Beer–Lambert calculator

Solve A = ε × c × l for whichever value you are missing, or turn an A260 reading into ng/µL.

Result

Mass concentration

Purity

What is the Beer–Lambert law?

Light passing through a solution is absorbed in proportion to how many absorbing molecules it meets, so absorbance rises with both concentration and the distance travelled through the sample. That is the Beer–Lambert law, and it is the basis of every spectrophotometer reading in a laboratory:

A = ε × c × l

A is absorbance, which has no unit. ε is the molar absorptivity, also called the molar extinction coefficient, of the substance at the wavelength used, in M⁻¹cm⁻¹. c is the molar concentration and l is the path length in centimetres, which is 1 cm for a standard cuvette. Fill any three of them above and the fourth is solved.

How to calculate concentration from absorbance

c = A / (ε × l)

Blank the instrument on the buffer, read the sample at the wavelength that ε was measured at, and divide. The result is molar, so convert with the molecular weight if you need mg/mL: enter the molecular weight under the result and the mass concentration appears beside it. To go the other way, or to work from a stock, use themolarity calculator and thedilution calculator.

How to calculate DNA concentration from A260

Nucleic acids absorb at 260 nm. Rather than a molar absorptivity, the convention is a mass conversion factor: how many µg/mL of sample give an absorbance of 1 in a 1 cm path.

concentration (ng/µL) = A260 × factor × dilution / path length
Sampleµg/mL per A260 unit
Double-stranded DNA50
Single-stranded DNA33
RNA40
Short oligonucleotideabout 33, sequence dependent

ng/µL and µg/mL are the same concentration, so the headline figure can be read either way. For picomoles, copy number or the weight of a given sequence seemass to moles andDNA copy number.

Worked example

Beer–Lambert. NADH has ε = 6220 M⁻¹cm⁻¹ at 340 nm. A cuvette of 1 cm path length reads A = 0.622, so c = 0.622 / (6220 × 1) = 1.0 × 10⁻⁴ M, which the calculator reports as100 µM. Entering the molecular weight of 663.4 g/mol turns that into 66.34 µg/mL.

Nucleic acid. A plasmid preparation diluted 100-fold reads A260 = 0.240. With the dsDNA factor of 50 the concentration is 0.240 × 50 × 100 = 1,200 ng/µL. The same dilution reads A280 = 0.133, so the A260/A280 ratio is 1.80, which is what clean DNA gives.

What the purity ratios mean

The A260/A280 ratio compares nucleic acid absorbance with the 280 nm absorbance of aromatic amino acids. Clean DNA sits near 1.8 and clean RNA near 2.0. A ratio clearly below that means protein or phenol is present; a DNA sample above 2.0 normally carries RNA. The ratio is a purity check, never a quantity: a sample can have a perfect 1.8 and still be far too dilute to use.

The A260/A230 ratio catches a different set of contaminants, mainly guanidine salts, EDTA, carbohydrates and phenol, and should be 2.0 to 2.2. A low A260/A230 with a normal A260/A280 usually means the column wash step was skipped or left too little contact time.

When Beer's law breaks down

  • Readings above about 1. Only a tenth of the light gets through, so noise takes over and the line bends. Dilute and multiply back with the dilution factor.
  • Turbid samples. Scattering from cells or precipitate adds apparent absorbance at every wavelength. A reading at 320 nm, where nucleic acids and proteins do not absorb, shows how much of the signal is scatter and should be subtracted.
  • No blank. Buffer components and the cuvette itself absorb. Blank on the same buffer in the same cuvette, and for a protein use the same procedure as theA280 protein calculator or acolorimetric assay.
  • Chemistry that changes with concentration. Dyes that stack or molecules that dimerise no longer give a straight line, and a narrow absorbance peak read on a wide slit also flattens the response.

Frequently asked questions

What is the Beer–Lambert law?

Absorbance is proportional to how much absorbing substance the light passes through: A = ε × c × l, where ε is the molar absorptivity of the substance at that wavelength, c is its molar concentration and l is the path length of the cuvette. Absorbance has no units, so ε carries the reciprocal of concentration times length, normally per molar per centimetre.

How do I calculate concentration from absorbance?

Rearrange to c = A / (ε × l). Read the absorbance at the wavelength the extinction coefficient was measured at, subtract a buffer blank, and divide by ε times the path length. With a 1 cm cuvette the path length term disappears, so the concentration is simply the absorbance divided by ε.

Why is a reading above 1 unreliable?

At A = 1 only a tenth of the light reaches the detector, and at A = 2 only a hundredth, so stray light and detector noise start to dominate and the response bends away from a straight line. Most instruments are specified as linear to about A = 1, a few to A = 1.5. Dilute the sample and multiply the result by the dilution factor instead.

What does an A260/A280 ratio of 1.8 mean?

It means the sample is essentially free of protein and phenol. Pure DNA reads about 1.8 and pure RNA about 2.0, because the aromatic amino acids that absorb at 280 nm are absent. A ratio well below those values points to protein or phenol carryover; a DNA sample above 2.0 usually has RNA in it.

Which conversion factor should I use for my sample?

One A260 unit in a 1 cm path is 50 µg/mL of double-stranded DNA, 33 µg/mL of single-stranded DNA, 40 µg/mL of RNA and about 33 µg/mL of a short oligonucleotide. The oligo figure is only a rough average, because a short oligo absorbs according to its own base composition; for an exact figure use the extinction coefficient calculated from its sequence.