What is the Beer-Lambert law?

The Beer-Lambert law states that the absorbance A of a solution equals the product of the molar absorptivity ε (L mol⁻¹ cm⁻¹), the path length l (cm), and the molar concentration c (mol/L): A = ε · l · c. It describes how much light a solution absorbs at a given wavelength and underpins quantitative UV-Vis spectrophotometry.

What are the units for molar absorptivity?

Molar absorptivity ε has SI units of L mol⁻¹ cm⁻¹ (equivalently M⁻¹ cm⁻¹). Values span a wide range: a weak absorber might have ε ≈ 10, while a strong chromophore such as haemoglobin (Soret band) reaches ε ≈ 100,000 L mol⁻¹ cm⁻¹.

How do I convert absorbance to transmittance?

Transmittance T is related to absorbance by T = 10^(−A), often expressed as a percentage: T% = 10^(−A) × 100. An absorbance of 0 means 100% transmittance (no absorption); A = 1 means 10% transmittance; A = 2 means 1%.

When does the Beer-Lambert law break down?

The law assumes monochromatic light, dilute solution (typically A < 1.5 for accurate results), no light scattering or fluorescence, and homogeneous sample. At high concentrations, intermolecular interactions alter ε; stray light in the spectrometer also introduces positive deviations. Always verify linearity with a calibration curve before using Beer-Lambert for quantification.

What is a standard cuvette path length?

The standard lab cuvette has a path length of exactly 1 cm. Micro-cuvettes or fibre-optic probes may use shorter paths (0.1 cm, 0.5 cm) to extend the useful range to higher concentrations. Enter whatever path length your instrument uses — the calculator accepts any positive value.

Can I use this for multi-component mixtures?

For a single absorbing species, yes. For mixtures, the total absorbance at any wavelength is the sum of individual contributions (additive Beer-Lambert). You would need to solve a system of equations at multiple wavelengths. This calculator handles one component at a time; for multi-component analysis, use matrix methods or dedicated chemometrics software.

Beer-Lambert Law Calculator

Q: What is a standard cuvette path length?

The standard lab cuvette has a path length of exactly 1 cm. Micro-cuvettes or fibre-optic probes may use shorter paths (0.1 cm, 0.5 cm) to extend the useful range to higher concentrations. Enter whatever path length your instrument uses — the calculator accepts any positive value.

Q: Can I use this for multi-component mixtures?

For a single absorbing species, yes. For mixtures, the total absorbance at any wavelength is the sum of individual contributions (additive Beer-Lambert). You would need to solve a system of equations at multiple wavelengths. This calculator handles one component at a time; for multi-component analysis, use matrix methods or dedicated chemometrics software.

The Beer-Lambert law — written A = ε · l · c — is the cornerstone equation of quantitative spectrophotometry. It predicts exactly how much light a solution absorbs based on three measurable properties: how strongly the molecule absorbs (molar absorptivity ε), how far the light travels through the solution (path length l), and how many molecules are in the way (concentration c). This calculator solves for any one of the four variables — A, ε, l, or c — from the other three, shows the substitution working, and derives the equivalent transmittance automatically.

How it works

Select the quantity you want to find from the Solve for drop-down. The three remaining input boxes accept any real number; scientific notation (1.2e-4) is supported. The calculation is:

A = ε · l · c

Rearranged for each unknown:

Concentration: c = A / (ε · l)
Molar absorptivity: ε = A / (l · c)
Path length: l = A / (ε · c)

Transmittance is derived in parallel using T (%) = 10^(−A) × 100, so you always see both representations of the measurement.

The tool flags division-by-zero gracefully — if you enter zero for a denominator variable, the result shows ”—” instead of Infinity.

Worked example

A biochemist measures the absorbance of a NADH solution at 340 nm. The known values are:

ε = 6220 L mol⁻¹ cm⁻¹ (literature value for NADH at 340 nm)
l = 1 cm (standard cuvette)
A = 0.497 (instrument reading)

Solving for concentration:

c = A / (ε · l) = 0.497 / (6220 × 1) = 7.99 × 10⁻⁵ mol/L ≈ 80 µmol/L

Transmittance: T = 10^(−0.497) × 100 ≈ 31.8 %

Scenario	ε (L mol⁻¹ cm⁻¹)	l (cm)	c (mol/L)	A
NADH at 340 nm	6220	1	8.0 × 10⁻⁵	0.50
DNA at 260 nm (approx.)	6600 (per nucleotide)	1	5.0 × 10⁻⁵	0.33
Typical dye tracer	25000	1	2.0 × 10⁻⁵	0.50
High-absorber check	10000	2	5.0 × 10⁻⁵	1.00

Formula note

Absorbance A is dimensionless and defined as log₁₀(I₀ / I), where I₀ is incident and I is transmitted intensity. Because it is a base-10 logarithm, the transmittance conversion is T = 10^(−A) — not the natural-log form used in some older texts. Molar absorptivity ε with units L mol⁻¹ cm⁻¹ is the modern IUPAC convention; the older term “molar extinction coefficient” (symbol ε or κ) is numerically identical. The law is strictly valid for dilute, non-scattering, non-fluorescent solutions illuminated with monochromatic light. For routine lab work, A values between 0.1 and 1.0 give the best accuracy; values above ~1.5 deviate measurably from linearity due to stray light and solute–solute interactions.