Beer-Lambert Law Calculator
Solve A = εcl for absorbance, molar absorptivity, concentration, or path length, and see the linear absorbance-vs-concentration relationship plotted live.
🌈 What is the Beer-Lambert Law?
The Beer-Lambert law (also called Beer's law) is the fundamental equation of absorption spectroscopy, describing how much light a sample absorbs as A = εcl. It states that absorbance is directly proportional to both the concentration of the absorbing substance and the distance light travels through it, connecting a simple instrument reading to the exact concentration of a dissolved compound.
This relationship is the working principle behind UV-Vis spectrophotometers used across chemistry, biology, and clinical laboratories: measuring protein concentration in a biochemistry lab with a 280 nm absorbance reading, tracking a reaction's progress by watching a colored product's absorbance rise over time, quantifying DNA or RNA purity and yield from a 260 nm reading, and verifying drug concentration in pharmaceutical quality control. Any time a lab reports "the sample absorbed this much light, therefore the concentration is this," the Beer-Lambert law is doing the underlying math.
A common misconception is that the law holds at any concentration. It does not. Beer-Lambert is a linear approximation that breaks down at high concentrations, where molecules start interacting with each other, the solution's refractive index shifts, and stray light inside the instrument becomes significant. Analytical chemists stay within the linear range, generally keeping absorbance between about 0.1 and 1.0 AU, and dilute samples that read too high rather than trusting an out-of-range number.
This calculator is useful because the same formula, A = εcl, has four different quantities, and a student or lab technician might need to solve for any one of them depending on what data they already have. Rather than rearranging algebra by hand each time, this tool switches between solving for absorbance, molar absorptivity, concentration, or path length, showing the full arithmetic and a live chart of the absorbance-versus-concentration line for the current inputs.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Finding absorbance
A dye solution has molar absorptivity 5000 M⁻¹cm⁻¹ at 0.0001 M concentration in a standard 1 cm cuvette.
Example 2 — Finding molar absorptivity
A newly measured compound reads 0.65 AU at 0.00025 M in a 1 cm cuvette. What is its molar absorptivity?
Example 3 — Finding an unknown concentration
A protein assay reads 0.85 AU. Its molar absorptivity is 12,000 M⁻¹cm⁻¹ and the cuvette path length is 1 cm.
Example 4 — Finding the required path length
A target absorbance of 1.2 AU is needed for a sample at 0.00015 M with molar absorptivity 8500 M⁻¹cm⁻¹. What cuvette path length is needed?
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Beer-Lambert law formula?
The Beer-Lambert law states A = εcl, where A is absorbance (unitless), ε is the molar absorptivity in M⁻¹cm⁻¹, c is concentration in mol/L, and l is the path length in cm. It describes how light absorption increases linearly with both concentration and the distance light travels through a sample.
How do you calculate concentration from absorbance?
Rearrange the formula to c = A / (ε × l). Enter the measured absorbance, the molar absorptivity of the compound at your measurement wavelength, and the cuvette path length, and the calculator solves directly for concentration in mol/L.
What is molar absorptivity and how do I find it?
Molar absorptivity (ε), also called the molar extinction coefficient, measures how strongly a specific molecule absorbs light at a specific wavelength, in units of M⁻¹cm⁻¹. It is a published property for many compounds, usually found in reference tables or determined experimentally by measuring absorbance for several known concentrations and taking the slope.
Why is absorbance unitless?
Absorbance is defined as A = log10(I0 / I), the base-10 logarithm of the ratio of incident light intensity to transmitted light intensity. Because it is a ratio of two intensities in the same units, the units cancel, leaving a dimensionless number, though it is often labeled AU (absorbance units) for clarity.
What path length should I use for a standard cuvette?
Most standard laboratory cuvettes have a 1 cm path length, which is why many textbook problems simplify the formula to A = εc. Always check the cuvette's specification sheet, since some microvolume or specialty cuvettes use a shorter path length, such as 0.5 cm or 1 mm.
Why does my absorbance reading exceed 2.0?
An absorbance above 2.0 AU means over 99% of the light is being absorbed, so very little signal reaches the detector, and stray light and instrument noise start to dominate the reading. Dilute the sample with solvent until the absorbance falls between roughly 0.1 and 1.0, then account for the dilution factor when reporting the original concentration.
Is Beer-Lambert law valid at all concentrations?
No. The law is only linear at low to moderate concentrations, typically where absorbance stays below about 1 to 1.5 AU. At higher concentrations, molecular interactions, changes in the refractive index of the solution, and stray light in the instrument cause deviations from linearity, so a calibration curve is more reliable at high concentrations.
How do I find molar absorptivity if I know absorbance and concentration?
Rearrange the formula to ε = A / (c × l). Select the Molar Absorptivity mode, enter the measured absorbance, the known concentration, and the path length, and the calculator solves for ε in M⁻¹cm⁻¹. This is exactly how ε is determined experimentally for a new compound.
What is the difference between absorbance and transmittance?
Transmittance (T) is the fraction of light that passes through a sample, T = I / I0, usually reported as a percentage. Absorbance is the negative log10 of transmittance, A = -log10(T). Absorbance is preferred for quantitative work because it is directly proportional to concentration, while transmittance is not.
Can absorbance be negative?
In principle no, since absorbance of zero means all light passes through unabsorbed. In practice a very small negative reading can appear due to instrument noise or an imperfect blank correction when the true absorbance is close to zero, but a genuinely negative absorbance has no physical meaning for a light-absorbing sample.
How is this calculator different from the Calibration Curve Calculator?
This calculator solves the Beer-Lambert equation A = εcl directly, when you already know (or want to find) all four quantities from a single measurement and a known or published molar absorptivity. The Calibration Curve Calculator instead fits a best-fit line through several standard measurements to determine the slope and intercept experimentally, which is more accurate when ε is not already known precisely.
Does temperature affect the Beer-Lambert law?
Temperature does not appear directly in the A = εcl formula, but it can affect the result indirectly, since molar absorptivity itself can shift slightly with temperature for some compounds, and solution density (and therefore concentration in a fixed volume) can also change with temperature. For precise work, measurements are usually taken at a controlled, stated temperature.