Beer-Lambert Concentration from Absorbance Calculator

Turn an absorbance reading into a concentration using the molar extinction coefficient and the true optical path length — which, in a microplate, is neither 1 cm nor the same from well to well.

Last updated 17 Sep 2026

Concentration from absorbance

A, ε, path → µmol/L

Absorbance (A)Blanked against the same buffer in the same vessel. Readings above about 1.0 are outside the reliable range of most instruments — dilute the sample and read again rather than trusting the number.

Molar extinction coefficient ε (L·mol⁻¹·cm⁻¹)For the wavelength, solvent and temperature you are actually using. NADH at 340 nm is 6,220; a coefficient quoted in mmol⁻¹ must be multiplied by 1,000, and one quoted in m²/mol by 10.

Optical path length (cm)1 cm for a standard cuvette. For a microplate well this is set by the fill volume and the well geometry — measured values run from about 0.23 to 0.88 cm — and must be corrected for, not assumed.

67.52µmol/LExample

A340 of 0.42 for NADH, ε = 6,220 L·mol⁻¹·cm⁻¹, read in a 1.00 cm cuvette

Formula

A = ε · c · l
c (mol/L) = A ÷ (ε × l)
c (µmol/L) = A ÷ (ε × l) × 10⁶

A: absorbance, a dimensionless log₁₀ ratio of incident to transmitted light. A of 1 means 10% of the light got through; A of 2 means 1%
ε: molar extinction coefficient in L·mol⁻¹·cm⁻¹ — the absorbance a 1 mol/L solution would give in a 1 cm path. It is specific to the species, the wavelength, the solvent and the temperature
l: the distance the light actually travels through the sample, in centimetres. 1 cm in a standard cuvette; something else entirely in a microplate
c: concentration in mol/L from the bare equation; this calculator multiplies by 10⁶ and reports µmol/L, which is a more readable size for most bench work
unit traps: ε is also published in mmol⁻¹·cm⁻¹ (multiply by 1,000) and in SI as m²/mol (multiply by 10). Getting this wrong moves the answer by three orders of magnitude or one

Worked example

A340 of 0.42 for NADH, ε = 6,220 L·mol⁻¹·cm⁻¹, read in a 1.00 cm cuvette
c = 0.42 ÷ (6,220 × 1.00) = 6.752 × 10⁻⁵ mol/L
× 10⁶ = 67.52 µmol/L
= 0.0675 mmol/L
Read the same solution in a microplate well with a 0.60 cm path and assume 1 cm, and you would report 40 µmol/L — 40% low

The same reading, three path lengths

The path lengths in the lower three rows bracket the range Molecular Devices measured across 75–300 µL in a 96-well plate: 0.23 cm to 0.88 cm. A plate reader that has not corrected for path length is not reporting the same quantity as a cuvette, and the discrepancy tracks how full the well is — which means it also tracks pipetting error and evaporation.
Vessel	Path length	A = 0.42, ε = 6,220	Error if you assume 1 cm
Standard cuvette	1.00 cm	67.5 µmol/L	None
96-well plate, well filled generously	0.88 cm	76.7 µmol/L	12% low
96-well plate, moderate fill	0.60 cm	112.5 µmol/L	40% low
96-well plate, sparsely filled	0.23 cm	293.6 µmol/L	77% low

Where the reading sits

The ceiling is arithmetic. If a fraction s of the light reaching the detector has bypassed the sample, the largest absorbance the instrument can ever display is −log₁₀ s: 2.0 at 1% stray light, 3.0 at 0.1%. As the true absorbance approaches that ceiling the readings flatten, so the error is always in the same direction — the result comes out too low, and a calibration curve built from over-range standards bends towards the x-axis.
Absorbance	Light transmitted	Status
0.05	89%	Low. The signal is close to the noise of the blank; relative error is large.
0.1 – 0.8	79% – 16%	The range Chemistry LibreTexts recommends working in — the best compromise between signal and noise.
1.0	10%	The point above which LibreTexts advises diluting rather than reading.
1.5	3.2%	Beyond the linear range of many instruments. Check your own photometric linearity specification before reporting a number from here.
2.0	1.0%	At 1% stray light the instrument cannot exceed this reading at all, whatever the concentration.

Two extinction coefficients with a traceable source

Both rows are the same physical quantity in different units: 1 L·mol⁻¹·cm⁻¹ = 0.1 m²/mol, so an SI figure multiplies by 10. This matters because 4-nitrophenol also circulates widely as 18,450 L·mol⁻¹·cm⁻¹ — a different value measured under different buffer and temperature conditions. An extinction coefficient belongs to a method, not to a molecule.
Species	Wavelength	As published	In L·mol⁻¹·cm⁻¹	Source
NADH (and NADPH)	340 nm	6.22 L·mmol⁻¹·cm⁻¹	6,220	Sigma-Aldrich alcohol dehydrogenase assay; University of Georgia LDH assay
4-nitrophenol	405 nm	1869 m²/mol	18,690	IFCC primary reference procedure for alkaline phosphatase

The path length is the part nobody checks

Beer’s law says absorbance is proportional to concentration, to the path length and to a proportionality constant characteristic of the absorbing species. Rearranged for concentration it is trivial arithmetic, and that triviality is the problem: the equation is so simple that the two quantities it depends on get treated as constants when neither is. The extinction coefficient belongs to a species at a wavelength in a solvent at a temperature, and is quoted in at least three different unit systems. The path length belongs to the vessel.

