Beer–Lambert Law Calculator
Solve A = εlc for absorbance, molar absorptivity, path length or concentration. Convert absorbance to percent transmittance and back, or paste a set of standards to fit a calibration curve by least squares and read off an unknown’s concentration with R².
How to Use
- Choose what to solve for: concentration, absorbance, molar absorptivity ε or path length. Transmittance converts between A and %T, and Calibration curve fits a line to your standards.
- Enter the other three quantities with their units: ε in L/(mol·cm), mM⁻¹ cm⁻¹ or cm²/mol, the path length in cm or mm, and the concentration in M, mM, µM or nM.
- Read the answer in its own field and in the readouts, with the transmittance and the share of light absorbed. The picture shows the beam fading as it crosses the cuvette.
- For a calibration curve, paste one standard per line as concentration, absorbance, choose the unit and whether the line must pass through zero, and enter the unknown’s absorbance.
- Watch the message under Calculate: above A ≈ 1 it warns that the reading may be outside the linear range (a guideline, not a hard limit).
Worked Example
NADH in an enzyme assay. NADH absorbs at 340 nm with ε = 6,220 L/(mol·cm). A reading of A = 0.311 in a 1 cm cuvette gives c = A ÷ (εl) = 0.311 ÷ (6,220 × 1) = 5.0 × 10⁻⁵ mol/L = 50 µM. The transmittance is 10^(−0.311) = 48.87%, so the sample absorbs 51.13% of the light.
A calibration curve. Standards of 0, 10, 20, 30, 40 and 50 µM read 0.003, 0.124, 0.249, 0.372, 0.494 and 0.621. Least squares gives A = 0.012351c + 0.00171 with R² = 0.99996, so an unknown reading 0.300 is (0.300 − 0.00171) ÷ 0.012351 = 24.15 µM, inside the range of the standards. With a 1 cm cell the slope also gives ε = 12,351 L/(mol·cm).
The common mistake: taking the log of the percentage. A sample transmitting 25% of the light does not have A = −log₁₀ 25 = −1.398; a negative absorbance would mean the sample makes light. Use the fraction: A = −log₁₀ 0.25 = 0.602, which is the same as 2 − log₁₀ 25.
Show Work
Formulas
Bouguer, Lambert and Beer
The law has three authors spread over more than a century. Pierre Bouguer, studying how sunlight dims through the atmosphere, showed in his 1729 Essai d’optique sur la gradation de la lumière that each equal thickness of a medium removes the same fraction of light. Johann Heinrich Lambert put this into mathematical form in his Photometria of 1760: intensity falls exponentially with path length.
August Beer added the concentration in 1852, showing that a solution’s absorption depends on the amount of dissolved substance in the beam. Combined, A = εlc became the basis of colorimetry and later of the spectrophotometer, which makes it one of the most used equations in analytical chemistry, biochemistry and clinical laboratories.
The law assumes monochromatic light, a dilute solution in which the molecules don’t interact, and no scattering or fluorescence. Stray light and the instrument’s bandwidth make real readings bend away from the straight line at high absorbance, which is why calibration standards should bracket the unknown.
About This Tool
This calculator solves A = εlc for whichever quantity you need, with units on every field, and shows the transmittance and the light absorbed alongside. It converts between absorbance and percent transmittance in both directions, and fits a calibration curve to up to 200 standards by least squares, with or without an intercept, giving the slope, intercept, R², residuals, ε and the unknown’s concentration, with a warning when the unknown lies outside the standards.
The linear-range warning above A ≈ 1 is a guideline, not a property of the law: how far the line stays straight depends on the instrument. Everything runs in your browser; nothing is sent anywhere.
Related tools: Dilution Calculator, Molarity Calculator, and Concentration Converter.
Frequently Asked Questions
What is the Beer–Lambert law?
A = εlc: absorbance equals the molar absorptivity times the path length times the concentration. NADH absorbs at 340 nm with ε = 6,220 L/(mol·cm), so a reading of A = 0.311 in a 1 cm cuvette means c = 0.311 ÷ (6,220 × 1) = 5.0 × 10⁻⁵ M, or 50 µM.
How do you convert absorbance to transmittance?
T = 10^(−A), and A = −log₁₀ T = 2 − log₁₀(%T). A = 1 lets 10% of the light through and A = 2 only 1%. A sample transmitting 25% has A = −log₁₀ 0.25 = 0.602, not −log₁₀ 25 = −1.398.
Why does the Beer–Lambert law fail at high absorbance?
At high A almost no light reaches the detector, so small errors dominate. If 0.1% stray light reaches the detector, a true absorbance of 2 reads as 1.959 and a true 3 as only 2.699. As a guideline, many instruments are most accurate for A ≈ 0.1–1, so dilute samples that read above about 1–1.5.
How do you use a calibration curve?
Measure standards of known concentration, fit a straight line A = m·c + b, then solve c = (A − b) ÷ m for the unknown. Six standards from 0 to 50 µM give m = 0.012351 per µM, b = 0.00171 and R² = 0.99996, so an unknown reading 0.300 is 24.15 µM.
What units does ε have?
L mol⁻¹ cm⁻¹ (the same as M⁻¹ cm⁻¹), so that A has no units when l is in cm and c in mol/L. Biochemists often write NADH’s value as 6.22 mM⁻¹ cm⁻¹, which is 6,220 L/(mol·cm). In a 1 mm cuvette the same solution gives a tenth of the absorbance: 0.0622 instead of 0.622 for 0.10 mM NADH.
How do I use the Beer–Lambert Law Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Enzyme assays
An NADH-linked assay falling by 0.0622 absorbance units per minute at 340 nm in a 1 cm cell is using 10 µM of NADH per minute.
DNA and protein quantification
With the standard factor of 50 µg/mL per A₂₆₀ unit for double-stranded DNA, A₂₆₀ = 0.75 means 37.5 µg/mL.
Water and food testing
Colorimetric kits for nitrate, phosphate or iron compare a sample against a calibration line; six standards give the line and R² in one step.
Finding ε
A dye at 30 µM reading A = 0.45 in a 1 cm cell has ε = 15,000 L/(mol·cm).
Choosing a cuvette
A 0.4 mM sample with ε = 15,000 L/(mol·cm) gives A = 6 in 1 cm but 0.6 in a 1 mm cell, back inside the useful range.
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