About the Beer-Lambert Law Calculator
This Beer-Lambert law calculator solves A = ε·l·c for whichever quantity you are missing. Use it to turn a spectrophotometer absorbance reading into a concentration, to find the molar absorptivity (extinction coefficient) of a compound from a standard, to predict the absorbance a sample will give, or to work out the cuvette path length needed to keep a reading on scale.
It is meant for students in analytical, general and biochemistry labs and for anyone quantifying samples by UV-Vis — NADH at 340 nm, proteins at 280 nm, dyes in the visible range. If your instrument reports percent transmittance instead of absorbance, switch the reading type and the calculator converts with A = −log₁₀(T).
The law is linear only for dilute solutions and monochromatic light. Readings between about 0.1 and 1.0 absorbance units are the most reliable; above roughly 1.5–2 stray light and molecular interactions make the response flatten, so dilute and re-measure rather than trusting a high value.
How to use the beer-lambert law calculator
- 1Choose the quantity you want to solve for.
- 2Enter your reading as absorbance, or switch to percent transmittance.
- 3Enter ε for your compound at the measurement wavelength and the cuvette path length.
- 4Pick the concentration unit you want to work in.
- 5Read the result and check that the absorbance falls in the reliable 0.1–1.0 range.
Formula and method
The Beer-Lambert law states that absorbance is directly proportional to the concentration of the absorbing species and to the distance light travels through the sample. The proportionality constant ε, the molar absorptivity, is specific to the compound, the wavelength and the solvent. Rearranging gives c = A/(εl), ε = A/(lc) and l = A/(εc).
Absorbance is logarithmic: transmittance T = I/I₀ is the fraction of light that passes through, and A = −log₁₀T. An absorbance of 1 lets 10% of the light through and 2 lets only 1% through. The calculator converts your concentration unit to mol/L before applying the law, so ε must be in L·mol⁻¹·cm⁻¹ and l in cm.
- A
- Absorbance (unitless)
- ε
- Molar absorptivity, L·mol⁻¹·cm⁻¹
- l
- Path length through the sample, cm
- c
- Concentration, mol/L
- T
- Transmittance I/I₀ (as a fraction)
Worked examples
NADH concentration from A₃₄₀
With A = 0.622, ε = 6,220 L/(mol·cm) and a 1 cm cuvette, c = 0.622 ÷ 6,220 = 1.0 × 10⁻⁴ M = 100 µM. That absorbance transmits 10^(−0.622) ≈ 23.9% of the light.
Predict absorbance of a 50 µM sample
A = 6,220 × 1 × 50 × 10⁻⁶ = 0.311, so about 48.9% of the light is transmitted — comfortably within the linear range.
Molar absorptivity from a standard
A 25 µM standard reading 0.45 in a 1 cm cell gives ε = 0.45 ÷ (1 × 25 × 10⁻⁶) = 18,000 L/(mol·cm).
Concentration from 35% transmittance
A = −log₁₀(0.35) = 0.4559. Dividing by ε·l = 6,220 gives 7.33 × 10⁻⁵ M, or 73.3 µM.
Frequently asked questions
How do you calculate concentration from absorbance?+
Rearrange Beer’s law to c = A ÷ (ε × l). With A = 0.5, ε = 10,000 L/(mol·cm) and a 1 cm cuvette, c = 0.5 ÷ 10,000 = 5 × 10⁻⁵ M (50 µM).
How do I convert percent transmittance to absorbance?+
Use A = 2 − log₁₀(%T), which is the same as −log₁₀ of the fractional transmittance. 50% T is A = 0.301, 10% T is A = 1 and 1% T is A = 2.
What are the units of molar absorptivity?+
L·mol⁻¹·cm⁻¹ (equivalently M⁻¹·cm⁻¹), so that multiplying by a path length in cm and a concentration in mol/L leaves absorbance unitless. Mass-based coefficients use L·g⁻¹·cm⁻¹ instead.
Why does the Beer-Lambert law fail at high absorbance?+
At high concentration, molecules interact and change their absorptivity, and stray light becomes a large share of the tiny transmitted signal. The calibration curve bends below the straight line, typically above about A = 1.5.
What absorbance range is most accurate?+
Most spectrophotometers give the lowest relative error between about 0.1 and 1.0 absorbance units. Dilute samples that read higher, or use a longer path length for very dilute ones.