Beer-Lambert Law Calculator
The Beer–Lambert law, A = ε·c·l, says absorbance grows in proportion to how much absorbing material the light crosses: the molar extinction coefficient ε, the concentration c, and the path length l. This calculator solves that one equation for whichever quantity you are missing — absorbance, concentration, ε or path length — and it folds in the two bench terms most general converters ignore: the dilution you made before reading, and (with a molecular weight) the mass concentration in µg/mL beside the molar one. Enter transmittance instead of absorbance and it converts A = −log₁₀(T) for you, and it flags readings outside the band your spectrophotometer can actually trust.
One absorbance reading plus one extinction coefficient is enough to know how much of a compound is in a tube — that is the whole idea behind UV/vis quantitation, and it is the equation the biochemistry calculators are built on. The arithmetic is two keystrokes, yet the errors are remarkably consistent: people mix centimetres with millimetres, forget the dilution in front of the machine, take ε from a page that used a different solvent or path length, and trust an absorbance of 3 the detector never measured linearly. This page keeps every term of A = ε·c·l visible so nothing is silently assumed.
Absorbance itself is just a logarithm of how much light survived: A = −log₁₀(T), where T is the fraction of light transmitted. A reading of 1.0 means 10% of the light got through; 2.0 means 1%. The law then says that loss is proportional to concentration and to the distance the light travels through the sample, with ε as the proportionality constant — how strongly one mole per litre absorbs over one centimetre at your chosen wavelength. ε is where the chemistry lives: for NADH it is 6,220 L·mol⁻¹·cm⁻¹ near 340 nm, and that single number is what turns a 340 nm reading into a reaction rate.
Nucleic-acid and protein work usually hides this law inside conventions — the familiar 50 µg/mL-per-A260 rule is just ε compressed for a heterogeneous polymer, and it is what the DNA concentration calculator and the protein A280 calculator apply. This page is the general tool: you bring your own ε (from a reference or from a calibration curve you generate here by solving for ε) for any absorbing species at any wavelength, and the same dilution-and-path-length discipline applies.
Because most bench samples are diluted before they are readable, the concentration result is reported twice — what was in the cuvette, and what was in your tube before the dilution (cuvette × dilution factor). Supply a molecular weight and the answer also appears as a mass concentration in µg/mL, so an absorbance can become the number your protocol actually asks for. And whenever your input absorbance falls outside the roughly 0.01–2 band where instruments stay linear, the result comes with a warning rather than false confidence.
Beer-Lambert Law Calculator
How to use the beer lambert law calculator
Choose what to solve for: absorbance, concentration, the extinction coefficient ε, or path length. The calculator shows only the inputs that equation needs.
Enter the measured absorbance — or enter transmittance instead (as a fraction or a percent, using the selector) and it converts with A = −log₁₀(T).
Enter ε in L·mol⁻¹·cm⁻¹ from a reference under similar solvent, pH and wavelength — for example 6,220 for NADH near 340 nm.
Enter concentration in whichever unit suits (M, mM, µM or nM) and path length in cm or mm; a standard cuvette is 1 cm.
In concentration mode, set the dilution factor if you diluted before reading — 10 for 1 µL sample into 9 µL buffer. The primary result is your original tube.
Optionally add a molecular weight to also see the concentration in µg/mL and g/L.
Press Calculate. Warnings appear automatically for readings outside the linear band; a note explains single-point ε when you solve for ε.
Ready to pipette? Carry the result into the dilution calculator or the molarity calculator, or follow the Beer–Lambert guide for the full workflow.
Beer-Lambert Law formula
Variables and units
| Symbol | Meaning | Unit |
|---|---|---|
| A | Absorbance at the chosen wavelength | — |
| ε | Molar extinction coefficient (molar absorptivity) | L·mol⁻¹·cm⁻¹ |
| c | Concentration of the absorbing species | mol/L (or mM/µM/nM) |
| l | Path length the light travels through the sample | cm (or mm) |
| T | Transmittance, fraction of light reaching the detector | — (or %) |
| DF | Dilution factor applied before measuring | × |
| MW | Molecular weight (optional, enables mass output) | g/mol |
How beer lambert law is calculated
- Convert anything non-canonical into the equation’s units: µM→M, mm→cm, %T→A.
- Pick the missing quantity and apply the matching rearrangement of A = ε·c·l.
- For concentration, multiply the cuvette result by the dilution factor to get the original sample.
- For a mass figure, multiply mol/L by the molecular weight (g/L) and by 1,000 (µg/mL).
- Check the reading against the linear band (~0.01–2); outside it, dilute and re-measure rather than extrapolate.
Worked laboratory examples
Example 1 — NADH: absorbance to concentration
Given: A340 = 0.622 · ε = 6,220 L·mol⁻¹·cm⁻¹ · path length 1 cm
- c = A / (ε · l) = 0.622 / (6,220 × 1) = 1.00 × 10⁻⁴ mol/L.
- That is 100 µM — the reading goes straight to a concentration.
- With the molecular weight of NADH (664.4 g/mol) the same sample is 0.0664 g/L, i.e. 66.4 µg/mL.
Result: 100 µM (66.4 µg/mL)
Example 2 — The dilution you made before reading
Given: A340 = 0.622 · ε = 6,220 L·mol⁻¹·cm⁻¹ · 1 cm · 10 µL sample into 90 µL buffer (DF = 10)
- The cuvette contains 0.622 / 6,220 = 1.00 × 10⁻⁴ mol/L = 100 µM.
