Beer's Law Path Length Calculator

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.

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.