Wrong ε conditions
Molar absorptivity depends on wavelength, solvent, pH, temperature, and chemical form. A literature ε can be wrong if your assay conditions differ.
Match conditions
Beer–Lambert Law Calculator (A = εlc)
Inputs
or
%T
Enter absorbance or percent transmittance
Result
Result: Enter any three fields and click Calculate.
Tips: Press Enter to calculate. Keep values within your spectrophotometer’s linear range (often A ≲ 1.0–1.5).
Calibration curve helper
Use one standard per line. Concentrations can be in any consistent unit, such as µM, mg/L, or ppm.
Enter at least two standards, then fit the curve.
How to use this calculator
- Enter any three of absorbance (A), molar absorptivity (ε), path length (l), and concentration (c).
- Choose the correct units for ε, l, and c before calculating.
- Use the %T field if your instrument reports percent transmittance instead of absorbance.
- Click Calculate to solve the missing value and view the calculation steps.
- Use the calibration curve helper when standards are more defensible than a literature ε value.
About the Beer–Lambert law
The Beer–Lambert law relates absorbance A to molar absorptivity ε, path length l, and concentration c. Provide any three, and the fourth is computed. If you enter percent transmittance, the tool converts %T to absorbance before solving.
Beer–Lambert law: A = ε × l × c
Concentration: c = A / (ε × l)
Percent transmittance: A = −log10(%T / 100)
- ε: often tabulated in L·mol⁻¹·cm⁻¹. SI m²·mol⁻¹ is supported (1 L·mol⁻¹·cm⁻¹ = 0.1 m²·mol⁻¹).
- l: typical cuvette path length is 1.00 cm (10 mm). You can pick cm, mm, or m.
- c: pick M, mM, or µM; conversions are handled automatically.
Worked example
NADH at 340 nm. Given ε = 6220 L·mol⁻¹·cm⁻¹, l = 1.00 cm, and c = 0.10 mM:
- Convert c = 0.10 mM = 1.0×10⁻⁴ mol·L⁻¹.
- A = ε × l × c = 6220 × 1.00 × 1.0×10⁻⁴ ≈ 0.622.
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Understanding the Beer–Lambert Law (Absorbance Spectroscopy)
The Beer–Lambert law, sometimes called the Beer–Lambert–Bouguer law, is a cornerstone of modern analytical chemistry and biochemistry. It provides a simple mathematical relationship between the absorbance of light by a sample and three key physical quantities: the molar absorptivity (ε), the path length of the light through the sample (l), and the concentration of the absorbing species (c). The equation is written as:
A = ε × l × c
Key terms explained
- Absorbance (A): A logarithmic measure of how much light is absorbed. It is dimensionless and directly proportional to concentration.
- Molar absorptivity (ε): Also called the extinction coefficient. It reflects how strongly a substance absorbs light at a given wavelength, usually in units of L·mol⁻¹·cm⁻¹.
- Path length (l): The distance the light travels through the sample. Standard cuvettes are typically 1.00 cm, but other sizes exist.
- Concentration (c): The amount of absorbing species, usually expressed in molarity (mol·L⁻¹, or M). Dilute samples often use mM or µM.
Absorbance and percent transmittance
Many spectrophotometers measure % transmittance (%T), the fraction of light that passes through the sample compared to a blank. Absorbance is related by:
A = −log10(%T / 100)
For example, if a sample transmits 25% of the incident light, then A = −log10(0.25) = 0.602.
Why it matters
The Beer–Lambert law is widely used in UV-Vis spectroscopy, biological assays (such as protein concentration by absorbance at 280 nm), enzyme kinetics, and even environmental monitoring (detecting pollutants in water). Because absorbance is linear with concentration under ideal conditions, it enables precise and reproducible quantification without destroying the sample.
Limitations and best practice
The relationship holds best for solutions that are dilute, homogeneous, and measured with monochromatic light. At very high absorbance values (A > 2), too little light passes through, leading to inaccuracies. Scattering, fluorescence, or chemical interactions can also cause deviations. For reliable results, always use an appropriate blank, keep within the linear range of your instrument, and report the wavelength used along with ε values.
In summary, the Beer–Lambert law bridges light and matter: by measuring how much light a solution absorbs, you can back-calculate concentration or other variables. This makes it one of the most versatile and important equations in laboratory science.
Common mistakes that affect Beer–Lambert results
Path length assumptions
Standard cuvettes are often 1.00 cm, but microplates, microvolume instruments, and short-path cells are not. Confirm the actual optical path length.
Check l
Nonlinear absorbance
Very concentrated or highly absorbing samples can leave the linear range. Dilute and remeasure when absorbance is high or standards stop forming a straight line.
Stay linear
Turbid or scattering samples
Particles, precipitate, fingerprints, bubbles, and dirty cuvettes scatter light and inflate apparent absorbance. Clear samples and clean optics matter.
Remove scatter
Blank mismatch
The blank should contain the same solvent, buffer, reagents, and cuvette background as the sample. A mismatch shifts the baseline and biases every result.
Blank carefully
Using literature ε when a calibration curve is needed
Complex matrices, coupled reactions, plate readers, and uncertain ε values often need standards. Use a calibration curve when the direct equation is not defensible.
Fit standards
Beer–Lambert calculator FAQ
What units should I use for ε?
Most handbooks list ε in L·mol⁻¹·cm⁻¹. You can also select SI m²·mol⁻¹; the tool converts 1 L·mol⁻¹·cm⁻¹ = 0.1 m²·mol⁻¹.
Can I use % transmittance?
Yes. Enter %T; the tool computes A = −log10(%T / 100) and keeps both A and %T synchronized.
Does the tool upload my data?
No. All calculations run locally in your browser; nothing is uploaded or stored.