Beer Lambert Law Calculator | Beer's Law

Calculate absorbance, concentration, or transmittance using the Beer-Lambert law (Beer\'s law). This is the fundamental equation of spectrophotometry: A = εbc. Find any variable when you know the other two.

In same units as ε

Usually 1 cm for cuvettes

M⁻¹cm⁻¹ at λmax

BEER-LAMBERT LAW: A = εbc Where: - A = Absorbance (unitless, -log₁₀(T)) - ε = Molar extinction coefficient (M⁻¹cm⁻¹) - b = Path length through sample (cm) - c = Concentration (M or mol/L) REARRANGED EQUATIONS: 1. Concentration: c = A / (εb) 2. Path Length: b = A / (εc) 3. Extinction: ε = A / (bc) RELATIONSHIPS: Transmittance: T = I / I₀ Absorbance: A = -log₁₀(T) Or: T = 10^(-A)
Example 1: Find concentration from absorbance Given: A = 0.500, ε = 10,000 M⁻¹cm⁻¹, b = 1 cm c = A / (εb) = 0.5 / (10000 × 1) = 0.5 / 10000 = 5 × 10⁻⁵ M Example 2: Find absorbance at given concentration ε = 6200 M⁻¹cm⁻¹ (NADH at 340 nm) c = 0.0001 M (100 μM) b = 1 cm A = εbc = 6200 × 0.0001 × 1 = 0.62 Example 3: Convert T% to A T = 50% A = -log₁₀(0.50) = -(-0.301) = 0.301

What is the Beer-Lambert law?

The Beer-Lambert law (Beer's law) relates absorbance to concentration: A = εbc, where A is absorbance (unitless), ε is molar extinction coefficient (M⁻¹cm⁻¹), b is path length (cm), and c is concentration (M). It's the foundation of spectrophotometry—absorbance is directly proportional to concentration for dilute solutions.

What is molar extinction coefficient?

The molar extinction coefficient (ε) measures how strongly a substance absorbs light at a given wavelength. Higher ε = stronger absorber. Values range from 10 to 10⁶ M⁻¹cm⁻¹. Found experimentally orLooked up (proteins: ε₂₈₀ ≈ 10⁴-10⁵, NADH: ε₃₄₀ = 6,200 M⁻¹cm⁻¹). Each compound has characteristic ε at its λmax.

What is absorbance vs transmittance?

Transmittance (T) = I/I₀ (light passing through / incident). Absorbance (A) = -log₁₀(T). T = 10^(-A). At T = 50%, A = -log₁₀(0.5) = 0.301. At T = 1%, A = 2. Most instruments read absorbance directly. The Beer-Lambert law uses absorbance, not transmittance.

What are the limitations of Beer's law?

Beer's law works only for dilute solutions (< 0.01 M). Deviations occur at high concentrations (intermolecular interactions), with polychromatic light (multiple wavelengths), with stray light, and when chemical equilibria shift with concentration. Check linearity with a standard curve.

How do I find concentration from absorbance?

Method 1: If you know ε, use c = A/(εb). Method 2: Run standards of known concentration, plot A vs c (should be linear),fit line, use equation to solve for unknown samples. Always use blank to zero the instrument.

How do I use this for protein concentration?

Proteins absorb at 280 nm (aromatic amino acids). Use epsilon = (5500 times number of Trp) + (1500 times number of Tyr) + (125 times number of Cystine). Or measure by A280 and dilute until A is about 0.5-1.0, then use Beer's law. Quick estimate: 1 A280 is about 1 mg/mL for most proteins.

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