Lambert-Beer Law Calculator
Solve A = ε·c·l for absorbance, concentration or ε, sweep concentration, path length or ε, and find the internal transmittance e^(−α·d) of a bulk sample.
Absorbance (A)
0.5000
= optical density for a clear sample
Transmittance
31.62 %
absorbed 68.38 %
Mass concentration
5.000 mg/L
ρ = c·M (mg/L = µg/mL)
Mass absorption coefficient
100.0 L·g⁻¹·cm⁻¹
a = ε/M: the A of 1 g/L over 1 cm
Beer-Lambert sweep
- Absorbance A
- Transmittance T
Bulk sample: absorption coefficient α and thickness
For a solid or a pure liquid the Napierian absorption coefficient α replaces ε·c: T = e^(−α·d) inside the sample. The absorption depth calculator gives α(λ) for silicon and water.
Internal transmittance
36.79 %
e^(−α·d); surface reflections not included
Absorbance (decadic)
0.4343
A = α·d / ln 10
Absorption loss
4.343 dB
4.343 dB/cm = 4.343·α
1/e depth
10.00 mm
δ = 1/α
A = ε · c · l, so c = A / (ε · l) and ε = A / (c · l)
T = I/I₀ = 10⁻ᴬ
a = ε / M, ρ = c · M
bulk: T = e^(−α·d), α = ln 10 · ε · c
ε is the molar decadic absorption coefficient (IUPAC; "extinction coefficient" is the older name), and a is the mass absorption coefficient (formerly "specific extinction coefficient"; for proteins at 280 nm it is the absorbance of a 1 mg/mL solution). The law holds for monochromatic light in dilute solutions: at high concentration (≳ 10 mM) absorbers interact and the refractive index changes, and above A ≈ 2 (T < 1 %) stray light and detector noise make measured absorbances read low. Scattering samples add to the optical density without absorbing.
Reference: IUPAC Compendium of Chemical Terminology (Gold Book), "absorbance", "molar (decadic) absorption coefficient", "mass absorption coefficient".
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
Exact for monochromatic light and a dilute solution of non-interacting absorbers; concentration and ε are A = ε·c·l solved for each, and a = ε/M. The bulk sample uses the Napierian α: T = e^(−α·d), A = α·d/ln 10, without surface reflections. Not modelled: scattering, fluorescence and stray light; absorbers interact above about 10 mM and absorbance reads low above A ≈ 2.
- IUPAC Compendium of Chemical Terminology (Gold Book), entries “absorbance”, “absorption coefficient”, “molar (decadic) absorption coefficient” and “mass absorption coefficient”.
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