Beer-Lambert Law Calculator
Solve the Beer-Lambert law, A = ε · l · c, for any one value: concentration, absorbance, molar absorptivity (extinction coefficient) or path length. Enter a reading as absorbance or percent transmittance and get molar or mass concentrations with the working shown.
Last updated:
Also written M⁻¹cm⁻¹ (multiply mM⁻¹cm⁻¹ by 1,000)
Also the unit for the answer when solving for concentration
For mass concentrations (e.g. BSA 66,430)
How to use the Beer-Lambert Law Calculator
- Choose what to solve for: concentration, absorbance, ε or path length.
- Enter your reading as absorbance, or switch the reading type to %T.
- Fill in the known values: ε in L·mol⁻¹·cm⁻¹, path length (1 cm for a standard cuvette) and the concentration if needed.
- Pick the concentration unit. Add a molar mass to work in mg/mL or µg/mL.
- Press Calculate to get the answer, the transmittance and a standard curve you can download.
Beer-Lambert law formulas
- Absorbance: A = ε · l · c
- Concentration: c = A / (ε · l)
- Molar absorptivity: ε = A / (l · c)
- Path length: l = A / (ε · c)
- Transmittance: T = I / I₀ = 10−A; A = −log₁₀ T = 2 − log₁₀(%T)
- Mass concentration: g/L = mol/L × molar mass. Mass absorptivity (L·g⁻¹·cm⁻¹) = ε ÷ molar mass.
Absorbance and transmittance
| Absorbance | % Transmittance | % Light absorbed |
|---|---|---|
| 0 | 100% | 0% |
| 0.1 | 79.4% | 20.6% |
| 0.301 | 50% | 50% |
| 0.5 | 31.6% | 68.4% |
| 1 | 10% | 90% |
| 1.5 | 3.16% | 96.8% |
| 2 | 1% | 99% |
| 3 | 0.1% | 99.9% |
Example molar absorptivities
Approximate literature values; check the value for your exact conditions (wavelength, buffer, pH) before relying on it.
| Substance | Wavelength | ε (L·mol⁻¹·cm⁻¹) |
|---|---|---|
| NADH / NADPH | 340 nm | 6,220 |
| Bovine serum albumin (BSA) | 280 nm | ≈ 43,800 |
| Tryptophan | 280 nm | ≈ 5,500 |
| Tyrosine | 280 nm | ≈ 1,490 |
| p-Nitrophenolate (alkaline) | 405 nm | ≈ 18,000 |
Tips for good measurements
- Blank first. Zero the instrument with a cuvette containing only the solvent or buffer so that only the sample's absorbance is measured.
- Stay in range. Aim for readings between 0.1 and 1.0. Dilute strong samples and remember to multiply the result by the dilution factor.
- Check the path length. Standard cuvettes are 1 cm, but microplate wells and micro-volume instruments use shorter, volume-dependent paths.
- Use the right wavelength. ε is only valid at the wavelength it was measured at, usually the absorption maximum.
- Build a standard curve when accuracy matters: the table below the results shows the absorbance you should expect at other concentrations.
Frequently asked questions
What is the Beer-Lambert law?
The Beer-Lambert law states that absorbance is proportional to concentration and path length: A = ε · l · c, where ε is the molar absorptivity (L·mol⁻¹·cm⁻¹), l is the path length in centimeters and c is the concentration in mol/L. Absorbance itself has no units.
How do I calculate concentration from absorbance?
Divide the absorbance by the molar absorptivity times the path length: c = A / (ε · l). For NADH at 340 nm (ε = 6,220 M⁻¹cm⁻¹) in a 1 cm cuvette, an absorbance of 0.45 means c = 0.45 / 6,220 = 7.23 × 10⁻⁵ M, or about 72 µM.
How do I convert transmittance to absorbance?
Use A = −log₁₀(T), where T is the fraction of light transmitted, or A = 2 − log₁₀(%T). For example 10% T is an absorbance of 1, 1% T is 2 and 50% T is about 0.301.
What is molar absorptivity?
Molar absorptivity, also called the molar extinction coefficient, measures how strongly a substance absorbs light at a particular wavelength. It is the absorbance of a 1 M solution in a 1 cm path. It depends on the substance, the wavelength and sometimes the solvent and pH.
What absorbance range is accurate?
Most spectrophotometers are most reliable between about 0.1 and 1.0 absorbance units. Above 1.5 to 2 so little light reaches the detector that stray light causes errors, and the law can also fail at high concentrations because molecules interact. Dilute concentrated samples into range.
How do I find ε from my own data?
Measure the absorbance of several known concentrations and plot absorbance against concentration. The slope of the straight line equals ε · l, so with a 1 cm cuvette the slope is ε. For a single standard, ε = A / (l · c).
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.