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Beer's Law Path Length Calculator

Enter absorbance, molar absorptivity, and concentration to find the path length.

How it is calculated

The Beer-Lambert law says absorbance is proportional to concentration and path length, A = ε × c × l. The tool rearranges it to l = A ÷ (ε × c). Inputs: A, the measured absorbance (dimensionless, zero or more); ε, the molar absorptivity in L/(mol·cm); and c, the molar concentration in mol/L. Both ε and c must be above zero. The path length comes out in centimetres, shown to four decimals. It also reports transmittance, T = 10−A × 100 in percent, which is the share of light that passes through, so A = 0 gives 100% and A = 1 gives 10%. Use values measured at the same wavelength. The law holds well for dilute solutions and breaks down at high concentration or high absorbance.

Worked example

A solution has absorbance A = 0.5, molar absorptivity ε = 5,000 L/(mol·cm) and concentration c = 0.0001 mol/L. Step 1: ε × c = 5000 × 0.0001 = 0.5 per cm. Step 2: l = 0.5 ÷ 0.5 = 1.0000 cm, a common cuvette width. Step 3: transmittance = 10−0.5 × 100 = 31.62 %.

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Common mistakes

  • Entering the concentration in mg/mL or mM when the field is mol/L. A millimolar solution of 0.5 mM must be typed as 0.0005.
  • Using ε measured at a different wavelength from the absorbance reading, which makes the path length meaningless.
  • Typing percent transmittance in the absorbance field. Absorbance is a log value, so 31.62 % transmittance corresponds to A = 0.5.
  • Trusting very high absorbance readings. The law is only approximate when absorbance is large, so the computed path length may be off.

About this calculator

The Beer-Lambert law relates how much light a sample absorbs to the concentration of the absorbing substance and the distance the light travels through it: A = ε · c · l, where A is absorbance, ε is the molar absorptivity (extinction coefficient, M⁻¹cm⁻¹, specific to the substance and wavelength), c is molar concentration, and l is the optical path length. Solving for path length rearranges this to l = A / (ε · c).

This is standard practice in UV-Vis spectrophotometry: analytical chemists use it to determine the path length of a non-standard cuvette or flow cell, or to check that a measured absorbance is consistent with an assay’s expected concentration and known molar absorptivity. The resulting transmittance, T = 10^(−A), is the fraction of incident light that makes it through the sample. This calculator solves for path length from your absorbance, molar absorptivity and concentration, and also reports the transmittance.

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Comments (1)

  • Editorial team

    Treat the path length as a consistency check on your other three numbers. If the result is far from the cuvette you actually used, one of absorbance, absorptivity or concentration is off, often by a unit slip on concentration. The law also loses accuracy at high absorbance: A = 2 passes only 1.00 % of the light, so dilute and remeasure. The standard case with 0.5, 15000 and 0.0001 returns 0.3333 cm. Where did your absorptivity value come from?

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