Beer-Lambert Law Calculator
Absorbance or concentration from molar absorptivity and path length.
What it does
Spectrophotometers read how much light a solution keeps, and one multiplication turns that into concentration. Absorbance equals molar absorptivity times path length times molarity, so A 0.70 through 1 cm at 8400 per M per cm means 8.33e-5 M. The tool above solves either direction with transmittance beside it.
The default replays the textbook guanosine case: 0.70 divided by 8400 times 1 is 8.33e-5 moles per liter, with 20% of light passing through. Flip the mode and the same three numbers predict absorbance from any concentration instead.
Two teaching sources state the identical law. LibreTexts derives A equals epsilon c l with the guanosine numbers above, and Vanderbilt frames the same linear A equals e b c relation behind calibration curves. Both stress picking the peak wavelength where absorptivity runs highest.
Linear range bounds every answer. Stray light, scattering, and chemistry shifts bend high absorbance readings, so labs dilute into the 0.1 to 1 band and calibrate rather than trusting single point math at the edges.
How to use
- Pick solving for concentration or absorbance.
- Type molar absorptivity from literature or calibration.
- Type the cuvette path in cm.
- Type the known absorbance or concentration.
- Read the answer first, transmittance beside it.
Formula
- A (AU)
- Unitless absorbance, log10(Io/I).
- eps
- Molar absorptivity in /M/cm at the wavelength.
- l, c
- Path in cm and concentration in M.
Monochromatic light and dilute clear solutions assumed. Units must match: M with cm against /M/cm absorptivity.
Worked example
Example: A 0.70, eps 8400, 1 cm
Defaults: find concentration, A 0.70, eps 8400, path 1.
- Denominator: 8400 x 1 = 8400.
- Concentration: 0.70 / 8400 = 8.33e-5 M.
- Transmittance: 100 x 10^-0.70 = 20 %T.
- Sense: 90% of light absorbed at A near 1.
- Tool shows 8.33e-5 M, 20 %T, 8400 /M/cm.
Reference table
| A | %T | Absorbed |
|---|---|---|
| 0.3 | 50.1 %T | 49.9% |
| 0.5 | 31.6 %T | 68.4% |
| 1.0 | 10 %T | 90% |
| 2.0 | 1 %T | 99% |
Limits
- Linear dilute range only.
- Clear solutions; scattering breaks it.
- Single wavelength per absorptivity.
- Bench estimates, not validated assays.
Common mistakes
- Mixing M with mg/L inputs.
- Forgetting path differs from 1 cm.
- Reading %T as absorbance directly.
- Trusting A above 2 without dilution.
- Using eps from another solvent blindly.
Try it yourself
Quick checks. Answers sit tucked under each question.
A 1.0, eps 10000, 1 cm?
1 / 10000 = 1e-4 M, 10 %T.
eps 5000, 1 cm, c 0.0002 M?
5000 x 1 x 0.0002 = 1 AU, 10 %T.
What does A 1 mean?
90% absorbed, 10% transmitted.
Questions
c from A 0.70 at 8400?
8.33e-5 M through 1 cm.
A versus %T?
A is logarithmic; %T is linear light share.
Why pick lambda max?
Highest absorptivity gives lowest detection limits.
Epsilon from data?
Slope of A versus c at known path.
A above 2?
Dilute into the linear band and remeasure.
Units of epsilon?
Per M per cm, often reported bare.