- Your tube is ten times stronger: 100 µM × 10 = 1.00 mM.
- Skipping the dilution factor is the most common way to report a sample ten-fold too weak.
Result: 1.00 mM original (100 µM in the cuvette)
Example 3 — Transmittance instead of absorbance
Given: T = 0.10 (10% of the light transmitted) · ε = 6,220 L·mol⁻¹·cm⁻¹ · 1 cm
- A = −log₁₀(0.10) = 1.000.
- c = 1.000 / 6,220 = 1.608 × 10⁻⁴ mol/L = 160.8 µM.
- At exactly one log of attenuation the reading is still inside the linear band; at T = 1% it would not be.
Result: 160.8 µM
Example 4 — Solving for ε (single-point calibration)
Given: A = 0.500 from a 20 µM standard · 1 cm path
- ε = A / (c · l) = 0.500 / (20 × 10⁻⁶ mol/L × 1 cm) = 25,000 L·mol⁻¹·cm⁻¹.
- Solve for path length just as easily: l = A / (ε · c) — handy when a short-path plate well is the unknown.
- One point carries that point’s error: a slope across several standards is sturdier, which the guide walks through.
Result: ε = 25,000 L·mol⁻¹·cm⁻¹
Want the reasoning behind the numbers? Read How to Use the Beer–Lambert Law.
How to interpret the result
The primary card answers exactly one question — the quantity you picked — and the cards beneath it keep the whole equation consistent: absorbance, ε, molar concentration (in the cuvette and in your original tube), transmittance, and mass concentration when you supplied a molecular weight. If two cards disagree with your mental math, the mistake is usually a unit that was never converted: µM entered as M is a 10⁶-fold error, and 10 mm entered as 10 cm is a 10-fold one.
The absorbance warning matters more than it looks. Above roughly 2, stray light reaching the detector makes readings compress — measured absorbance rises more slowly than concentration — so a 3.0 reading is not three times a 1.0 reading. Between 1 and 2 the deviation is instrument-dependent, and the calculator notes it. Below about 0.01 you are comparing a signal to the blank’s drift. The fix in both directions is sample preparation, not arithmetic: dilute toward the 0.1–1 band, or concentrate the sample.
When you solve for ε, the result is a single-point calibration coefficient. It is honest for checking a reference value and fragile for everything else: one contaminated standard silently rescales every future concentration that uses it. Three or more standards in the linear band and a slope give the same ε with the scatter visible.
Scattering is the silent bias no equation can see. Turbid suspensions, bubbles and particulates deflect light out of the beam, and the detector reports the loss as absorbance — the reading inflates at all wavelengths even though nothing “absorbs”. For turbid samples the convention is to blank against the same matrix and keep the wavelength away from the analyte’s peak when checking the background.
Assumptions
- A single absorbing species dominates at the measurement wavelength.
- The solution is dilute enough that molecules do not interact (deviations start around 0.01–0.02 M for many dyes).
- Monochromatic light at the wavelength ε refers to; broadband instrument settings shift effective ε.
- The blank zeroed the solvent and cuvette contributions; the path length entered is the one the light actually travelled.
- Dilution factor is folded in only in concentration mode, where it has a meaning.
Limitations
- Near absorbances above ~2 results carry systematic error no rearrangement can fix; treat them as estimates pending a re-measure.
- ε depends on solvent, pH, temperature and ionic strength — take it from a source matched to your conditions or measure it.
- The tool is molar (ε-based); the nucleic-acid and protein conventions with their fixed per-A260/A280 factors live in their own calculators.
- No background correction: the calculator assumes the instrument’s blank already removed solvent and cuvette absorption.
Common mistakes
- Forgetting the dilution factor, so the reported concentration is of the cuvette, not the tube.
- Using ε from one wavelength or solvent with a reading taken at another.
- Entering a 10 mm micro-volume path as 10 cm — a 10-fold error hiding in a unit.
- Trusting absorbances above ~2 instead of diluting into the linear band.
- Reading transmittance where absorbance is expected (or vice versa) — always check which scale your instrument outputs.
- Using A260 conventions for a purified small molecule, or a molecular ε for a heterogeneous polymer.
FAQ
How do you calculate concentration from absorbance?
What are the units of the molar extinction coefficient?
How is transmittance related to absorbance?
Why is the path length 1 cm?
When does the Beer-Lambert law stop being linear?
Can I find an extinction coefficient with this calculator?
Is this the same as the A260 DNA calculator?
Scientific Sources
- Wikipedia — Beer–Lambert law (A = ε·c·l, transmittance relation) · Tier 3 source
- Wikipedia — Molar absorptivity (ε units L·mol⁻¹·cm⁻¹) · Tier 3 source
- Wikipedia — NADH (ε = 6,220 M⁻¹cm⁻¹ at ~340 nm) · Tier 3 source
External links open in a new tab and carry rel="nofollow". We cite primary references (NIST, NIH/NCBI, peer-reviewed papers) and established manufacturer technical documentation (NEB, Thermo Fisher, Promega, IDT). Calculated results are estimates; your protocol and manufacturer guidance take precedence.
Last reviewed: 2026-10 · Method version: 1.0