# Beer-Lambert Law Calculator

Calculate absorbance, concentration, molar absorptivity, or path length using Beer-Lambert law A = εbc. Includes transmittance calculation.

## What this calculates

Calculate any variable in the Beer-Lambert law equation: A = εbc. Solve for absorbance, concentration, molar absorptivity (extinction coefficient), or path length. Also computes percent transmittance.

## Inputs

- **Solve For** — options: Absorbance (A), Concentration (c), Molar Absorptivity (ε), Path Length (b) — Select which variable to calculate.
- **Absorbance (A)** — min 0 — Absorbance (dimensionless). Typically measured 0–3 for reliable results.
- **Molar Absorptivity (ε)** (L/(mol·cm)) — min 0 — Molar absorptivity (extinction coefficient) in L/(mol·cm).
- **Path Length (b)** (cm) — min 0 — Optical path length through the sample in cm. Standard cuvette = 1 cm.
- **Concentration (c)** (mol/L) — min 0 — Molar concentration of the absorbing species.

## Outputs

- **Result** — formatted as text — The calculated value with label and units.
- **Value** — Numeric result.
- **Transmittance (%T)** (%) — Percent transmittance of the sample.
- **Calculation** — formatted as text — Step-by-step calculation.

## Details

The Beer-Lambert law (also called Beer's law) is the fundamental equation of UV-Vis spectrophotometry. It relates the absorbance of a sample to the concentration of the absorbing species, the path length of light through the sample, and the molar absorptivity of the species.

The Law: A = εbc

- A = absorbance (dimensionless, also called optical density)

- ε = molar absorptivity (extinction coefficient) in L/(mol·cm)

- b = path length in cm (typically 1 cm for standard cuvettes)

- c = concentration in mol/L

Transmittance Relationship

Absorbance and transmittance are related by: A = -log₁₀(T) = -log₁₀(I/I₀), where T is the fraction of light transmitted and I/I₀ is the ratio of transmitted to incident light intensity. Percent transmittance = T × 100 = 10^(-A) × 100.

Limitations

Beer's law is linear only at low to moderate concentrations (typically A < 2). At high concentrations, molecular interactions, scattering, and detector limitations cause deviations from linearity. Always verify linearity with a calibration curve.

## Frequently Asked Questions

**Q: What is molar absorptivity (ε)?**

A: Molar absorptivity (also called the extinction coefficient) is a constant that describes how strongly a chemical species absorbs light at a given wavelength. Higher ε means stronger absorption. Typical values range from 10 (weak absorption) to 100,000+ L/(mol·cm) (strong absorption, such as porphyrins).

**Q: Why does Beer's law fail at high concentrations?**

A: At high concentrations (typically A > 2), deviations occur due to solute-solute interactions changing the absorption properties, refractive index changes, detector non-linearity, and stray light in the spectrophotometer. Always calibrate with standards spanning your expected range.

**Q: What is the typical path length?**

A: Standard UV-Vis cuvettes have a 1 cm path length. Microvolume spectrophotometers (like NanoDrop) use much shorter paths (0.05–1 mm). Flow cells may have paths from 1 mm to 10 cm. Longer paths increase sensitivity for dilute solutions.

**Q: How do I determine concentration from absorbance?**

A: Rearrange Beer's law: c = A/(εb). You need to know the molar absorptivity at your measurement wavelength and the path length. Alternatively, prepare a calibration curve of known concentrations and use the measured absorbance to interpolate the unknown concentration.

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Source: https://vastcalc.com/calculators/chemistry/beer-lambert
Category: Chemistry
Last updated: 2026-04-21