Last updated: July 3, 2026
Beer–Lambert Law Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
Beer–Lambert law states A = εcl: absorbance equals molar absorptivity times concentration times path length. The calculator rearranges the equation to solve any one unknown and converts absorbance to transmittance using A = −log₁₀(T). For example, ε = 6300, c = 0.001 mol/L, and l = 1 cm gives A = 6.3.
Beer–Lambert law says absorbance equals molar absorptivity times concentration times path length: A equals epsilon c l. It can be rearranged to find concentration, path length, or molar absorptivity, and absorbance relates to transmittance by A equals negative log base ten of T.
Key Takeaways
- Beer–Lambert law is A = εcl for absorbance, molar absorptivity, concentration, and path length.
- Absorbance is dimensionless; ε is usually L·mol⁻¹·cm⁻¹ when c is mol/L and l is cm.
- Concentration is c = A/(εl), the most common rearrangement for UV–Vis assays.
- A = −log₁₀(T), so A = 1 corresponds to 10% transmittance and A = 2 to 1%.
- Dilute samples with absorbance above about 1 to reduce stray-light and nonlinearity errors.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
A = ε · c · l; A = −log₁₀(T); %T = 10^(−A) × 100
Where:
- A=Absorbance(dimensionless)
- ε=Molar absorptivity / extinction coefficient(L·mol⁻¹·cm⁻¹)
- c=Analyte concentration(mol/L)
- l=Optical path length(cm)
- T=Transmittance (I/I₀)(dimensionless)
- %T=Percent transmittance(%)
Worked Examples
Strongly absorbing sample
A dye has ε = 6300 L·mol⁻¹·cm⁻¹ at the analytical wavelength, c = 0.001 mol/L, and l = 1 cm.
- 1Use A = εcl.
- 2Substitute: A = 6300 × 0.001 × 1.
- 3A = 6.3, which is above the usual linear working range.
Typical dilute UV–Vis standard
A calibration standard has ε = 1000 L·mol⁻¹·cm⁻¹, c = 1 × 10⁻⁴ mol/L, and l = 1 cm.
- 1Apply A = εcl.
- 2A = 1000 × 1 × 10⁻⁴ × 1.
- 3A = 0.1, a useful low absorbance value for calibration.
Solve concentration from absorbance
Find the concentration when A = 0.5, ε = 5000 L·mol⁻¹·cm⁻¹, and l = 1 cm.
- 1Rearrange Beer–Lambert law: c = A/(εl).
- 2Substitute: c = 0.5/(5000 × 1).
- 3c = 1 × 10⁻⁴ mol/L.
Convert absorbance to transmittance
An absorbance of 1 means one tenth of the incident light reaches the detector.
- 1Use A = −log₁₀(T), so T = 10^(−A).
- 2For A = 1, T = 10⁻¹.
- 3T = 0.1, equivalent to 10% transmittance.
Convert A = 2 to percent transmittance
A sample with absorbance 2 transmits only one percent of incident light.
- 1Use %T = 10^(−A) × 100.
- 2For A = 2, %T = 10⁻² × 100.
- 3%T = 1%.
Introduction
The Beer–Lambert law connects light absorption to concentration: A = εcl. Absorbance A is unitless, ε is the molar absorptivity in L·mol⁻¹·cm⁻¹, c is concentration in mol/L, and l is path length in cm. This calculator solves for any one unknown and also converts between absorbance, transmittance, and percent transmittance. It is useful for UV–Vis calibration curves, colorimetric assays, and checking whether a sample should be diluted before measurement.
Beer–Lambert law formula
The working equation is A = ε · c · l. It says absorbance increases linearly with concentration and path length when the chemical species, wavelength, solvent, and instrument conditions stay constant. If you know three of A, ε, c, and l, the fourth is found by simple rearrangement. Pair this with the molarity calculator when preparing standards and the molar mass calculator when converting weighed mass to concentration.
- Solve absorbance:
A = εcl.
- Solve concentration:
c = A/(εl).
- Solve molar absorptivity:
ε = A/(cl).
- Solve path length:
l = A/(εc).
Absorbance, transmittance, and %T
Spectrophotometers compare transmitted intensity I with incident intensity I₀. Transmittance is T = I/I₀, and absorbance is A = −log₁₀(T). Percent transmittance is simply %T = 100T = 10^(−A) × 100. Because this is logarithmic, A = 1 means 10% transmission, A = 2 means 1%, and A = 3 means 0.1%. The IUPAC Gold Book defines absorbance using the same common logarithm convention.
Absorbance is formally dimensionless, but instrument readouts often display AU (absorbance units) for convenience.
