Solve A = ε·l·c for absorbance, concentration, molar absorptivity, or path length. Convert absorbance to percent transmittance, or back out an unknown concentration from a calibration curve's slope and intercept.
Inputs
Unitless. Leave blank to solve for absorbance from the other three values.
In L·mol⁻¹·cm⁻¹. Leave blank to solve for ε.
In cm — a standard cuvette is 1 cm. Leave blank to solve for l.
In mol/L (M). Leave blank to solve for c.
Result
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Leave exactly one field blank to solve for it, or fill all four to check consistency.
Transmittance—
Inputs
Enter this to solve for transmittance, or leave blank and enter %T instead.
Percent of light transmitted, 0–100. Enter this to solve for absorbance instead.
Result
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Enter absorbance or percent transmittance — the other converts automatically.
Calibration curve
Absorbance per unit concentration (M⁻¹), from a linear fit of standards (A vs. c).
Absorbance at zero concentration from the calibration fit. Usually near 0.
Measured absorbance of the sample whose concentration you want.
Result
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Enter the calibration slope/intercept and the unknown's absorbance to back out its concentration.
4 min read3 steps7 terms3 examples6 FAQsA = ε · l · c
The Beer-Lambert law is the equation behind every UV-Vis spectrophotometer reading: absorbance rises in direct proportion to how much of the light-absorbing substance is in the light's path.
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Walk-through
How to Use This Calculator
3 steps▸
1
Enter three of the four Beer-Lambert values
On the Solve tab, enter any three of absorbance (A), molar absorptivity (ε), path length (l), and concentration (c). Leave the fourth field blank — the calculator solves for it using A = ε·l·c. A standard cuvette path length is 1 cm.
2
Read the absorbance and transmittance
The result card shows the solved value along with the percent transmittance, computed as %T = 100 × 10⁻ᴬ. Switch to the Transmittance tab to convert between absorbance and %T directly in either direction.
3
Back out a concentration from a calibration curve
If you've already run a set of known standards through a spectrophotometer and fit a line (A = slope·c + intercept), use the Calibration tab: enter the slope and intercept from that fit plus your unknown sample's measured absorbance to get its concentration.
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Reference
Formula & Methodology
3 formulas▸
Beer-Lambert law
A = ε · l · c
A is absorbance (unitless). ε (epsilon) is the molar absorptivity of the substance at the wavelength being measured, in L·mol⁻¹·cm⁻¹. l is the path length of light through the sample, in cm. c is the molar concentration, in mol/L (M). Rearrange for whichever variable you need: ε = A/(lc), l = A/(εc), c = A/(εl).
Transmittance
T = 10⁻ᴬ, %T = 100 · 10⁻ᴬ
Transmittance is the fraction of incident light that passes through the sample. It relates to absorbance on a logarithmic scale — every increase of 1 in absorbance corresponds to a 10-fold decrease in transmitted light. The inverse relation is A = −log₁₀(T) = −log₁₀(%T/100).
Calibration-curve concentration
c = (A_unknown − b) / slope
From a linear regression of absorbance vs. concentration for known standards (A = slope·c + intercept), the slope equals ε·l for that instrument setup. Solving for c lets you find an unknown sample's concentration directly from its measured absorbance without knowing ε separately.
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Glossary
Key Terms Explained
7 terms▸
Beer-Lambert law ↗The relationship stating that absorbance is directly proportional to the concentration of an absorbing species and the path length light travels through it: A = ε·l·c. It is the foundation of quantitative spectrophotometry.
Absorbance ↗A unitless, logarithmic measure of how much light a sample absorbs at a given wavelength, defined as A = −log₁₀(I/I₀), where I₀ is the incident light intensity and I is the transmitted intensity. Higher absorbance means more light is absorbed.
Molar absorptivity ↗Also called the molar extinction coefficient (ε), a substance-specific and wavelength-specific constant describing how strongly it absorbs light, in units of L·mol⁻¹·cm⁻¹. Larger values mean the substance absorbs strongly even at low concentration.
Path length ↗The distance light travels through the sample, in cm. Most spectrophotometer cuvettes have a standard 1 cm path length, which is why many published ε values assume l = 1 cm.
Concentration ↗The molar concentration of the absorbing species in the sample, in mol/L (M). In Beer-Lambert calculations this refers specifically to the concentration of the species being measured, not the total solute concentration.
