What this calculator does
The Beer-Lambert law says absorbance is proportional to concentration, path length and the molar absorptivity of the substance. An absorptivity of 1,000 with a 0.001 mol/L solution in a 1 cm cell gives an absorbance of exactly 1.
Absorbance is logarithmic while transmittance is not, and the relationship catches people out. An absorbance of 1 means 10% of the light gets through; an absorbance of 2 means 1%. Each additional unit of absorbance blocks another factor of ten, which is why instruments become unreliable above about 2.
The formula
Absorbance is the molar absorptivity multiplied by concentration and path length. Transmittance is ten to the power of minus absorbance, expressed as a percentage. The linear relationship between absorbance and concentration is what makes spectrophotometry quantitative, and it is also the part that fails at high concentration.
| Term | Meaning |
|---|---|
| Absorbance (A) | The log of the ratio of incident to transmitted light. Dimensionless. |
| Molar absorptivity (ε) | How strongly a substance absorbs at a given wavelength, in L/(mol·cm). |
| Path length | The distance light travels through the sample. Standard cuvettes are 1 cm. |
| Transmittance | The fraction of light passing through, which falls tenfold per unit of absorbance. |
The inputs explained
| Field | What to enter |
|---|---|
| Molar absorptivity ε (L/(mol·cm)) | Molar absorptivity at the wavelength being used. It is wavelength-specific, so a value from one peak does not apply at another. |
| Concentration (mol/L) | Concentration in mol/L. |
| Path length (cm) | Path length in cm. A standard cuvette is 1 cm. |
When to use it
Quantifying a solution
Measuring absorbance against a calibration curve is the standard route to a concentration in analytical chemistry.
Choosing a dilution
Readings above about 2 absorbance units are unreliable, so a sample often needs diluting into range first.
Checking a protein or DNA sample
Nucleic acid and protein concentrations are routinely read from absorbance at fixed wavelengths.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does concentration change absorbance?
A range of concentrations through the same cell.
| Concentration | Absorbance | Transmittance | % absorbed |
|---|---|---|---|
| 0.0002 mol/L | 0.2000 | 63.1% | 36.9% |
| 0.0005 mol/L | 0.5000 | 31.6% | 68.4% |
| 0.001 mol/L | 1.000 | 10.0% | 90.0% |
| 0.002 mol/L | 2.000 | 1.00% | 99.0% |
Questions
What absorbance range is reliable?
Roughly 0.1 to 1.0, and certainly below 2. Below 0.1 the signal is too close to the noise; above 2 less than 1% of the light reaches the detector and small errors in that tiny signal translate into large concentration errors. Dilute the sample into range rather than trusting a high reading.
Why does the law break down at high concentration?
Because the derivation assumes absorbing molecules act independently. At high concentration they interact, the refractive index shifts and molecules may associate, all of which break proportionality. Deviations typically appear above about 0.01 mol/L, though it depends on the substance.
What is the difference between absorbance and transmittance?
Transmittance is the fraction of light getting through; absorbance is the negative log of it. Absorbance is used because it is proportional to concentration, while transmittance is not, which makes calibration curves straight lines rather than curves.
Does molar absorptivity depend on wavelength?
Entirely. It is a property of the substance at one specific wavelength, which is why measurements are made at an absorption peak where it is both large and relatively flat. Using a value measured at a different wavelength will give a wrong concentration.
For preparing the standards, see the molarity calculator. For diluting a sample into range, see the dilution calculator.