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Beer–Lambert Law Calculator (A = εlc)
In short: Beer–Lambert law calculator: solve A = εlc for absorbance, ε, path length or concentration, convert %T to absorbance and find an unknown from a calibration curve. It is free, works in your web browser and needs no download.
Enter any three of absorbance, molar absorptivity, path length and concentration to find the fourth. Choose mol/L, mmol/L or µmol/L and cm or mm. Switch to calibration mode to paste your standards and get the best-fit line, R² and the unknown concentration.
Fill in three values and leave the one you want to find blank.
Transmittance ↔ absorbance
Beer–Lambert law formulas
A = ε × l × c c = A / (ε l) ε = A / (l c) l = A / (ε c)
A = −log₁₀ T = log₁₀(I₀/I) A = 2 − log₁₀(%T) %T = 10^(2 − A)
A is absorbance (no units). ε is the molar absorptivity (also called the molar extinction coefficient) in L mol⁻¹ cm⁻¹. l is the path length in cm. c is the concentration in mol/L. A standard cuvette has l = 1.00 cm.
| Absorbance A | 0 | 0.1 | 0.3 | 0.5 | 1.0 | 2.0 | 3.0 |
|---|---|---|---|---|---|---|---|
| % transmitted | 100 | 79.4 | 50.1 | 31.6 | 10 | 1 | 0.1 |
Calibration curve
Measure several standards of known concentration and plot A against c. A least-squares line A = m·c + b gives the slope m = εl. Read an unknown from c = (A − b)/m. R² close to 1 (above about 0.995) shows a good straight line. Only trust results inside the range of your standards.
Worked examples
NADH concentration
NADH has ε = 6220 L mol⁻¹ cm⁻¹ at 340 nm. A sample in a 1.00 cm cell reads A = 0.311.
c = A/(εl) = 0.311 / (6220 × 1.00)
c = 5.00 × 10⁻⁵ M = 50.0 µM
Transmittance to absorbance
A solution transmits 25.0% of the light. Find A.
A = 2 − log₁₀(25.0) = 2 − 1.398
A = 0.602
Find ε (AP style)
A 2.50 × 10⁻⁵ M dye solution in a 1.00 cm cell has A = 0.452.
ε = A/(lc) = 0.452 / (1.00 × 2.50 × 10⁻⁵)
ε = 1.81 × 10⁴ L mol⁻¹ cm⁻¹
Dilution plus Beer–Lambert (JEE style)
A stock is diluted 10 times. The diluted solution gives A = 0.250 with ε = 5000 L mol⁻¹ cm⁻¹ and l = 1 cm.
Diluted c = 0.250/5000 = 5.0 × 10⁻⁵ M. Multiply by the dilution factor.
Stock = 5.0 × 10⁻⁴ M
Unknown from a calibration curve
Standards of 0 to 50 µM give A = 0.01231·c + 0.0013 (R² = 0.99998). The unknown reads A = 0.300.
c = (0.300 − 0.0013) / 0.01231
c ≈ 24.3 µM (ε ≈ 1.23 × 10⁴ L mol⁻¹ cm⁻¹)
Double the path length
A = 0.40 in a 1 cm cell. The same solution is put in a 2 cm cell.
A is proportional to l, so A doubles.
A = 0.80 (%T falls from 39.8% to 15.8%)
Units and common mistakes
- Path length in cm. 10 mm = 1 cm. A 5 mm cell is 0.5 cm, not 5.
- Concentration in mol/L. Convert µM or mM first, or let the calculator do it. If ε is given per mg/mL (or as A for 1 mg/mL), use mass concentration instead.
- Absorbance has no units. Do not write "A = 0.5 M". The units of ε cancel the units of l and c.
- Use log base 10. A = −log₁₀T. Using ln gives values 2.303 times too large.
- %T or T. T is a fraction (0.25). %T is a percentage (25). A = −log T = 2 − log %T.
- Stay in the linear range. Most spectrophotometers are reliable for A between about 0.1 and 1.0. Above about 1.5, stray light and chemical effects bend the curve. Dilute the sample instead.
- Blank first. Zero the instrument with the solvent (and reagents) so that A comes only from the analyte.
- Measure at λmax. ε depends on wavelength. Use the same wavelength for standards and unknowns.
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Open MolDraw editorFrequently asked questions
What is the Beer–Lambert law?
It says absorbance is proportional to concentration and path length: A = εlc. Double the concentration or the path length and the absorbance doubles. It holds well for dilute solutions at a single wavelength.
What are the units of molar absorptivity ε?
L mol⁻¹ cm⁻¹ (also written M⁻¹ cm⁻¹). These units make A = εlc unitless when l is in cm and c in mol/L. Strongly absorbing dyes have ε above 10⁴; weak d–d transitions can be below 100.
How do I convert transmittance to absorbance?
A = −log₁₀T, or A = 2 − log₁₀(%T). For example 50% T gives A = 0.301, 10% T gives A = 1, and 1% T gives A = 2.
Why is my calibration curve not straight at high absorbance?
Above about A = 1 to 1.5 very little light reaches the detector, so stray light and noise matter. Concentrated solutions can also show molecular interactions. Dilute samples into the linear range.
What does the slope of an absorbance vs concentration graph mean?
The slope equals εl. With a 1 cm cell the slope (in L/mol) is the molar absorptivity ε. If concentration is in µM, divide the slope by 10⁻⁶ to get ε in L mol⁻¹ cm⁻¹.
Should a calibration line pass through zero?
Ideally yes, after blanking. A small intercept is normal because of blank and cuvette errors. This calculator fits the intercept rather than forcing it to zero, and uses it when it finds the unknown.
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