In a cuvette the path length is 1 cm and nobody thinks about it. In a microplate it is whatever height the liquid happens to stand at, because the light goes down through the well rather than across it. Molecular Devices measured path lengths from 0.23 cm to 0.88 cm across fill volumes of 75 to 300 µL in a 96-well plate — a factor of nearly four, in the same plate, from the same instrument. Read a plate as though it were a cuvette and every result is low by the shortfall, typically by a third to a half. Worse, the error is not constant: it follows the fill volume, so it varies with pipetting precision across the plate and creeps upward as the outer wells evaporate during a long kinetic run. The meniscus adds its own contribution, since a concave surface makes the path longer at the wall than at the centre.

There are three honest ways out, and assuming 1 cm is not one of them. The first is to let the instrument correct: readers with path-length correction measure water’s near-infrared absorbance in each well — Thermo Fisher uses 975 nm against a 900 nm reference, with a K-factor of 0.173 for pure water; BMG Labtech describes the same water window as 930 to 1100 nm — compare it with the value for a 1 cm layer, and scale the sample reading accordingly. The second is to avoid the question by running a standard curve in the same plate at the same fill volume, so that the path length cancels: this is why a plate-based assay is almost always calibrated rather than computed from ε. The third is to move the sample to a cuvette. What does not work is measuring in a plate and applying a coefficient from a cuvette method.

The other systematic failure is reading too high. Beer’s law is a limiting law, valid while the absorbing particles behave independently of each other; at high concentration they do not, and the refractive index of the solution — on which the absorptivity depends — starts to shift with concentration as well. Before either of those becomes visible the instrument itself gives way. Any light that reaches the detector without passing through the sample sets a hard ceiling on absorbance: if a fraction s of the light is stray, the maximum displayed absorbance is −log₁₀ s, so 1% stray light caps the instrument at 2.0 no matter how concentrated the sample is. As the reading approaches that ceiling the response flattens and the result is biased low. Chemistry LibreTexts puts the practical working range at 0.1 to 0.8 absorbance and advises diluting rather than recording above 1. Dilution is the correct response in every case: extrapolating a calibration curve upward through the bend is not a workaround, it is the error itself, written down.

For nucleic acids the same law is usually applied in a shortcut form, where a fixed number of micrograms per millilitre is assigned to an absorbance of 1.0 at 260 nm — 50 for double-stranded DNA, 33 for single-stranded, 40 for RNA. Those factors are Beer’s law with the extinction coefficient and the unit conversion already folded in for a 1 cm path, which is why the site keeps them on a separate page: nucleic acid concentration from A260. Everything said here about path length and linear range applies there unchanged, and the path-length point applies with particular force to the small-drop spectrophotometers used for DNA, which work at path lengths of a millimetre or less by design.

Frequently asked questions

How do I calculate concentration from absorbance?

Divide the absorbance by the product of the molar extinction coefficient and the path length in centimetres. With A = 0.42, ε = 6,220 L·mol⁻¹·cm⁻¹ and a 1 cm cuvette, the concentration is 6.75 × 10⁻⁵ mol/L, or 67.5 µmol/L.

What path length should I use for a microplate?

Not 1 cm. The path length in a well is set by the fill volume and the well geometry; Molecular Devices measured 0.23 to 0.88 cm across 75 to 300 µL in a 96-well plate. Either use a reader that corrects path length from water’s near-infrared absorbance, or calibrate against standards run in the same plate at the same volume.

Why is my plate reader result lower than my cuvette result?

Because the light travels a shorter distance through the sample in a well than across a cuvette. If the real path is 0.6 cm and you assumed 1 cm, every concentration you report is 40% low. The gap also varies with how full each well is.

What is the highest absorbance I can trust?

Chemistry LibreTexts recommends working between 0.1 and 0.8 and advises against recording above 1. The absolute ceiling is set by stray light: at 1% stray light no reading above 2.0 is possible at all. Above the linear range the result is always biased low, never high.

Should I extrapolate a standard curve for an over-range sample?

No. The curve bends because the instrument is failing, not because the relationship has a different slope up there. Dilute the sample into the linear range and multiply the result by the dilution factor.

My extinction coefficient is in m²/mol — what do I do?

Multiply by 10 to get L·mol⁻¹·cm⁻¹. The IFCC value for 4-nitrophenol at 405 nm, 1869 m²/mol, is 18,690 L·mol⁻¹·cm⁻¹. A coefficient quoted per millimole multiplies by 1,000 instead.

Related calculators

References

Chemistry LibreTexts. Beer’s Law (Wenzel, Molecular and Atomic Spectroscopy, §1.2) — the 0.1 to 0.8 working range, the advice to dilute rather than read above 1, and the stray-radiation ceiling.
Chemistry LibreTexts. Beer’s Law (Providence College CHM 331, §8.2) — Beer’s law as a limiting law, and the refractive-index and particle-interaction reasons it fails at high concentration.
Molecular Devices. Optical density measurements automatically corrected to a 1 cm pathlength with PathCheck Technology — measured well path lengths of 0.23 to 0.88 cm across 75 to 300 µL.
Thermo Fisher Scientific. Microplate-Based Pathlength Correction Method (SkanIt technical note) — 975 nm against a 900 nm reference, K-factor 0.173 for pure water.
International Federation of Clinical Chemistry and Laboratory Medicine. IFCC primary reference procedures for the measurement of catalytic activity concentrations of enzymes at 37 °C. Part 9: alkaline phosphatase. Clin Chem Lab Med 2011;49:1439–1446 — ε₄₀₅ = 1869 m²/mol for 4-nitrophenol.
Sigma-Aldrich. Enzymatic Assay of Alcohol Dehydrogenase; University of Georgia CMBE. Lactate dehydrogenase assay — NADH ε₃₄₀ = 6.22 L·mmol⁻¹·cm⁻¹.

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