What is the Beer-Lambert Law?

It states that the absorbance of a solution is proportional to the concentration and path length of light through the solution. The formula is A = ε·l·c. The proportionality factor ε, also called molar extinction coefficient, is a material constant for a given wavelength. This law forms the basis of quantitative spectrophotometry.

How do you calculate concentration from absorbance?

We rearrange the formula to c = A / (ε·l). To determine concentration with a spectrophotometer, measure the absorbance (A) and divide it by the molar extinction coefficient (ε) and path length of the cell (usually 1 cm). In this calculator select the Beer-Lambert mode, enter A, ε and l and leave the field for concentration blank.

Why does absorption have no units?

Absorbance is defined as the logarithm to base 10 of the ratio of the intensity of incident light to that of transmitted light. The ratio of two intensities of light is dimensionless. Therefore, ε has units of L mol−1 cm−1 and these units cancel out so that the result of ε·l·c is a dimensionless number.

What is the difference between transmittance (T) and percent transmittance (%T)?

The transmittance T is the fraction of light that passes through a sample, and ranges from 0 to 1. The percent transmittance %T is the result of multiplying this fraction by 100, so it ranges from 0 to 100. Both are related to absorbance by the formula A = −log₁₀(T) = 2 − log₁₀(%T).

How do you find molar extinction coefficient from a calibration curve?

To ensure a constant path length of light, the absorbance values and concentrations of a series of standard samples are plotted to obtain a linear relationship. The slope corresponds to ε·l, so ε = slope/l. In this calibration mode of the calculation tool these steps can be performed, and ε can also be calculated from a single measurement point. The formula is: ε = A/(l·c).

When does the law of Lambert-Beer not apply?

For dilute and transparent solutions this law is reliable. At higher concentrations the absorbing molecules interact with each other so that the absorbance no longer increases linearly. Scattering by turbid samples, as well as chemical processes that change with concentration can also lead to deviations. To ensure accurate results, the absorbance should be kept at or below 1 and an experimentally determined calibration curve used.

Beer–Lambert Law Calculator

Set up your calculation

What do you want to calculate?

Pick which calculation to run: the Beer–Lambert law (solve for any of A, ε, l, c), an absorbance↔transmittance conversion, or find ε from a calibration.

Beer–Lambert (A = εlc)

Transmittance ↔ Absorbance

Calibration (find ε)

Absorbance (A)

Molar absorptivity (ε)

Path length (l, cm)

Concentration (c)

Please input values into the fields

Understanding the Beer–Lambert law

Why A is unitless: it comes from a logarithm of light-intensity ratios. ε, l and c carry the units, chosen so that ε·l·c cancels to a pure number.

T vs %T: transmittance T is the fraction of light that gets through (0–1); %T is that times 100. Convert with A = −log₁₀(T) or A = 2 − log₁₀(%T); a clear blank reads 100% T and 0 absorbance.

When it breaks down: Beer–Lambert stays linear only for dilute, non-scattering samples. At high concentration, with cloudy samples, or when the chemistry changes with concentration, absorbance stops tracking concentration — use a calibration curve instead of the bare equation.

The Lambert-Beer law states a relationship between the amount of light absorbed by a solution and two controllable factors: the concentration of the solution and the path length of the light through the solution. It is expressed by the formula A = ε·l·c.

This calculator has three applications: it allows solving the Lambert-Beer law for any of the four quantities, converting between absorbance and transmittance, and determining the molar extinction coefficient (ε) from calibration results. Select the mode, enter the known values, leaving the unknown fields blank.

What the Lambert-Beer law says is this.

When a beam of light passes through a colored solution its intensity is reduced. The more concentrated the solution and the longer the path length for the light, the more light will be absorbed. This relationship is linear.

A = \varepsilon \, l \, c

Here, A is the absorbance (a dimensionless number), ε is the molar extinction coefficient with units of L·mol−1·cm−1, l is the optical path length in centimeters, and c is the concentration in mol/L. Since A has no units, the units of ε must exactly cancel the units of l and c.

Calculation of any size.

This equation can be rearranged to give four different forms of the relationship. Therefore if any three quantities are known then the fourth one can be calculated. If a field is left blank in the Beer-Lambert mode, the calculation tool will automatically select the appropriate form.

A = \varepsilon l c \qquad \varepsilon = \frac{A}{l c} \qquad l = \frac{A}{\varepsilon c} \qquad c = \frac{A}{\varepsilon l}

The determination of concentration from measured absorbance is one of the most common applications in chemical laboratories. By reading A with a spectrophotometer and dividing by ε (molar absorptivity) and path length, the concentration of an unknown sample can be obtained.

Absorption and transmission

What a spectrophotometer actually measures is the transmission of light through the sample. This value is then logarithmically converted into absorbance. The range for transmission T is between 0 and 1, while the percent transmittance %T represents the same result but with an expansion to 0–100.

