Beer–Lambert Law Calculator — Absorbance & Transmittance
Select which quantity to solve for, enter the other three values, and get the absorbance, transmittance and percentage absorbed — the core calculation of UV-Vis spectroscopy.
Solve for
L·mol⁻¹·cm⁻¹
mol/L
cm
A = ε × c × l — dimensionless log-scale measure of attenuation
- 1
ε × c
15,000 × 0.0001 = 1.5 - 2
Absorbance A = ε × c × l
1.5 × 1 = 1.5000
How does this calculator work?
Beer–Lambert law: A = ε × c × l, where A is absorbance (dimensionless), ε is molar absorptivity (L·mol⁻¹·cm⁻¹), c is concentration (mol/L), and l is path length (cm). Transmittance T = 10^(−A). The law is linear and accurate for dilute solutions (A ≈ 0.1–1.0).
Formula
How this is calculated
The Beer–Lambert law (also called the Beer–Lambert–Bouguer law) states that the absorbance A of a solution equals the product of the molar absorptivity ε (L·mol⁻¹·cm⁻¹), the molar concentration c (mol/L), and the optical path length l (cm): A = ε × c × l. Absorbance is a dimensionless logarithmic quantity defined as A = −log₁₀(T), where T is the transmittance (the fraction of incident light that passes through). So A = 0 means all light passes (T = 100%), A = 1 means 10% passes, and A = 2 means only 1% passes.
This calculator rearranges the law to solve for any one unknown. The most common use is forward calculation — given a known ε and c, compute A — or quantitative analysis — given a measured A and a known ε, back-calculate the unknown concentration c. Path length (l) is usually fixed by the cuvette (1 cm is the laboratory standard).
The law assumes a monochromatic light source, a dilute homogeneous solution (typically c below 0.01 mol/L), and no scattering or fluorescence. At high concentrations the molecules interact, ε changes, and the linear relationship breaks down. Always verify linearity with a calibration curve.
Frequently asked questions
Transmittance (T) is the fraction of light that passes through the sample (0–1). Absorbance (A = −log₁₀T) converts this to a logarithmic scale that is directly proportional to concentration (the Beer–Lambert linear relationship). An absorbance of 1 corresponds to 10% transmittance; an absorbance of 2 corresponds to 1%.
At high concentrations solute molecules are close enough to interact electrically, altering the molar absorptivity ε. Scattering, association, and dissociation effects also emerge. As a result the A vs. c plot curves away from linearity. A working range of A = 0.1–1.0 (roughly) gives the most reliable quantitative results.
The SI unit of molar absorptivity (ε) is L·mol⁻¹·cm⁻¹, matching concentration in mol/L and path length in cm so that A is dimensionless. Some older literature uses M⁻¹·cm⁻¹, which is identical to L·mol⁻¹·cm⁻¹. Values range widely: from a few L·mol⁻¹·cm⁻¹ for some transitions to over 100 000 for strongly absorbing chromophores.
TG we-Calculate Editorial Team. (2026). Beer–Lambert Law Calculator — Absorbance & Transmittance [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/beer-lambert-law-calculator
TG we-Calculate Editorial Team. "Beer–Lambert Law Calculator — Absorbance & Transmittance." TG we-Calculate. 2026. https://we-calculate.com/calculator/beer-lambert-law-calculator.
TG we-Calculate Editorial Team, "Beer–Lambert Law Calculator — Absorbance & Transmittance," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/beer-lambert-law-calculator
@misc{wecalculate_beer_lambert_law_calculator, title = {Beer–Lambert Law Calculator — Absorbance & Transmittance}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/beer-lambert-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?