Beer's Law Calculator

Calculate concentration from absorbance using the Beer-Lambert Law

Beer's Law Calculator

Beer's Law (Beer-Lambert Law): A = εbc
Relates the absorption of light to the properties of the material through which light travels.

Unitless (optimal: 0.1-1.0)

L/(mol·cm) or M⁻¹cm⁻¹

cm (typical: 1.0 cm cuvette)

Notes:

  • • Beer's Law is valid only for dilute solutions and monochromatic light
  • • Optimal absorbance range: 0.1 - 1.0 for accurate measurements
  • • Molar absorptivity (ε) is a constant for a given substance at a specific wavelength
  • • Standard cuvette path length is 1.0 cm
  • • Transmittance (T) = 10^(-A), where %T = T × 100

Understanding Beer's Law

Beer's Law (also known as the Beer-Lambert Law or Beer-Lambert-Bouguer Law) is a fundamental principle in spectroscopy that establishes a linear relationship between the absorbance of light by a solution and the concentration of the absorbing species. It's one of the most important equations in analytical chemistry.

The Beer-Lambert Law Equation

A = εbc

Absorbance as a Function of Concentration

A = Absorbance

Unitless measure of light absorption (also called optical density)

ε = Molar Absorptivity

Constant for a given substance at specific wavelength (L/(mol·cm) or M⁻¹cm⁻¹)

b = Path Length

Distance light travels through sample (usually 1.0 cm in standard cuvettes)

c = Concentration

Molar concentration of absorbing species (mol/L or M)

Relationship with Transmittance

Absorbance and transmittance are inversely related:

T = I / I₀

A = -log₁₀(T) = log₁₀(I₀ / I)

%T = T × 100

Where:

  • T = Transmittance (fraction of light passing through)
  • I₀ = Incident light intensity
  • I = Transmitted light intensity
  • %T = Percent transmittance

Optimal Absorbance Range

Absorbance Range%TransmittanceAccuracyRecommendation
0 - 0.1100% - 79%PoorToo dilute - concentrate sample
0.1 - 1.079% - 10%ExcellentOptimal range ✓
1.0 - 2.010% - 1%GoodAcceptable - some deviation
> 2.0< 1%PoorToo concentrated - dilute sample

Practical Example: Protein Concentration

Problem: A protein solution shows an absorbance of 0.450 at 280 nm. The molar absorptivity of the protein at 280 nm is 43,824 L/(mol·cm). Using a standard 1.0 cm cuvette, what is the protein concentration?

Given:

  • A = 0.450 (within optimal range ✓)
  • ε = 43,824 L/(mol·cm)
  • b = 1.0 cm

Solution:

c = A / (εb)
c = 0.450 / (43,824 × 1.0)
c = 1.027 × 10⁻⁵ M
c = 10.27 μM

The transmittance is: T = 10^(-0.450) = 35.5% (65% of light absorbed)

Typical Molar Absorptivity Values

Biological Molecules

  • • DNA (260 nm): ~6,600 M⁻¹cm⁻¹
  • • Proteins (280 nm): 5,000-100,000 M⁻¹cm⁻¹
  • • NADH (340 nm): 6,220 M⁻¹cm⁻¹
  • • Chlorophyll a (428 nm): 112,000 M⁻¹cm⁻¹

Common Dyes

  • • Methylene Blue (664 nm): 95,000 M⁻¹cm⁻¹
  • • Crystal Violet (590 nm): 87,000 M⁻¹cm⁻¹
  • • p-Nitrophenol (400 nm): 18,000 M⁻¹cm⁻¹
  • • Bromothymol Blue (616 nm): 13,000 M⁻¹cm⁻¹

Limitations of Beer's Law

⚠️ High Concentrations

At high concentrations (>0.01 M), molecular interactions cause deviations from linearity

⚠️ Chemical Changes

Dissociation, association, or pH-dependent equilibria can affect absorbance

⚠️ Polychromatic Light

Beer's Law assumes monochromatic light; broad wavelength ranges reduce accuracy

⚠️ Scattering

Particulates or turbidity cause light scattering, leading to apparent higher absorbance

Applications

  • 🔬
    Analytical Chemistry: Quantitative analysis of chemical species in solution
  • 🧬
    Biochemistry: Protein and nucleic acid concentration determination
  • 🌊
    Environmental Science: Water quality testing and pollutant monitoring
  • 💊
    Pharmaceutical Industry: Drug concentration analysis and quality control
  • 🍷
    Food Science: Color intensity and additive concentration measurement
  • 🩺
    Clinical Chemistry: Medical diagnostics and blood analysis

📊Quick Reference

Formula:

A = εbc

Optimal A:

0.1 - 1.0 (best accuracy)

Standard Path:

1.0 cm cuvette

Transmittance:

T = 10^(-A)

Level:

General Chemistry / Analytical

🔗Related Calculators

📐Related Formulas

🎯Where It's Used

  • 🔬

    Spectroscopy

    UV-Vis concentration analysis

  • 🧬

    Biochemistry

    Protein/DNA quantification

  • 💊

    Pharmaceuticals

    Drug quality control

  • 🌊

    Environmental

    Water quality testing