Phenol red at 560 nm: ε ≈ 52,000 M⁻¹cm⁻¹. Very high ε indicates strong UV-Vis visibility; dyes with ε > 10⁵ M⁻¹cm⁻¹ are suitable for single-molecule detection.
Select what you want to solve for: Absorbance (A), Concentration (c), or Molar Absorptivity (ε). Enter the other two values. Path length (l) defaults to 1 cm (standard cuvette). The calculator returns the solved value, transmittance (%T), and confirms absorbance and concentration for reference. Default: solving for A with NADH ε=6220, l=1 cm, c=0.1 mM → A = 0.622 (well within linear range, A 0.1–1.0).
Transmittance (%T) = (I/I₀) × 100, where I = transmitted light intensity, I₀ = incident intensity. Absorbance A = −log₁₀(T/100) = −log₁₀(I/I₀). They are inversely related on a logarithmic scale: T = 100 × 10^(−A). At A=0: T=100% (no absorption). At A=1: T=10%. At A=2: T=1%. At A=3: T=0.1%. UV-Vis instruments measure T directly (photodetector ratio) and convert to A by software. Linear range: 0.1 ≤ A ≤ 1.0 is ideal — above A=1.5, stray light and detector non-linearity cause Beer-Lambert deviations; dilute the sample.
Real deviations from Beer-Lambert Law: (1) High concentration: intermolecular interactions (aggregation, quenching) change ε — most common above 10 mM. Dilute sample. (2) High absorbance (A > 1): stray light in the monochromator reaches the detector, causing apparent absorbance plateau — work below A=1.5. (3) Polychromatic radiation: Beer-Lambert strictly applies to monochromatic light; bandwidth errors if ε changes steeply with wavelength across the monochromator bandwidth. (4) Scattering: turbid solutions (cell suspensions, colloidal nanoparticles) scatter light, causing apparent absorbance overestimation — subtract baseline at a non-absorbing wavelength. NABL-accredited labs calibrate instruments with NIST-traceable standards to verify Beer-Lambert linearity.
Standard nucleic acid quantification: A₂₆₀ measurement in 1 cm path, with conversion factors: dsDNA: concentration (μg/mL) = A₂₆₀ × 50. ssDNA: concentration = A₂₆₀ × 33. RNA: concentration = A₂₆₀ × 40. These factors are derived from average ε values for nucleotide bases (A, T, G, C averages). NanoDrop instruments (Thermo Fisher) automate this — they use a 0.5–2 mm path length with software path length correction. Important: A₂₆₀/A₂₈₀ ratio ≥ 1.8 for DNA (≥ 2.0 for RNA) indicates adequate purity (free of protein contamination). The [Resuspension Calculator](/resuspension-calculator/) uses these concentrations to calculate buffer volumes for DNA stock preparation.
Bradford protein assay (595 nm): Coomassie Brilliant Blue G-250 absorbance; ε varies with protein species; BSA standard curve used — the [Calibration Curve Calculator](/calibration-curve-calculator/) builds this curve from standard data. Biuret assay (546 nm): ε = 7100 M⁻¹cm⁻¹ per peptide bond; less sensitive, used for concentrated samples. BCA assay (562 nm): most sensitive; ε ≈ 7500 M⁻¹cm⁻¹. DNS (dinitrosalicylic acid) assay (540 nm): reducing sugar quantification; used in carbohydrate analysis of Indian foods (starch, sucrose in jaggery/gur). Phenol-sulfuric acid (490 nm): total carbohydrate. Folin-Ciocalteu (760 nm): total polyphenols in Indian spices, tea, Ayurvedic herbs — standard in FSSAI food testing.
Clinical laboratory analysers (Siemens ADVIA, Roche COBAS, used in AIIMS and Narayana Health) apply Beer-Lambert Law for: (1) Haemoglobin: cyanmethaemoglobin method (540 nm); ε = 11,000 M⁻¹cm⁻¹; WHO reference method for Hb in NABL-accredited Indian haematology labs. (2) Bilirubin: 455–460 nm; jaundice diagnosis in NICU. (3) Creatinine (Jaffe reaction): 510 nm; renal function test. (4) Glucose (GOD-POD method): 505 nm; diabetes monitoring — critical in India with 77 million diabetics. (5) Cholesterol: Liebermann-Burchard reaction (620 nm). All these assays are validated against Beer-Lambert linearity before clinical use.
Standard path length l = 1 cm (1 cm cuvette). Common variations: Micro-volume: NanoDrop uses 0.5–2 mm path length (selectable) with software correction to 1 cm equivalent. Flow cells: 1 cm or 2 cm (doubles absorbance for same concentration). Micro-cuvettes (Hellma): 1 cm, 100 μL volume (reduces sample amount). For Beer-Lambert: A = ε × l × c → A is proportional to l. If l = 0.5 mm = 0.05 cm: A_measured = ε × 0.05 × c → corrected to 1 cm equivalent by multiplying by 20. Using the correct l is critical — an error of 2× in l gives 2× error in calculated concentration.
Dye extinction coefficients at absorption maxima: Ethidium bromide (EtBr, 520 nm): ε = 5600 M⁻¹cm⁻¹ (intercalated in DNA: ε_DNA-EtBr ≈ 3900 M⁻¹cm⁻¹ at 254 nm). SYBR Green I (497 nm): ε ≈ 75,000 M⁻¹cm⁻¹ (bound to dsDNA). SYBR Safe (280, 502 nm): ε ~ 40,000 M⁻¹cm⁻¹. Coomassie R-250 (595 nm): ε_Bradford complex ≈ 28,000 M⁻¹cm⁻¹. GelRed (300 nm in water, 535 nm in DNA): safer EtBr alternative widely used in Indian labs under Biosafety Committee (IBSC) guidelines. FITC: ε = 93,000 M⁻¹cm⁻¹ at 494 nm — conjugated to antibodies for flow cytometry at CCMB, AIIMS.