Molar Extinction Coefficient Calculator
Enter absorbance A, molar concentration c and path length l; by the Beer–Lambert law the tool instantly computes the molar extinction coefficient ε (M⁻¹·cm⁻¹), used to quantify nucleic acids and proteins.
Input Data
Results
At a glance:The molar extinction coefficient (also called molar absorptivity, symbol ε) is a constant describing how strongly a substance absorbs light at a specific wavelength per unit concentration and path length, defined by the Beer–Lambert law A = ε × c × l, so ε = A ÷ (c × l). Here A is absorbance (dimensionless), c is molar concentration (M = mol/L), l is path length (cm), so ε has unit M⁻¹·cm⁻¹. ε depends only on the substance and wavelength; it is the key physical constant for back-calculating unknown concentrations and quantifying DNA, RNA, proteins and various pigments by spectrophotometry.
Formula
Beer–Lambert law: A = ε × c × l.
Molar extinction coefficient: ε = A ÷ (c × l).
Reverse for concentration: c = A ÷ (ε × l).
$$A = \varepsilon \, c \, l$$$$\varepsilon = \frac{A}{c \times l}$$$$c = \frac{A}{\varepsilon \times l}$$How to Use
- Enter the absorbance A measured by the spectrophotometer (keep within the 0.1–1.0 linear range).
- Enter the sample molar concentration c (M) and path length l (cm; standard cuvette 1 cm).
- The tool instantly computes the molar extinction coefficient ε (M⁻¹·cm⁻¹); with known ε you can also reverse-calculate an unknown concentration.
Molar extinction coefficients of common biomolecules (approx.)
| Substance | Wavelength | ε (M⁻¹·cm⁻¹) |
|---|---|---|
| Double-stranded DNA | 260 nm | ≈ 6,600 (per nucleotide) |
| Tryptophan (Trp) | 280 nm | ≈ 5,500 |
| Tyrosine (Tyr) | 280 nm | ≈ 1,490 |
| NADH | 340 nm | ≈ 6,220 |
| p-Nitrophenol | 405 nm | ≈ 18,000 |
Values are approximate; actual ε varies with wavelength, pH and solvent; a protein's ε is usually estimated from its Trp, Tyr and Cys residue counts.
Case Studies
Find ε from a standard
A 10 µM (c = 0.00001 M) standard solution in a 1 cm cuvette reads A = 0.5.
ε = 0.5 ÷ (0.00001 × 1) = 50,000 M⁻¹·cm⁻¹.
This ε is the substance's intrinsic constant at this wavelength, for later reverse-calculating unknown concentrations.
Reverse-calculate concentration with known ε
A protein's ε at 280 nm = 43,824 M⁻¹·cm⁻¹; at 1 cm path length A = 0.876.
c = A ÷ (ε × l) = 0.876 ÷ (43,824 × 1) ≈ 2.0 × 10⁻⁵ M = 20 µM.
This is exactly how labs quickly quantify protein concentration with a NanoDrop spectrophotometer.
FAQ
Why is the unit of ε M⁻¹·cm⁻¹?
From ε = A ÷ (c × l): A is dimensionless, c is in M (mol/L), l is in cm, so ε has unit 1 ÷ (M × cm) = M⁻¹·cm⁻¹. This keeps both sides of A = ε × c × l dimensionally consistent, making A dimensionless.
Does ε change with concentration?
No. ε is an intrinsic constant of a substance at a specific wavelength, depending only on the substance, wavelength and solvent conditions, not concentration. That is why it can be used for quantification — for the same substance at the same wavelength, ε is the same regardless of concentration, and absorbance only varies linearly with concentration and path length.
Why keep absorbance between 0.1 and 1.0?
The Beer–Lambert law is linear only at low absorbance. Too low (<0.1) the signal approaches noise with large error; too high (>1.5) stray light, self-absorption and detector saturation break linearity, making ε or concentration inaccurate. Dilute the sample or shorten the path length to stay in the linear range.
How to use ε to quantify DNA or protein?
Look up or compute the substance's ε at a specific wavelength, measure absorbance A, then c = A ÷ (ε × l) gives the molar concentration. DNA is commonly at 260 nm, protein at 280 nm. A protein's ε can be estimated from its Trp, Tyr and Cys residue counts by an empirical formula.
What is the difference between molar extinction coefficient and absorptivity?
Molar extinction coefficient ε is based on molar concentration (M), unit M⁻¹·cm⁻¹; specific (mass) absorptivity is based on mass concentration (e.g. g/L or %), different unit. The two interchange via molar mass: ε = specific absorptivity × molar mass. Always confirm the concentration unit of the coefficient you use.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.