A = -\log_{10}(T) \qquad T = 10^{-A} \qquad \%T = 100\,T \qquad A = 2 - \log_{10}(\%T)

For each whole number increase in the absorbance, the amount of light transmitted is reduced to one-tenth. A completely transparent reference sample transmits all the light, i.e., it has a transmission of 100%, and an absorbance of zero. If A = 1 then only 10% percent of the light can pass through, and if A = 2 then only 1% percent can pass through.

Example calculation

Example 1 - Determination of Absorbance. A particular dye substance has a molar extinction coefficient ε = 12,500 L·mol−1·cm−1. It is placed in a cell with length 1.00 cm and concentration 2.00×10−5 mol/L.

A = \varepsilon l c = 12{,}500 \times 1.00 \times 2.00\times10^{-5} = 0.250

Example 2 - Converting transmittance (%T) to absorbance. The measured transmittance of a particular sample is 25%.

A = 2 - \log_{10}(25) = 2 - 1.398 = 0.602

Example 3 - Calculation of the molar extinction coefficient from the slope of a calibration curve. The slope of the standard curve for absorbance and concentration is 6.25×10⁵ (absorbance per mol/L), with path length fixed at 1.00 cm. Since Slope = ε·l,

\varepsilon = \frac{\text{slope}}{l} = \frac{6.25\times10^{5}}{1.00} = 6.25\times10^{5}\ \text{L·mol}^{-1}\text{cm}^{-1}

How does absorption increase with increasing concentration?

With a molar extinction coefficient of ε = 12,500 L·mol−1·cm−1 and the use of a cell with length of 1.00 cm, absorption increases linearly as concentration increases. However, this is only true until the sample concentration becomes so high that it causes distortions.

Concentration	Absorbance (A)	Transmittance (%T)
10 µM	0.125	75.0%
20 µM	0.250	56.2%
40 µM	0.500	31.6%
80 µM	1.000	10.0%
160 µM	2.000	1.0%

Under what conditions does the Lambert-Beer law not apply?

This law assumes that the absorbing molecules act independently of each other. This assumption holds for dilute solutions but not at higher concentrations. This is because the molecules interact with each other, changing the index of refraction and causing stray light and scattering to lead to erroneous measurements. Chemical processes that depend on concentration such as dye dimerization or shifts in equilibrium also invalidate this law.

To maximize the reliability of your results, keep the absorbance values for practical work below about 1. If you are working with higher concentrations, use an empirically-derived calibration curve instead of a simple formula.

This calculation tool is for learning purposes in spectrophotometry and general chemistry. In quantitative work, you must follow the instrument calibration requirements and laboratory procedures.

Frequently asked questions

What is the Beer-Lambert Law?: It states that the absorbance of a solution is proportional to the concentration and path length of light through the solution. The formula is A = ε·l·c. The proportionality factor ε, also called molar extinction coefficient, is a material constant for a given wavelength. This law forms the basis of quantitative spectrophotometry.
How do you calculate concentration from absorbance?: We rearrange the formula to c = A / (ε·l). To determine concentration with a spectrophotometer, measure the absorbance (A) and divide it by the molar extinction coefficient (ε) and path length of the cell (usually 1 cm). In this calculator select the Beer-Lambert mode, enter A, ε and l and leave the field for concentration blank.
Why does absorption have no units?: Absorbance is defined as the logarithm to base 10 of the ratio of the intensity of incident light to that of transmitted light. The ratio of two intensities of light is dimensionless. Therefore, ε has units of L mol−1 cm−1 and these units cancel out so that the result of ε·l·c is a dimensionless number.
What is the difference between transmittance (T) and percent transmittance (%T)?: The transmittance T is the fraction of light that passes through a sample, and ranges from 0 to 1. The percent transmittance %T is the result of multiplying this fraction by 100, so it ranges from 0 to 100. Both are related to absorbance by the formula A = −log₁₀(T) = 2 − log₁₀(%T).
How do you find molar extinction coefficient from a calibration curve?: To ensure a constant path length of light, the absorbance values and concentrations of a series of standard samples are plotted to obtain a linear relationship. The slope corresponds to ε·l, so ε = slope/l. In this calibration mode of the calculation tool these steps can be performed, and ε can also be calculated from a single measurement point. The formula is: ε = A/(l·c).
When does the law of Lambert-Beer not apply?: For dilute and transparent solutions this law is reliable. At higher concentrations the absorbing molecules interact with each other so that the absorbance no longer increases linearly. Scattering by turbid samples, as well as chemical processes that change with concentration can also lead to deviations. To ensure accurate results, the absorbance should be kept at or below 1 and an experimentally determined calibration curve used.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

IUPAC — Beer–Lambert law (Gold Book)
The IUPAC definition of the Beer–Lambert (Beer–Bouguer) law and its quantities.
LibreTexts — The Beer–Lambert Law
Open chemistry text covering absorbance, molar absorptivity, transmittance, and the law's limitations.
Beer–Lambert law — Wikipedia
Encyclopedic overview of the law, its derivation, and where it deviates from linearity.