All calculatorsBeer–Lambert Law Calculator
Convert absorbance, transmittance, and concentration in seconds. Use Beer–Lambert A = εlc to solve for any variable — with steps, unit hints, and a quick “%T ↔ A” converter.
Background
Beer–Lambert Law links how much light a solution absorbs to its concentration and path length: A = ε · l · c. Higher concentration (or longer path length) usually means higher absorbance.
How to use this calculator
- Choose a mode: Beer–Lambert, Transmittance, or Calibration.
- Enter the known values (leave blank the variable you want to solve for).
- Click Calculate to get the answer + optional steps and callouts.
How this calculator works
- Beer–Lambert: A = εlc and rearrangements.
- Transmittance: A = −log₁₀(T) and A = 2 − log₁₀(%T).
- Calibration: if A = (slope)·c + b, then slope = εl.
Formula & Equations Used
Beer–Lambert Law: A = ε · l · c
Rearranged: ε = A/(lc), l = A/(εc), c = A/(εl)
Transmittance: A = −log₁₀(T), T = 10^(−A)
%T: %T = 100·T, A = 2 − log₁₀(%T)
Example Problems & Step-by-Step Solutions
Example 1 — Find absorbance
ε = 12,500 L·mol⁻¹·cm⁻¹, l = 1.00 cm, c = 2.00×10⁻⁵ M → A = εlc = 0.250.
Example 2 — Convert %T to absorbance
If %T = 25, then A = 2 − log₁₀(25) ≈ 0.602.
Example 3 — Find ε from a calibration slope
If slope = 6.25×10⁵ (A per M) and l = 1.00 cm, then ε = slope/l = 6.25×10⁵ L·mol⁻¹·cm⁻¹.
Frequently Asked Questions
Q: Why is absorbance unitless?
Absorbance is defined from a logarithm of intensity ratios. ε, l, and c carry the units that cancel out.
Q: What’s the difference between T and %T?
T is a fraction between 0 and 1. %T is that fraction times 100.
Q: When does Beer–Lambert break down?
At very high concentrations (nonlinear effects), scattering samples, or if the chemistry changes with concentration.