Transmittance ↗The fraction (or percentage) of incident light that passes through a sample without being absorbed, T = I/I₀. Transmittance and absorbance are inversely related on a logarithmic scale: T = 10⁻ᴬ.
Spectrophotometry ↗The technique of measuring how much light a sample absorbs or transmits at specific wavelengths, used to determine the concentration of a dissolved substance via the Beer-Lambert law.
A = 15,000 × 1 × 0.00001 = 0.15. This absorbance corresponds to about 70.8% transmittance — the sample lets most of the light through, which is typical for a dilute solution.
c = A/(εl) = 0.45 / (9,000 × 1) = 0.00005 M (50 µM). Leaving concentration blank and filling the other three fields solves for it directly — no algebra required.
c = (0.3 − 0) / 5,000 = 0.00006 M (60 µM). This is the standard workflow when the instrument's exact ε isn't known separately — the calibration slope already bakes in ε·l for that setup.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
The Beer-Lambert law is the equation behind every UV-Vis spectrophotometer reading: absorbance rises in direct proportion to how much of the light-absorbing substance is in the light's path. It's how chemists turn a simple light-transmission measurement into an exact concentration, and it underlies techniques from protein quantification to water-quality testing.
How the formula works
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When light passes through a solution, each molecule of the absorbing species has some chance of intercepting a photon. Double the concentration, and you double the number of molecules in the light's path — but because absorption compounds exponentially as light travels deeper into the sample, the practical measurement (absorbance) is defined on a logarithmic scale so that it stays linear with both concentration and path length. That's exactly what A = ε·l·c captures: absorbance scales linearly with concentration and with the distance light travels through the sample, and the molar absorptivity ε is the proportionality constant that depends on the specific substance and wavelength.
Because the relationship is linear, it can be inverted freely — the calculator uses the same equation to solve for any single unknown once you supply the other three.
Inputs and what they mean
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Absorbance (A) is unitless and typically read directly from a spectrophotometer; reliable readings are usually between about 0.1 and 1.0 — above roughly 1.5–2, stray light and instrument nonlinearity make the law less accurate, so dilute the sample instead of trusting very high readings. Molar absorptivity (ε) is a published, substance- and wavelength-specific constant (in L·mol⁻¹·cm⁻¹) — look it up for your specific compound and wavelength rather than reusing a value from a different assay. Path length (l) matches your cuvette, almost always 1 cm unless you're using a specialty microcuvette. Concentration (c) is in mol/L; for very dilute biological samples this is often a very small number like 10⁻⁵ or 10⁻⁶ M.
Limits and edge cases
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The Beer-Lambert law assumes a dilute, homogeneous, non-scattering solution measured with monochromatic light — it breaks down at high concentrations where molecules start interacting with each other, and in samples with particulates or turbidity that scatter light in addition to absorbing it. In practice, most labs don't compute ε directly; instead they build a calibration curve from several known standards and use its slope and intercept to read unknown concentrations, which is exactly what the Calibration tab automates. If your absorbance readings for known standards don't fall on a straight line, that's a signal the assay has drifted outside the law's valid range.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for the Beer-Lambert law?+
A = ε·l·c, where A is absorbance (unitless), ε is the molar absorptivity (L·mol⁻¹·cm⁻¹), l is the path length (cm), and c is the molar concentration (mol/L).
How do I solve for concentration?+
Rearrange the formula to c = A/(ε·l). On the Solve tab, just leave the concentration field blank and fill in absorbance, molar absorptivity, and path length — the calculator solves it for you.
How is absorbance related to transmittance?+
Transmittance is T = 10⁻ᴬ (or %T = 100 × 10⁻ᴬ). They describe the same measurement from opposite directions — as absorbance increases, transmittance decreases on a logarithmic scale.
What path length should I use?+
Whatever your cuvette actually is — almost always 1 cm for a standard spectrophotometer cuvette. Check your instrument's documentation if you're using a specialty microcuvette or flow cell, since those are often shorter.
What units does the calculator use?+
Absorbance is unitless. Molar absorptivity is in L·mol⁻¹·cm⁻¹. Path length is in cm. Concentration is in mol/L (M). Transmittance is reported as a percentage.
When does the Beer-Lambert law break down?+
At high concentrations (typically above roughly A = 1.5–2), where molecular interactions and instrument stray light cause deviations from linearity, and in samples with scattering particulates or turbidity. Dilute the sample and re-measure if your absorbance is unusually high.
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