Beer – Lambert Law Calculator
Calculate absorbance and percent transmittance from molar absorptivity, concentration, and optical path length.
Example workbook is ready.
Inputs
Live results
Calculation details
| Quantity | Entered value | Canonical value | Role |
|---|---|---|---|
| Molar absorption coefficient | 8,400 L/(mol·cm) | 8,400 L/(mol·cm) | ε |
| Concentration | 43.3 µmol/L | 0.0000433 mol/L | c |
| Path length | 1 cm | 1 cm | l |
| Absorbance | 0.3637 | 0.3637 | A = εcl |
| Transmittance | 43.29% | 0.4329 | T = 10⁻ᴬ |
The table and workbook use unrounded canonical values. Display rounding is applied only for readability.
How to use the Beer – Lambert law calculator
What this calculator does
This calculator applies the Beer – Lambert relationship, A = εcl, to estimate how strongly a homogeneous sample absorbs monochromatic light. It combines the molar absorption coefficient, amount concentration, and optical path length to calculate dimensionless absorbance. It then converts absorbance to the fraction and percentage of light transmitted through the sample. The tool is useful for ideal or approximately linear spectrophotometric conditions; it does not determine whether a real instrument, sample matrix, wavelength choice, chemical equilibrium, scattering, or high-concentration behavior actually satisfies the law.
When to use it
- Predict the absorbance expected from a prepared standard before a UV – visible measurement.
- Check whether a concentration and cuvette path length are likely to produce a measurable signal.
- Convert a calculated absorbance into percent transmittance for reporting or instrument comparison.
- Verify hand calculations used in laboratory notes, calibration planning, or chemistry coursework.
How to calculate
- The calculator opens with a complete demonstration: 8,400 L/(mol·cm), 43.3 µmol/L, and 1 cm. Its example workbook is immediately ready to download.
- Replace Molar absorption coefficient with the value for the absorbing species at the selected wavelength.
- Enter Concentration and choose mol/L, mmol/L, or µmol/L. Changing the unit converts the current value so the physical concentration stays the same.
- Enter Path length and choose cm, mm, or m. The calculator converts that value to centimeters before applying the formula.
- Read Absorbance, Transmittance, and Transmitted fraction. The calculation details table shows the entered and canonical units.
- Select Download Excel to create a current-state OOXML workbook. Reset clears the demonstration values and disables export until all required fields are valid again.
Input guide
Molar absorption coefficient is a required positive decimal in L/(mol·cm). A realistic example is 8,400. Larger values produce proportionally larger absorbance at the same concentration and path length. Use the coefficient for the same chemical species, solvent, and wavelength as the measurement; confusing mass absorptivity with molar absorptivity is a common mistake. Concentration is a required nonnegative decimal. The unit selector accepts mol/L, mmol/L, or µmol/L; 43.3 µmol/L is the startup value. Increasing concentration increases absorbance linearly in the ideal model. Do not type unit symbols into the numeric box, and do not use decimal commas. Path length is a required positive decimal. Select cm, mm, or m; 1 cm is typical for a standard cuvette. A longer optical path increases absorbance linearly. Use the distance the beam travels through the sample, not the outside width of a holder unless they are equal.
Output guide
Absorbance is dimensionless and equals εcl. Zero absorbance means the ideal model predicts no attenuation; higher absorbance means less light is transmitted. Transmittance is the transmitted percentage, calculated as 100 × 10 – A. It ranges from above 0% through 100% for valid nonnegative absorbance. Transmitted fraction is the same quantity on a 0-to-1 scale. The summary pills repeat absorbance, transmittance, and the selected concentration for quick scanning. The table columns Entered value and Canonical value distinguish the selected display unit from the mol/L and cm values used by the formula. These outputs are mathematical estimates, not instrument-quality guarantees.
Worked example
With ε = 8,400 L/(mol·cm), c = 43.3 µmol/L = 0.0000433 mol/L, and l = 1 cm, the calculator gives A = 8,400 × 0.0000433 × 1 = 0.36372, displayed as 0.3637. Transmittance is 10 – 0.36372 = 0.4329, or 43.29%. These values match the first-open controls, result cards, detail table, and exported workbook.
Learn more
The IUPAC Gold Book definition of the Beer – Lambert law states the proportional relationship between absorbance, path length, and amount concentration. For a fuller derivation and discussion of assumptions, see the Chemistry LibreTexts Beer – Lambert law tutorial.
Formula, interpretation, and limitations
Absorbance is logarithmic with respect to transmitted light but linear with respect to ε, c, and l under the ideal Beer – Lambert assumptions. The conversion is A = – log10(T), where T is the transmitted fraction, so a one-unit increase in absorbance reduces transmittance by a factor of ten. This explains why apparently modest changes in absorbance can produce large changes in percent transmittance.
Real measurements can depart from linearity because of chemical association or dissociation, refractive-index changes at higher concentration, polychromatic radiation, stray light, detector limits, scattering, fluorescence, or an incorrect blank. A calibration curve prepared from standards is therefore usually more reliable for quantitative analysis than assuming ideal behavior across an unlimited range. The NIST spectrophotometry program describes the broader measurement context for absorbance and transmittance.