Beer–Lambert Law Calculator
Pick the unknown — absorbance, molar absorption coefficient, path length or concentration — and enter the other three in the units you have. The calculator solves A = εlc, shows the working, and gives the matching percent transmittance. A second mode converts between absorbance and transmittance on its own. Free, no sign-up.
ε at the wavelength you measure. M⁻¹ cm⁻¹ is the same as L mol⁻¹ cm⁻¹; the SI unit m² mol⁻¹ is 10 times smaller in number.
Results
0.622
Absorbance (A)
23.9%
Transmittance (%T)
76.1%
Light absorbed
The working
A = ε × l × c
Concentration (c): 100. µM = 1.0000 × 10⁻⁴ mol/L
A = 6220 × 1 × 1.0000 × 10⁻⁴ = 0.6220
%T = 10^(2 − A) = 10^(2 − 0.622) = 23.878113%
How to Use the Beer–Lambert Law Calculator
- 1. Choose the mode. "A = εlc for any term" solves the Beer–Lambert law; "Absorbance ↔ transmittance" converts a single reading.
- 2. Pick what you want to find. Most often it is the concentration of a sample from its measured absorbance, but ε and l can be found too. The answer box turns into a unit menu.
- 3. Enter the rest with units. The molar absorption coefficient can be in M⁻¹ cm⁻¹, mM⁻¹ cm⁻¹ or m² mol⁻¹; path length in cm, mm or m; concentration from nM to M. A reading given as %T or as a fraction T is converted to absorbance first.
- 4. Check the range note. The calculator warns when absorbance is below about 0.1 or above about 1, where most instruments lose accuracy.
The Beer–Lambert Law
Law
A = ε × l × c
Absorbance
A = log₁₀(I₀ / I) = −log₁₀ T
Transmittance
%T = 100 × 10^(−A)
Concentration
c = A / (ε × l)
A is the absorbance (a pure number), ε the molar absorption coefficient at the wavelength used, l the path length through the sample (1 cm for a standard cuvette) and c the concentration of the absorbing species. IUPAC calls ε the molar (decadic) absorption coefficient; "molar extinction coefficient" is the older, still common name, and IUPAC advises against "molar absorptivity". Its usual unit is L mol⁻¹ cm⁻¹, which is the same as M⁻¹ cm⁻¹; the SI unit is m² mol⁻¹, and 1 m² mol⁻¹ equals 10 M⁻¹ cm⁻¹.
Absorbance is logarithmic: each unit of A removes 90% of what is left. That is why a reading of 2 means only 1% of the light gets through, and why absorbance adds up for stacked samples while transmittance multiplies.
| Absorbance (A) | Transmittance (%T) | Light absorbed |
|---|---|---|
| 0 | 100 | 0% |
| 0.1 | 79.4 | 20.6% |
| 0.3 | 50.1 | 49.9% |
| 0.5 | 31.6 | 68.4% |
| 1 | 10 | 90% |
| 2 | 1 | 99% |
| 3 | 0.1 | 99.9% |
Worked Examples
Absorbance of NADH (the default inputs). NADH absorbs at 340 nm with ε ≈ 6220 M⁻¹ cm⁻¹, a value widely used in enzyme assays (some references give about 6300, so use your lab's). A 100. µM solution in a 1.00 cm cuvette has A = 6220 × 1.00 × 1.00 × 10⁻⁴ = 0.622, which is 23.9% transmittance.
Concentration from a reading. A sample of the same compound reads A = 0.450. Then c = 0.450 ÷ (6220 × 1) = 7.23 × 10⁻⁵ M, or 72.3 µM. Taking the reading as %T instead: 35.5% transmittance is the same A = 0.450.
Finding ε. A 40.0 µM solution gives A = 0.800 in a 1.00 cm cell, so ε = 0.800 ÷ (1.00 × 4.00 × 10⁻⁵) = 20 000 M⁻¹ cm⁻¹. Halving the path length to 0.5 cm would halve the absorbance.
When the Law Stops Working
- High absorbance. Above A ≈ 1 the detector sees mostly stray light, and the plot of A against c bends over. Dilute and remeasure.
- Concentrated solutions. Above about 10 mM, molecules interact and ε changes.
- Wide bandwidth. The law assumes narrow, monochromatic light; IUPAC states it holds only when the bandwidth is narrow compared with the spectral lines.
- Chemistry in the cuvette. Dimerization, ionization or a pH-sensitive dye changes the absorbing species as you dilute it.
- Scattering and cloudy samples. Light scattered out of the beam is counted as absorbed. Filter or centrifuge first.
If you have several standards rather than a literature ε, fit a calibration line instead: the Standard Curve Calculator takes absorbances of known concentrations and reads off the unknown. Remember to subtract a blank, and keep unknowns inside the range of the standards.
Frequently Asked Questions
- What is the Beer–Lambert law formula?
- A = εlc: absorbance equals the molar absorption coefficient times the path length times the concentration. It says that a dilute solution absorbs light in proportion to how much absorbing material the beam passes through.
- How do I calculate concentration from absorbance?
- Divide the absorbance by ε and by the path length: c = A ÷ (ε × l). With A = 0.450, ε = 6220 M⁻¹ cm⁻¹ and l = 1 cm, c = 7.23 × 10⁻⁵ M. Make sure the absorbance has been blank-corrected.
- How do I convert absorbance to transmittance?
- Transmittance is 10 raised to the power of minus the absorbance, T = 10^(−A); multiply by 100 for percent. So A = 1 is 10% T and A = 2 is 1% T. In reverse, A = 2 − log₁₀(%T).
- What is a good absorbance range for a spectrophotometer?
- Roughly 0.1 to 1.0, equal to about 80% down to 10% transmittance. Below 0.1 the signal is close to noise, and above about 1 stray light makes the response non-linear. Dilute or change the path length to bring a sample into range.
- What is the difference between the molar extinction coefficient and the molar absorption coefficient?
- They are the same quantity. IUPAC recommends "molar (decadic) absorption coefficient"; "molar extinction coefficient" is the older name. "Molar absorptivity" is also used, but IUPAC advises against it.
- Why is my calibration curve not a straight line at high concentration?
- The Beer–Lambert law is a limiting law. At high absorbance stray light, wide bandwidth, molecular interactions or chemical equilibria bend the curve. Keep standards below about A = 1, or dilute the unknown into the linear region.