Beer-Lambert Law Calculator | Absorbance, Transmittance & Concentration
Apply the Beer-Lambert law A = εlc to compute absorbance, percent transmittance, molar absorptivity (ε), path length, or concentration from any four known quantities. Supports multi-wavelength analysis and mixture concentration estimation.
PRESET: CHLOROPHYLL a AT 663 nm
SOLVE FOR
Absorbance A
0.8400
%T — Percent transmittance
14.45 %
%A — Percent absorbed
85.55 %
ε computed (L·mol⁻¹·cm⁻¹)
8.400e+4
Path length l (cm)
1.0000
Concentration c (mol/L)
1.000e-5
COMMON MOLAR ABSORPTIVITIES
| Compound | λmax (nm) | ε (L·mol⁻¹·cm⁻¹) | Solvent |
|---|---|---|---|
| Chlorophyll a | 663 | 84,000 | Acetone |
| Chlorophyll b | 645 | 56,100 | Acetone |
| β-Carotene | 450 | 140,000 | Hexane |
| Hemoglobin (oxy) | 415 | 125,000 | Water (pH 7) |
| NADH | 340 | 6,220 | Water |
| Cytochrome c (ox) | 410 | 106,000 | Water |
| Phenol red (pH 7) | 558 | 54,000 | Water |
| p-Nitroaniline | 375 | 13,000 | Ethanol |
What Is the Beer-Lambert Law Calculator | Absorbance, Transmittance & Concentration?
The Beer-Lambert law relates the attenuation of light passing through a solution to the properties of the material. It forms the quantitative basis of UV-Vis spectrophotometry, used daily in analytical chemistry, biochemistry, and clinical diagnostics.
The law holds under conditions of monochromatic light, dilute solutions (typically below 0.01 M), and absence of scattering or fluorescence. Deviations occur at high concentrations (chemical and physical), when stray light reaches the detector, or when the absorbing species undergoes equilibria over the measured concentration range.
Molar absorptivity ε is a fundamental molecular property — it quantifies how strongly a compound absorbs at a given wavelength. Values range from near zero (forbidden transitions) to above 10⁵ L·mol⁻¹·cm⁻¹ for strongly allowed π→π* transitions. The wavelength of maximum absorbance is called λmax and is used analytically to maximise sensitivity and Beer-Lambert linearity.
Formula
Beer-Lambert Law: A = ε · l · c A = absorbance (dimensionless, also called optical density OD) ε = molar absorptivity / extinction coefficient (L·mol⁻¹·cm⁻¹) l = optical path length (cm) c = molar concentration (mol/L) Transmittance: T = I/I₀ = 10^(−A) % Transmittance: %T = 100 × 10^(−A) % Absorbance: %A = 100 − %T
How to Use
- 1
Choose Solve for Unknown mode to calculate one missing quantity from A = εlc.
- 2
Select which variable to solve for using the radio buttons (A, ε, l, or c).
- 3
Enter the three known values: molar absorptivity in L·mol⁻¹·cm⁻¹, path length in cm, and concentration in mol/L.
- 4
Read Absorbance A, percent transmittance %T, and percent absorbance %A from the result boxes.
- 5
For Wavelength Scan mode, enter c and l, then add (wavelength, absorbance) pairs to find λmax and ε at each wavelength.
- 6
Click the preset button to load chlorophyll a example values (ε=84000, l=1 cm, c=1×10⁻⁵ mol/L).
Select a mode, enter the known values, and read the computed unknown. Use Wavelength Scan to find λmax from a series of measurements.
Example Calculation
Problem: A solution of chlorophyll a in acetone (ε = 84,000 L·mol⁻¹·cm⁻¹ at 663 nm) is measured in a 1 cm cuvette. The concentration is 1×10⁻⁵ mol/L. Find A and %T.
Solution:
A = ε × l × c = 84,000 × 1 × 1×10⁻⁵ = 0.840
%T = 100 × 10^(−0.840) = 100 × 0.1445 = 14.45%
%A = 100 − 14.45 = 85.55%
This means only 14.45% of the incident light passes through the sample; 85.55% is absorbed.
Understanding Beer-Lambert Law | Absorbance, Transmittance & Concentration
Absorbance vs. Transmittance Conversion Table
| A | %T | %A | Practical note |
|---|---|---|---|
| 0.000 | 100.0 | 0.0 | Blank — no absorption |
| 0.100 | 79.4 | 20.6 | Low absorption, near linear range |
| 0.300 | 50.1 | 49.9 | Mid-range |
| 0.500 | 31.6 | 68.4 | Optimal working range |
| 0.840 | 14.5 | 85.5 | Chlorophyll a preset example |
| 1.000 | 10.0 | 90.0 | Conventional upper working limit |
| 2.000 | 1.0 | 99.0 | High absorption, noise issues |
| 3.000 | 0.1 | 99.9 | Detector noise limits accuracy |
Applications of the Beer-Lambert Law
- ›Protein concentration determination (A280 using extinction coefficient from Trp/Tyr content)
- ›DNA/RNA quantification (A260: 1 OD ≈ 50 µg/mL dsDNA, 40 µg/mL ssRNA)
- ›Enzyme kinetics: track substrate or product absorbance change over time
- ›Blood glucose, bilirubin, and hemoglobin quantification in clinical analyzers
- ›Environmental monitoring: NO₂, SO₂, ozone concentration in air via DOAS
- ›Pharmaceutical QC: potency assay of active ingredients in formulations
- ›Reaction monitoring: follow conversion in real time for process chemistry
Frequently Asked Questions
What is the Beer-Lambert law used for?
It is used to determine the concentration of an absorbing species in solution by measuring how much light the solution absorbs at a specific wavelength. Applications range from protein and DNA quantification to clinical diagnostics and environmental analysis.
What is molar absorptivity (ε) and what are typical values?
Molar absorptivity ε (L·mol⁻¹·cm⁻¹) is a measure of how strongly a substance absorbs light at a given wavelength. Typical values range from ~10 for forbidden transitions to over 100,000 for strongly allowed π→π* transitions in aromatic or conjugated systems. Hemoglobin at the Soret band (415 nm) has ε ≈ 125,000.
Why does Beer-Lambert law fail at high concentrations?
At high concentrations (>0.01 M), solute-solute interactions alter the refractive index and each molecule's electronic environment, causing ε to change with concentration. Hydrogen bonding, aggregation, and dimerisation also change spectral characteristics. Chemically, equilibria such as pH-dependent speciation shift the absorbing species distribution.
What is the optimal absorbance range for accurate measurements?
The most accurate measurements are obtained between A = 0.1 and A = 1.0 (10%–80% absorption). Below A = 0.1, the difference in I and I₀ is small and noise-limited. Above A = 1.0, very little light reaches the detector, increasing noise from stray light. Most protocols target A ≈ 0.5.
How is Beer-Lambert law used for mixture analysis?
For a mixture of n absorbing species all following Beer-Lambert independently, the total absorbance is additive: A_total = Σ(εᵢ·l·cᵢ). By measuring absorbance at multiple wavelengths equal to the number of unknown components and solving the resulting linear system, individual concentrations can be determined — the basis of multicomponent spectrophotometric analysis.
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