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Beer-Lambert Law Calculator

A = εlc — solve for any variable, plan dilutions, and fit calibration curves

A = ε × l × c
A(dimensionless)
ε(L·mol⁻¹·cm⁻¹)
l(cm)
c

Common Calculations

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The Beer-Lambert law calculator solves A = εlc for any unknown variable — enter three values and get the fourth instantly. Use it to determine concentration from absorbance measurements, plan dilutions for calibration standards, or fit a calibration curve to your experimental data. The Calibration tab accepts up to 12 data points and returns the best-fit line with R², slope, and intercept. For background on the theory, see our Beer-Lambert law guide.

Worked Example: DNA Concentration from A₂₆₀

Suppose you measured an absorbance of 0.5 at 260 nm for a double-stranded DNA sample in a 1 cm cuvette. Here's how to calculate the DNA concentration step by step:

  1. Identify known values: A = 0.5, ε = 6,600 L mol⁻¹ cm⁻¹ (dsDNA at 260 nm), l = 1 cm
  2. Rearrange Beer-Lambert law: c = A / (ε × l)
  3. Substitute values: c = 0.5 / (6,600 × 1) = 7.576 × 10⁻⁵ mol/L
  4. Convert units: 7.576 × 10⁻⁵ M = 75.76 μM, or approximately 2.5 mg/mL for a typical dsDNA with average MW ~330 g/mol per nucleotide
  5. Verify: The absorbance of 0.5 is within the ideal 0.1–1.0 range, confirming reliable results. Click the “DNA concentration from A₂₆₀” preset above to check this calculation instantly.

The Beer-Lambert law (A = εlc), also called the Beer Lambert law or Beer's law, is foundational to quantitative spectroscopy, linking the absorbance of a sample to its concentration, path length, and molar absorptivity. Whether you're determining an unknown concentration from a measured absorbance or planning an experiment around a target optical density, this calculator gives you the answer instantly.

Enter any three of the four variables and SpectralBench solves for the fourth. The built-in graph visualizes how absorbance changes with concentration, making it easy to identify the linear range and spot potential deviations at high optical densities. The new Calibration tab lets you enter real experimental data points and fit a best-fit line with R², just like you would in the lab. Pair it with the SNR Calculator to evaluate whether your measurement has sufficient signal quality, or use the Unit Converter to convert between concentration units.

New to Beer-Lambert law? Start with our comprehensive guide →

How It Works

Select which variable you want to solve for: absorbance, molar absorptivity, path length, or concentration. Enter the three known values into the corresponding fields and SpectralBench calculates the fourth instantly — no page reload, no submit button.

The interactive graph below the calculator plots absorbance as a function of concentration using your current molar absorptivity and path length values. Drag the concentration slider to see how the absorbance reading changes in real time. This visualization makes it easy to identify the linear range where Beer's Law holds and to see where deviations begin at higher concentrations.

The built-in dilution calculator uses the C₁V₁ = C₂V₂ equation to help you plan serial dilutions for calibration curves. Enter your stock concentration and desired final concentration to calculate the required volumes. An extinction coefficient database lets you look up molar absorptivity values for common chromophores, so you can estimate expected absorbance readings before running your experiment.

The Calibration tab accepts up to 12 concentration-absorbance data points and performs ordinary least squares regression. The resulting slope equals ε × l, the intercept should be near zero for well-behaved data, and R² quantifies the linearity of your calibration. Export your data as CSV or copy the plot as SVG for reports and publications.

The Beer-Lambert Law Explained

The Beer-Lambert law describes the linear relationship between the absorbance of a sample and its concentration in dilute solutions. The equation A = εlc connects four quantities:

  • A— Absorbance (dimensionless). The log₁₀ ratio of incident light intensity to transmitted light intensity.
  • ε— Molar absorptivity (L mol⁻¹ cm⁻¹), also called the molar extinction coefficient. An intrinsic property of the analyte at a specific wavelength.
  • l— Path length (cm). The distance light travels through the sample, typically 1 cm for standard cuvettes.
  • c— Concentration (mol/L or M). The molar concentration of the absorbing species in solution.

The law assumes monochromatic light, dilute solutions, no scattering, and no chemical interactions between analyte molecules. When these conditions hold, a plot of absorbance versus concentration yields a straight line passing through the origin.

Limitations and Deviations

Understanding when Beer's Law breaks down is as important as knowing how to apply it. Deviations fall into three categories:

Real deviations occur at high concentrations (typically when absorbance exceeds 1.0) where intermolecular interactions — electrostatic, hydrogen bonding, or aggregation — alter the effective molar absorptivity. The relationship between absorbance and concentration becomes non-linear.

