Beer-Lambert Law Calculator

Calculate solution concentration, absorbance, or path length using Beer-Lambert law (A = εlc).

Solve for

Molar absorptivity ε (L/mol·cm)

Path length l (cm) (cm)

Standard cuvette = 1 cm

Concentration c (mol/L) (mol/L)

Absorbance A (0–3)

Linear range: A < 1.5

Please check your inputs and try again.

Why Absorbance Is Logarithmic

Light passing through a solution loses a constant fraction of its intensity in each thin layer, not a constant amount. That produces exponential decay, and taking the logarithm converts it into something linear and additive — which is exactly what makes absorbance useful.

A = εlc A = −log₁₀(T) = −log₁₀(I/I₀)

Term	Meaning	Units
A	Absorbance	Dimensionless
ε	Molar absorptivity	L/(mol·cm) — intrinsic to the compound at a given wavelength
l	Path length	cm — usually 1.00 for a standard cuvette
c	Concentration	mol/L
T	Transmittance	Fraction of light passing through

Absorbance	Transmittance	Light absorbed
0	100%	None
0.3	50%	Half
1.0	10%	90%
2.0	1%	99%
3.0	0.1%	99.9%

Each unit of absorbance means another tenfold reduction in transmitted light. At A = 2 only 1% reaches the detector, and at A = 3 only 0.1% — which is why high absorbance readings become unreliable. Stray light and detector noise start to dominate the tiny remaining signal.

The Linear Range

Beer–Lambert holds well for A between roughly 0.1 and 1.0. Below 0.1 the signal is too close to the blank; above about 1.5 several effects break linearity:

Cause of deviation	What happens
Stray light	Detector sees light that bypassed the sample, capping apparent A
Chemical association	Dimers or aggregates at high concentration absorb differently
Refractive index change	Concentrated solutions alter light path
Polychromatic light	ε varies across the finite bandwidth of real monochromators

The practical response to a reading above 1.5 is dilution, not extrapolation. A calibration curve should also be constructed across the working range rather than assuming linearity from a single standard.

Worked Examples

Example 1: Find A: ε=5000, l=1cm, c=0.001 mol/L

A = 5000×1×0.001

Result: A = 5.0 (very high — dilute more)

A>2 is outside linear range

Example 2: Find c: A=0.5, ε=10000, l=1cm

c = 0.5/(10000×1)

Result: c = 5×10⁻⁵ mol/L = 50 μM

Standard spectrophotometry calculation

Example 3: Converting absorbance to transmittance

A = 0.30

Result: T = 50%

T = 10^−A = 10^−0.3 = 0.50. Half the light passes through — a useful benchmark for judging whether a reading sits in a sensible range.

Example 4: Sample too concentrated

A = 2.8 measured

Result: Dilute tenfold and re-measure

Only 0.16% of light reaches the detector at A = 2.8. Diluting tenfold brings A to about 1.8, and a further dilution reaches the reliable range.

Example 5: Determining ε from a calibration curve

Slope of A versus c is 12,400 with l = 1 cm

Result: ε = 12,400 L/(mol·cm)

Since A = εlc, the slope of a calibration plot equals εl. This is the standard way to measure molar absorptivity experimentally.

Common Mistakes

⚠️

Working outside the linear range

Readings above about 1.5 deviate from linearity because of stray light and chemical effects. Dilute the sample and re-measure rather than trusting the number.

⚠️

Forgetting to blank against the solvent

Absorbance must be measured relative to a blank containing everything except the analyte. Cuvette and solvent absorbance would otherwise be attributed to the sample.

⚠️

Using ε from the wrong wavelength

Molar absorptivity varies strongly with wavelength. Values are quoted at a specific λ, usually the absorption maximum, and are not transferable.

⚠️

Assuming the cuvette path length is always 1 cm

Standard cuvettes are 1.00 cm but micro-cuvettes and flow cells differ. Using the wrong path length scales every concentration incorrectly.

Frequently Asked Questions

What is the linear range of Beer-Lambert law?

A = 0.1–1.5 is the reliable range. Above A=2, stray light and detector saturation cause deviations. Dilute samples to keep A < 1.0 for best accuracy.

What is transmittance T?

T = I/I₀ = 10⁻ᴬ. A=1 means T=10%; A=2 means T=1%. %T = 100 × 10⁻ᴬ. Older spectrometers read %T directly.

What is the linear range of Beer–Lambert law?

Roughly A = 0.1 to 1.0 for reliable work, extending to about 1.5 with care. Beyond that, stray light and chemical effects cause systematic deviation.

What is transmittance?

The fraction of incident light passing through the sample. It relates to absorbance as T = 10^−A, so A = 1 corresponds to 10% transmittance.

Why does high absorbance become unreliable?

Each absorbance unit reduces transmitted light tenfold. At A = 3 only 0.1% reaches the detector, where stray light and noise dominate the measurement.

What is molar absorptivity?

An intrinsic property of a compound at a given wavelength, describing how strongly it absorbs. Values above 10,000 L/(mol·cm) indicate strong absorption suitable for trace analysis.

How do I find concentration from absorbance?

Rearrange to c = A/(εl). In practice a calibration curve across several standards is preferred, since its slope accounts for the actual instrument and cuvette.

Formula Explorer connections

Interpretation: This analytical relationship converts an instrument signal, separation measure or optical response into concentration, identity or performance. Assumption: Calibration, blank correction, linear range, path length, matrix effects and instrument settings must match the sample and method.

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