Beer-Lambert Law Calculator

The Beer–Lambert relationship for a uniform sample is:

A = ε · l · c

• A is absorbance (base-10, unitless).
• ε is molar absorptivity, commonly in L·mol⁻¹·cm⁻¹.
• l is optical path length (converted to cm here).
• c is concentration (converted to mol/L here).

Transmittance is linked to absorbance by:

T = I / I₀ = 10^−A   and   %T = 100 · T

If you use the natural-log form, the optical depth is τ = ln(I₀/I) and relates to absorbance by τ = ln(10) · A.

1. Select a calculation mode based on your measurements.
2. Choose base-10 absorbance (A) or natural optical depth (τ).
3. Enter your known values. Use correct units and keep them consistent.
4. Press Calculate to show results above the form.
5. Use the CSV or PDF buttons to export your computed outputs.

These examples assume base-10 absorbance with ε in L·mol⁻¹·cm⁻¹.

Absorbance as a logarithmic measurement

Absorbance is unitless and logarithmic, so equal changes in A represent multiplicative changes in transmitted intensity. For example, A = 0.30 corresponds to T ≈ 50%, while A = 1.00 corresponds to T = 10%. This scaling is why spectrometers report absorbance for wide dynamic ranges.

Typical values used in laboratory optics

In UV–Vis work, practical absorbance often falls between 0.10 and 1.50. Below 0.05, noise and stray light can dominate; above about 2.0, very little light reaches the detector. Path lengths are commonly 1 cm cuvettes, but microcells can be 0.1–0.5 cm for concentrated samples.

Choosing path length for sensitivity

Sensitivity increases with path length because A = εlc. Doubling l doubles A at fixed ε and c. If your analyte is weakly absorbing (small ε), using a 5 cm or 10 cm cell can bring absorbance into a measurable range. For strongly absorbing dyes, shorter paths prevent saturation.

Molar absorptivity and wavelength dependence

Molar absorptivity ε depends on wavelength, temperature, and chemical environment. Many organic chromophores have ε from about 1×10³ to 1×10⁵ L·mol⁻¹·cm⁻¹ near absorption peaks. Reporting ε should include wavelength (nm) and solvent conditions for reproducibility.

Working with concentration units

This calculator supports mol/L, mmol/L, mol/m³, and g/L. A useful conversion is 1 mol/m³ = 0.001 mol/L. When using g/L, concentration in mol/L equals (g/L) divided by molar mass (g/mol). This is important for proteins, salts, and formulations specified by mass.

Base-10 absorbance versus optical depth

Some fields use the natural-log form I = I₀e^−τ, where τ = ln(I₀/I). The two are equivalent through τ = ln(10)·A ≈ 2.3026A. Switching bases does not change the physics; it changes the numerical scale and how you interpret “one unit” of attenuation.

Measurement tips that improve linearity

Use a proper blank, keep cuvettes clean, and match the reference solvent. Stray light and detector limits can bias high-absorbance readings. Mix solutions thoroughly and allow temperature to equilibrate. If you are fitting a calibration curve, collect at least 5 standards spanning the expected concentration range.

When Beer–Lambert assumptions fail

Departures from linearity can occur at high concentration due to molecular interactions, scattering, fluorescence, or refractive-index changes. Turbid samples may require integrating spheres or scattering corrections. If A versus c deviates from a straight line, dilute the sample or choose a different wavelength where absorbance is lower.

1) What is a good absorbance range for accurate readings?

Many instruments perform best around A = 0.10 to 1.50. Very low absorbance can be noise-limited, and very high absorbance can be biased by stray light and detector floor.

2) Can I use this calculator for infrared or fluorescence experiments?

You can use it for any wavelength if Beer–Lambert assumptions apply. For fluorescence, intensity is not simply transmitted light, so Beer–Lambert may not describe the signal without additional modeling.

3) Why does the calculator convert path length to centimeters?

ε is commonly reported in L·mol⁻¹·cm⁻¹. Converting l to cm keeps the calculation consistent and helps avoid unit mistakes when you enter mm, m, inches, or feet.

4) How do I compute concentration from g/L?

Convert mass concentration to molar concentration using c (mol/L) = (g/L) ÷ (g/mol). Enter molar mass so the calculator can perform this conversion correctly.

5) What is the difference between absorbance A and optical depth τ?

Absorbance uses log base 10, while optical depth uses the natural logarithm. They relate by τ = ln(10)·A, so they represent the same attenuation expressed with different log bases.

6) What if my transmitted intensity I is larger than I₀?

That usually indicates a measurement setup issue, such as incorrect blanking, detector saturation, or a changing light source. Re-measure I₀, check alignment, and confirm consistent units.

7) Does Beer–Lambert law always produce a straight line calibration?

Not always. High concentrations, scattering, chemical equilibria, and instrumental stray light can cause curvature. Dilution, wavelength selection, and improved sample preparation often restore linear behavior.