Instrumental deviations arise from polychromatic light sources (no monochromator produces truly monochromatic light), stray light reaching the detector, and detector non-linearity at extreme absorbance values.

Chemical deviations occur when the analyte undergoes fluorescence, scattering, association, dissociation, or chemical equilibria that shift with concentration. In these cases the effective absorbing species changes with dilution.

The interactive graph in SpectralBench's calculator helps you visualize where the linear range ends for your specific parameters, so you can design experiments that stay within the valid regime.

Assessing measurement quality? Use the SNR Calculator →

Need to convert concentration or wavelength units? Spectroscopy Unit Converter →

Learning about UV-Vis techniques? UV-Vis Spectroscopy Guide →

Frequently Asked Questions

How do I calculate concentration from absorbance?

Rearrange the Beer-Lambert law to c = A / (ε × l). Enter your measured absorbance, the molar absorptivity of your analyte at the measurement wavelength, and the cuvette path length. SpectralBench solves for concentration instantly.

What is molar absorptivity and what are its units?

Molar absorptivity (ε), also called the molar extinction coefficient, is an intrinsic property of a substance that describes how strongly it absorbs light at a given wavelength. Its units are L mol⁻¹ cm⁻¹. Higher values mean stronger absorption — a small amount of the substance produces a large absorbance reading.

When does Beer's Law fail?

Beer's Law assumes dilute solutions, monochromatic light, no scattering, and no chemical interactions between analyte molecules. It breaks down at high concentrations (typically A > 1) due to intermolecular interactions, with polychromatic light sources, in scattering samples, and when chemical equilibria shift with concentration.

What units does the Beer-Lambert calculator use?

The calculator uses SI-compatible units: absorbance is dimensionless (log₁₀ ratio), molar absorptivity is in L mol⁻¹ cm⁻¹, path length is in cm, and concentration is in mol/L (M). These are the standard units used in analytical chemistry and spectroscopy.

How do I calculate a dilution?

Use the built-in dilution calculator. Enter your stock concentration (C₁), stock volume (V₁), and desired final concentration (C₂). SpectralBench solves for the final volume (V₂) using the C₁V₁ = C₂V₂ relationship. This is useful for planning serial dilutions when building calibration curves for Beer-Lambert quantitation.

How do I calculate molar absorptivity from absorbance?

Rearrange the Beer-Lambert law to ε = A / (l × c). Measure the absorbance of a solution with known concentration in a cuvette of known path length. For more accurate results, build a calibration curve using the Calibration tab — the slope of the best-fit line equals ε × l, so dividing by path length gives you ε directly.

What is a typical absorbance range for Beer-Lambert law?

The ideal absorbance range for accurate Beer-Lambert measurements is 0.1 to 1.0 A. Absorbance values from 0.01 to 2.0 are generally acceptable, but above 2.0 less than 1% of light reaches the detector, making readings unreliable. If your absorbance is too high, dilute the sample and measure again.

How do I prepare a dilution series for a calibration curve?

Start with a stock solution of known concentration. Use the dilution calculator (C₁V₁ = C₂V₂) to prepare 5–8 standards spanning your expected concentration range. Measure each standard's absorbance, then enter the data in the Calibration tab to get a best-fit line with R². An R² above 0.99 confirms good linearity.

What is the extinction coefficient of DNA at 260 nm?

Double-stranded DNA has a molar extinction coefficient of approximately 6,600 L mol⁻¹ cm⁻¹ per base pair at 260 nm (or about 50 μg/mL per absorbance unit for a 1 cm path length). Single-stranded DNA absorbs more strongly, at approximately 8,100 L mol⁻¹ cm⁻¹. Use the Reference tab to quickly load this value into the calculator.

Can I use Beer-Lambert law for FTIR spectroscopy?

Yes, Beer-Lambert law applies to FTIR spectroscopy. Absorbance spectra (not transmittance) follow A = εlc at each wavenumber. For FTIR, path length may be the thickness of a KBr pellet, ATR penetration depth, or liquid cell path length. Keep in mind that ATR spectra require a correction factor for the effective path length, which varies with wavenumber.

Features(7)
  • Solve for absorbance, molar absorptivity, path length, or concentration
  • Interactive absorbance-vs-concentration graph with concentration slider
  • Dilution calculator — C₁V₁ = C₂V₂ for serial dilution planning
  • Calibration curve fitting — enter data points, get best-fit line with R²
  • CSV export and SVG copy for calibration data and plots
  • Extinction coefficient database — look up ε for 16 common chromophores
  • Shareable links and QR codes for any calculation

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