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Beer-Lambert Law Calculator

Calculate concentration from absorbance using the Beer-Lambert law (A = εlc). Also computes transmittance.

About this calculator

This calculator solves the Beer-Lambert law, A = εlc, for solute concentration: c = A / (εl), where A is measured absorbance (unitless), ε is the molar absorptivity (extinction coefficient) in L/(mol·cm), and l is the cuvette path length in cm. Concentration is directly proportional to Absorbance -- doubling the measured absorbance doubles the calculated concentration -- and inversely proportional to both Molar Absorptivity and Path Length, since either one appears in the denominator. The calculator also reports % Transmittance, T% = 10^(-A) x 100, the fraction of incident light that passes through the sample; this relationship is logarithmic rather than linear, so Transmittance falls sharply as Absorbance rises and drops toward zero at high absorbance rather than declining in a straight line.

The Beer-Lambert law itself is a linear approximation that holds well at low-to-moderate absorbance (roughly 0.1-1.0, per the input's own guidance) but becomes unreliable at very high concentrations, where stray light, chemical interactions between solute molecules, and instrument non-linearity cause real absorbance to deviate from the ideal linear relationship with concentration. The default Molar Absorptivity of 6600 L/(mol·cm) corresponds to double-stranded DNA measured at 260 nm, a standard reference value used in molecular biology for estimating nucleic acid concentration from a spectrophotometer reading.

Inputs

Results

Concentration

0 M

% Transmittance

31.62%

Concentration0.076 mM
Concentration75.76 µM
Transmittance (T)0.3162
How to Use This Calculator
  1. Enter Absorbance (A), Molar Absorptivity (ε), and Path Length (cm).
  2. Review Concentration (M) and % Transmittance.
  3. Use Concentration (mM) and Concentration (µM) to inform your decision.
  4. Use the chart to visualize the results and explore different scenarios by adjusting inputs.

What each input means

Absorbance (A)
Measured absorbance (unitless). Reliable range is typically 0.1–1.0.
Molar Absorptivity (ε)
Molar extinction coefficient in L/(mol·cm). Example: dsDNA at 260nm ≈ 6600.
Path Length (cm)
Cuvette path length in centimeters. Standard cuvettes are 1 cm.

How this is calculated

Formula

A = εlc → c = A / (ε × l)

Worked example, using the default values

  1. Identify Input Parameters
    Absorbance (A) = 0.5, Molar Absorptivity (ε) = 6600, Path Length (cm) = 1 = 3 input(s) provided
  2. Calculate Concentration
    Concentration = c
    0.000075758 = 0.000075758
  3. Calculate % Transmittance
    % Transmittance
    31.62 = 31.62
  4. Calculate Concentration
    Concentration
    0.076 = 0.076
  5. Calculate Concentration
    Concentration
    75.76 = 75.76

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

How does increasing measured absorbance affect the calculated concentration?

Concentration is directly proportional to Absorbance in the Beer-Lambert law (c = A / (εl)), so a higher Absorbance reading always produces a proportionally higher calculated Concentration, holding Molar Absorptivity and Path Length fixed. Doubling the Absorbance input exactly doubles the resulting Concentration.

Why does a longer path length reduce the calculated concentration?

Path Length sits in the denominator of c = A / (εl): for the same measured Absorbance, a longer path length (more solution for light to travel through) means less concentration is needed to produce that absorbance, so the calculator reports a lower Concentration. This is why using a shorter or longer cuvette than assumed changes the result even when the reading itself is identical.

Is the relationship between Absorbance and % Transmittance linear?

No. % Transmittance is T% = 10^(-A) x 100, a logarithmic (inverse exponential) relationship, not a straight line. Small increases in Absorbance at low values cause large drops in Transmittance, while at high Absorbance, Transmittance approaches zero and further increases in Absorbance barely change it further in absolute terms.

Why does the default Molar Absorptivity value equal 6600?

6600 L/(mol·cm) is the standard molar extinction coefficient for double-stranded DNA measured at a wavelength of 260 nm, one of the most common spectrophotometry measurements in molecular biology labs for estimating nucleic acid concentration. Different molecules and wavelengths have very different molar absorptivity values, so this input should always be set to match the actual substance being measured.

Why does the Beer-Lambert law become less accurate at very high absorbance?

The law assumes each absorbing molecule acts independently of the others, which is a good approximation only at low-to-moderate concentration. At high concentration (typically above an absorbance of about 1.0-2.0), solute molecules can interact with each other, and instrument effects like stray light become significant, causing real measured absorbance to deviate from the ideal linear relationship with concentration this calculator assumes.

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