Beer–Lambert Law Calculator

Frequently Asked Questions

What is the Beer–Lambert law?

Absorbance A = ε·c·l, linking absorbance to molar absorptivity ε, concentration c, and path length l.

What can this solve for?

Any one of absorbance, ε, concentration, or path length when the other three are known - useful for spectrophotometry.

How is absorbance related to transmittance?

A = −log₁₀(T), where T is the fraction of light transmitted; an absorbance of 1 means 10% transmitted.

When does the law break down?

At high concentrations (chemical interactions, scattering) the linear relationship fails, so dilute samples are preferred.

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Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

The Beer–Lambert law links how strongly a solution absorbs light to how much absorbing species it contains: A = ε · l · c, where A is absorbance (unitless), ε is the molar absorptivity in L·mol⁻¹·cm⁻¹, l is the path length through the sample in cm, and c is the molar concentration in mol/L. Absorbance also relates to measured light intensities by A = log₁₀(I₀ ÷ I) and to transmittance by A = −log₁₀(T), so T = 10⁻ᵀ. This calculator solves the law five ways - for A, c, ε, l, or absorbance from %transmittance - and always reports the corresponding transmittance alongside.

Worked Example: Finding an Unknown Concentration

A dye has ε = 15,000 L·mol⁻¹·cm⁻¹ at its λₘₐₓ. In a standard 1 cm cuvette the spectrophotometer reads A = 0.75. Solving for concentration: c = A ÷ (ε · l) = 0.75 ÷ (15,000 × 1) = 5.0 × 10⁻⁵ mol/L (50 µM). Its transmittance is T = 10⁻⁰.⁷⁵ ≈ 0.178, meaning only about 17.8% of the incident light passes through - the rest is absorbed. Halve the concentration and A drops to 0.375 while transmittance rises to ≈ 42%, illustrating the logarithmic relationship between the two.

Real-World Uses

Analytical chemistry: determine unknown concentrations from a calibration curve of A vs. c.

Biochemistry: quantify DNA/RNA at 260 nm and protein at 280 nm.

Environmental testing: measure pollutants, nitrate, or chlorophyll in water.

Pharmaceutical QC: verify drug content and dissolution rates.

Kinetics: track reactant or product concentration over time via absorbance.

Common Mistakes

Confusing transmittance with absorbance is the classic error - they are inversely and logarithmically related, not the same quantity. Another is mismatching units: ε is usually tabulated per cm and per mol/L, so the path length must be in cm and concentration in mol/L. Reading A at the wrong wavelength (not λₘₐₓ) gives a small, noisy signal. Forgetting to blank the instrument with pure solvent introduces a systematic offset.

Limitations & Related

Beer's law is linear only at low absorbance - typically A < 1, ideally 0.1–0.8. At high concentration the law deviates due to solute–solute interactions, refractive-index changes, and stray light, so the apparent ε is no longer constant. It assumes monochromatic light, a homogeneous non-scattering sample, and no fluorescence or photochemical reaction. For turbid or strongly absorbing samples, dilute the sample or use a shorter path length rather than extrapolating. Related tools include the dilution (C₁V₁ = C₂V₂) and pH calculators often used in the same workflow.

Beer–Lambert Law Calculator

Frequently Asked Questions

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