Beer-Lambert Law Calculator
Beer-Lambert law calculator. Solve A = epsilon * c * l for concentration, absorbance, molar absorptivity or path length in spectrophotometry. Educational.
Beer-Lambert Law Calculator
How to use the Beer-Lambert calculator
Choose the unknown
Select which of the four quantities — concentration, absorbance, molar absorptivity, or path length — you want to solve for. The matching input is hidden.
Enter the other three
Most often you measure the absorbance, know the molar absorptivity for your compound and wavelength, and use a 1 cm cuvette, then solve for concentration.
Calculate
The result follows directly from A = ε·c·l. Concentration is also shown in micromolar, and the absorbance is translated into percent transmittance.
Stay in the linear range
Beer's law is reliable at low absorbance (roughly below 1). For higher readings, dilute the sample and re-measure, or use a calibration curve. Verify against a standard.
Beer-Lambert law — turning light into concentration
Absorbance is proportional to concentration
Spectrophotometry — measuring how much light a solution absorbs — is one of the most common ways to find the concentration of a coloured or UV-active compound, and the Beer-Lambert law is the relationship that makes it work. It states that the absorbance A of a solution is the product of three things: the molar absorptivity ε (a constant that describes how strongly the substance absorbs at a particular wavelength), the concentration c, and the path length l the light travels through the sample. In symbols, A = ε·c·l. Two of these are usually fixed in an experiment — the molar absorptivity is a property of the compound at the chosen wavelength, and the path length is set by the cuvette, almost always 1 cm — so absorbance becomes directly proportional to concentration. Measure the absorbance, divide by ε times l, and you have the concentration. That linear proportionality is what lets a spectrophotometer read out concentration so conveniently, and it underpins countless assays in chemistry, biochemistry, and clinical and environmental labs.
Absorbance is defined logarithmically: it is the base-ten logarithm of the ratio of incident to transmitted light, so an absorbance of 1 means only 10% of the light gets through, and an absorbance of 2 means just 1%. This logarithmic scale is why absorbance, rather than raw transmittance, is the quantity that varies linearly with concentration. The molar absorptivity ε, with units of M⁻¹cm⁻¹, can be very large for strongly absorbing species — tens of thousands for many dyes and biological chromophores — which is what makes the technique sensitive enough to measure micromolar and even nanomolar concentrations.
"Fix the cuvette and the wavelength, and absorbance becomes a straight-line readout of concentration. That simple proportionality, A = ε·c·l, is the workhorse of the spectrophotometer."
Where the straight line bends
The Beer-Lambert law is an idealisation, and it holds best for dilute solutions at low absorbance. As concentration rises, deviations appear: the absorbance stops increasing linearly, usually curving below the predicted line. Several effects cause this — at high concentration the molecules are close enough to interact and to alter each other's absorption; chemical equilibria can shift, changing the absorbing species; and stray light and the finite bandwidth of real instruments distort high readings. As a practical rule, keep absorbance below about 1 (some labs say 1.5) for reliable quantification, and dilute and re-measure anything higher. The law also assumes monochromatic light, a homogeneous, non-scattering sample (turbidity or bubbles ruin a reading), and that the molar absorptivity you use was determined at the same wavelength and conditions. For accurate work, rather than trusting a single ε value, chemists build a calibration curve from standards of known concentration and read unknowns off it, which automatically corrects for the instrument and any mild non-linearity. Use this calculator to do the quick A = ε·c·l arithmetic and to understand the relationship, and validate concentrations against standards for results that matter.
10 Facts About the Beer-Lambert Law
A = ε · c · l — absorbance = absorptivity × conc × path.
Fix ε and l, and absorbance is proportional to concentration.
Cuvettes are almost always 1 cm path length.
Absorbance is the log of incident ÷ transmitted light.
A = 1 means only 10% of light passes; A = 2, just 1%.
ε has units of M⁻¹cm⁻¹ and is wavelength-specific.
Large ε makes the method sensitive to µM–nM levels.
Linearity holds best at A < 1 — dilute if higher.
Turbidity, bubbles, and stray light break the law.
Best practice: read unknowns off a calibration curve.
Frequently asked questions
It states that a solution's absorbance equals the molar absorptivity times the concentration times the path length: A = ε·c·l. Because the molar absorptivity (a property of the compound at a given wavelength) and the path length (the cuvette) are usually fixed, absorbance becomes directly proportional to concentration. This lets a spectrophotometer measure concentration from a light-absorption reading, which is the basis of countless laboratory assays.
Rearrange the law to c = A / (ε·l). Measure the absorbance, use the molar absorptivity for your compound at the measurement wavelength, and the path length of your cuvette (usually 1 cm). For example, an absorbance of 0.5 with ε = 10,000 M⁻¹cm⁻¹ and a 1 cm path gives c = 0.5 / 10,000 = 5×10⁻⁵ M, or 50 µM. The calculator does this when you select "concentration" as the unknown.
Molar absorptivity (or extinction coefficient), ε, measures how strongly a substance absorbs light at a particular wavelength, with units of M⁻¹cm⁻¹. It is an intrinsic property of the compound and the wavelength, so it must be quoted for the specific conditions used. Strongly coloured dyes and many biological molecules have very high ε values (tens of thousands), which makes the method sensitive. You can determine ε by measuring a standard of known concentration and rearranging the law.
Because the linear relationship breaks down at high absorbance. As concentration rises, molecular interactions, shifting equilibria, stray light, and the instrument's finite bandwidth all cause the absorbance to fall below the value the law predicts, so concentrations read low. Keeping absorbance under about 1 (some labs allow up to 1.5) stays in the reliable, linear region. If a reading is higher, dilute the sample by a known factor, re-measure, and multiply back.
Transmittance is the fraction of light that passes through the sample (often given as a percentage), while absorbance is the base-ten logarithm of the inverse of transmittance. They're two views of the same measurement: 100% transmittance is zero absorbance, 10% transmittance is absorbance 1, and 1% is absorbance 2. Absorbance is used for quantification because it, not transmittance, is linear with concentration. The calculator reports the equivalent percent transmittance alongside the result.
A calibration curve — absorbances of several standards of known concentration — is more robust than relying on a textbook ε. It automatically accounts for your specific instrument, cuvette, wavelength setting, and any mild non-linearity, and it lets you check that the response really is linear over your working range. You then read unknowns off the fitted line. Using a single literature ε is convenient and fine for rough work, but standards are the gold standard for accurate quantification.
Several things: a turbid or scattering sample (suspended particles, bubbles), a dirty or scratched cuvette, the wrong or no blank, absorbance outside the linear range, and using an ε measured at a different wavelength or in a different solvent. Fingerprints on the cuvette and incorrect cuvette orientation also matter. Always blank against the solvent, keep the cuvette clean, ensure the sample is clear and homogeneous, and work within the linear absorbance range for trustworthy results.
Yes — absorbance is directly proportional to it. Standard cuvettes are 1 cm, which is why path length is often "1" and quietly ignored, but micro-volume instruments and plate readers use much shorter paths (sometimes a fraction of a millimetre), which lowers the absorbance for the same concentration and must be accounted for. If you switch cuvette sizes or use a plate reader, put the correct path length into the calculation, or your concentrations will be off by that ratio.
Use it for learning and quick calculations. For results that matter, validate against standards or a calibration curve, work within the linear range, and follow your instrument's procedure. This tool runs the exact A = ε·c·l relationship and is educational; reproducing the quantification with proper standards and a validated method is good laboratory practice.
No. The values you enter are processed entirely in your browser. Nothing is sent to a server, stored, or shared, and no account is required. The calculation runs on your device only.
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