Choosing a reliable absorbance range
Many UV–Vis methods are most precise between about A = 0.1 and A = 1.0. Below 0.1 the signal is small relative to baseline noise; above 1.0 little light reaches the detector and stray light can distort linearity. If this calculator returns a high absorbance, dilute the sample, choose a lower-concentration standard, or use a shorter path length. NIST spectroscopy resources at NIST Chemistry WebBook are useful for checking wavelengths and reference spectra.
For a 1 cm cuvette, an absorbance target around 0.2–0.8 usually gives robust calibration points.
Using Beer–Lambert law with calibration curves
In real analytical chemistry, ε is often determined from standards rather than taken from a table. Prepare known concentrations, measure absorbance at a fixed wavelength, and fit a line A = slope × c + intercept. The slope equals εl when the intercept is near zero. This workflow complements the Nernst equation calculator for electrochemical concentration measurements and the pKa calculator when absorbance depends on acid–base form.
Blank the instrument with solvent and reagents but no analyte.
Use standards that bracket the unknown concentration.
Reject points outside the linear absorbance range.
Report wavelength, cuvette path length, and temperature.
Common path lengths and examples
Standard square UV–Vis cuvettes usually have a 1 cm path length, but microvolume instruments may use 0.1 mm to 1 mm paths, and gas cells can be several centimetres or metres. Molar absorptivity varies enormously: weak bands may have ε below 100, while strongly absorbing dyes or biomolecules can exceed 10,000 L·mol⁻¹·cm⁻¹.
| Quantity | Typical value | Comment |
|---|---|---|
| Standard cuvette path length | 1 cm | Most bench UV–Vis methods |
| DNA at 260 nm | A₂₆₀ = 1 | ≈ 50 µg/mL dsDNA |
| Preferred calibration absorbance | 0.1–1.0 | Often most linear and precise |
| A = 2 | %T = 1% | Usually dilute sample |
Assumptions and limitations
Beer–Lambert law assumes monochromatic light, a homogeneous non-scattering solution, stable chemical speciation, and no instrumental saturation. Deviations occur with high concentrations, fluorescence, turbidity, stray light, chemical equilibria, or wavelength bandwidth that is too broad. For exact reporting, state whether ε is decadic molar absorption coefficient and use consistent units from the IUPAC Green Book.
Do not mix cm and metres for path length.
Do not use ε measured at a different wavelength.
Filter or centrifuge turbid samples before UV–Vis measurement.
Dilute high-absorbance samples and multiply back by the dilution factor.
Quick Reference Card
Beer–Lambert Law — Quick Reference
Quick reference • Beer–Lambert Law Calculator
A = εcl | c = A/(εl) | A = −log₁₀(T) | %T = 10^(−A) × 100Valid range: Best quantitative range is often A ≈ 0.1–1.0; validate your method experimentally.
Common Values
⚠ Watch Out
- •Use the same wavelength for ε and absorbance measurements.
- •Dilute samples when absorbance is above the validated linear range.
- •Turbidity and scattering make apparent absorbance too high.
- •Path length must be in cm when ε is reported in L·mol⁻¹·cm⁻¹.
- •Blank the instrument with matching solvent and reagents.
Pro Tips
- →Use standards bracketing the unknown concentration for calibration.
- →If A is too high, dilute by a known factor and multiply the calculated concentration back.
- →Record cuvette path length, wavelength, solvent, and temperature with ε values.
- →Check calibration residuals rather than assuming every point follows a perfect line.
- →Use lower path length cuvettes for very concentrated or strongly absorbing samples.
FAQs
What is the Beer–Lambert law?
Beer–Lambert law states that absorbance is proportional to molar absorptivity, concentration, and path length: A = εcl. It is the standard equation for quantitative UV–Vis absorption spectroscopy.
How do I calculate concentration from absorbance?
Rearrange A = εcl to c = A/(εl). For A = 0.5, ε = 5000 L·mol⁻¹·cm⁻¹, and l = 1 cm, c = 0.5/(5000 × 1) = 1 × 10⁻⁴ mol/L.
What is the unit of molar absorptivity?
When concentration is in mol/L and path length is in cm, molar absorptivity ε has units L·mol⁻¹·cm⁻¹. Absorbance itself is dimensionless.
How are absorbance and percent transmittance related?
A = −log₁₀(T), where T is fractional transmittance. Percent transmittance is %T = 10^(−A) × 100. Thus A = 1 gives 10%T and A = 2 gives 1%T.
What absorbance range is best for UV–Vis measurements?
A practical range is often about 0.1 to 1.0. Very low absorbance is noise-sensitive, while high absorbance can suffer from stray light and nonlinearity.
Why does Beer–Lambert law fail at high concentration?
At high concentration, molecular interactions, refractive-index changes, chemical association, and instrumental stray light can break the simple proportionality between absorbance and concentration.