What is the Beer–Lambert law?

It links absorbance to concentration and path length with A = ε·c·ℓ and connects to transmittance with A = −log10(T).

Which units should I use for molar absorptivity?

Use M−1·cm−1 for the decadic form. The calculator can convert compatible units to that base.

Why does my absorbance become nonlinear at high values?

Stray light and instrument limits cause deviations. Dilute the sample and keep A within the linear range near 0.1–1.0.

Chemistry Calculators

Beer-Lambert Law Calculator: Precise Absorbance & Concentration Tool

Aniruddh

September 13, 2025

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Beer-Lambert Law Calculator: the fast way to convert between absorbance, transmittance, concentration, and path length

The Beer-Lambert law gives you a clean bridge between how much light a sample absorbs and how much of a substance it holds. This Beer-Lambert Law Calculator lets you solve for absorbance (A), transmittance (T), molar absorptivity (ε), concentration (c), or path length (ℓ) with a couple of inputs. It follows the decadic form that labs use every day, so your numbers drop straight into reports.

How the calculator works

You choose what you want to solve for. Then you provide the remaining values in any sensible unit. The calculator normalizes everything behind the scenes. It uses the decadic version of the Beer-Lambert law. That is the version that pairs with base-10 logarithms and spectrophotometers that display absorbance as optical density.

See also:

Solve for A when you know ε, c, and ℓ.
Solve for T when you know ε, c, and ℓ. Output appears as a percentage.
Solve for ε when you ran a standard and measured A or T.
Solve for c when you know A or T and the method’s ε and the cuvette length.
Solve for ℓ when you have a custom cell or a microfluidic channel.

You can enter transmittance as a fraction or as a percent. You can switch units for concentration and length. Results display in base units for clarity. ε reports as M⁻¹·cm⁻¹. Concentration reports as molar. Path length reports as centimeters. This mirrors how most methods are written.

Quick start guide

Pick the unknown in the Solve for toggle.
Enter the known values. Choose units that match your lab setup.
If you enter T then select % or fraction. The calculator converts it to A for the math.
Hit Copy results to move values to your LIMS or lab notes. Download a CSV if you want a record.
Use Reset to clear the slate between samples.

Beer-Lambert law formula

The Beer-Lambert law connects absorbance with concentration and path length:

A = ε · c · ℓ

Absorbance also connects to transmittance:

T = I / I₀ where I is transmitted intensity and I₀ is incident intensity
A = −log₁₀(T)
T = 10^−A

Use the decadic version in most analytical protocols. You will also find an Napierian version that uses natural logs. The form is A_e = ε_e·c·ℓ where A_e uses ln rather than log₁₀. You can convert between ε and ε_e with the factor 2.303.

Units and common conversions

Units matter. The calculator handles the conversion for you. This table summarizes what goes in and how the output appears.

Quantity	Typical input units	Internal base unit	Notes
Molar absorptivity (ε)	1/(M·cm), 1/(mM·cm), 1/(M·mm), 1/(M·m)	M⁻¹·cm⁻¹	Also called molar extinction coefficient
Concentration (c)	M, mM, μM, nM, pM	M	Choose molarity that fits your sample
Path length (ℓ)	cm, mm, m, in, ft	cm	Standard cuvette equals 1 cm
Absorbance (A)	unitless	unitless	Spectrophotometer display often calls this OD
Transmittance (T)	% or fraction	fraction	100% equals 1.0 fraction

Worked examples

Example 1: Calculate absorbance from ε, c, ℓ

You run a sample with an ε of 18,000 M⁻¹·cm⁻¹. The solution concentration equals 4.0 μM. The cuvette length equals 1 cm. What is A?

Convert 4.0 μM to molar. 4.0 μM equals 4.0 × 10⁻⁶ M.
Use the formula A = ε·c·ℓ.
A = 18,000 × 4.0×10⁻⁶ × 1 = 0.072

The measured absorbance should sit near 0.072 at the chosen wavelength. The transmittance would sit at T = 10^−0.072 ≈ 0.85. That equals about 85%.

Example 2: Find concentration from a measured A

Your spectrophotometer reports A = 0.560 at 595 nm. You use a protein dye with ε = 43,000 M⁻¹·cm⁻¹. The cuvette has ℓ = 1 cm. What is c?

Rearrange the equation. c = A / (ε·ℓ).
c = 0.560 / (43,000 × 1) = 1.3023×10⁻⁵ M.
That equals 13.0 μM.

Example 3: Determine ε from a standard

You need ε for a new chromophore. A 20 μM solution gives A = 0.244 at 410 nm. The path length equals 1.00 cm. What is ε?

Convert c to molar. 20 μM equals 2.0×10⁻⁵ M.
ε = A / (c·ℓ) = 0.244 / (2.0×10⁻⁵ × 1.00).
ε ≈ 12,200 M⁻¹·cm⁻¹.

Example 4: Work with transmittance directly

A film transmits 12% of light at 550 nm. What is A?

T fraction equals 0.12.
A = −log₁₀(0.12) ≈ 0.9208.

Example 5: Microfluidic channel path length

You test an assay in a 250 μm channel. That equals 0.025 cm. You measure A = 0.150 at ε = 30,000 M⁻¹·cm⁻¹. What is c?

c = A / (ε·ℓ) = 0.150 / (30,000 × 0.025) = 0.0002 M.
That equals 200 μM.

Best practices for accurate readings

Work in the linear range. Most spectrophotometers stay linear up to A ~ 1.0 or 1.5. Above that range small stray light errors grow. Dilute the sample rather than force a high absorbance.
Use matched cuvettes. Scratched or mismatched cells shift readings. A lint-free wipe and a gentle polish save a lot of grief.
Pick the correct wavelength. Use the absorbance maximum for your analyte. That improves sensitivity and tolerance to small wavelength drift.
Blank the instrument. Solvent and matrix absorb too. A proper blank removes the background so the Beer-Lambert model fits.
Mind scattering. Suspensions and turbid samples scatter light. That adds to apparent absorbance. Centrifuge or filter when the chemistry allows.
Check pH and temperature. Many chromophores change protonation state or structure with pH or heat. That change modifies ε. Control conditions for consistent results.

Troubleshooting and common deviations

Real samples do not always behave like ideal solutions. These effects cause departures from the straight line.

High concentration. Solute molecules interact at high c. The ε·c·ℓ product stops telling the whole story. Dilute and re-run.
Polychromatic light. A broad lamp band can bend the curve. A monochromator or a narrow bandpass filter solves it.
Stray light. Scattered light sneaks past the sample. Absorbance reads lower than expected at high A. Clean optics, check slits, and verify lamp alignment.
Chemical equilibrium. If your analyte forms complexes or tautomerizes then ε changes with composition. Run a calibration curve over the working range rather than assume ε stays fixed.
Fluorescence. Emission can backfill the detector. That reduces apparent absorbance. Use right-angle geometry or suppress fluorescence when possible.

Where the Beer-Lambert law shines

Beer–Lambert law: absorbance depends linearly on molar absorptivity (ε), concentration (c), and path length (ℓ).

You meet this law in many places. It shows up in quality control lines and in greenhouses and in ocean sensors.

Clinical and biotech labs. Protein assays, nucleic acid quantification, enzyme kinetics.
Environmental monitoring. Nitrate, phosphate, and metal complex assays in water.
Food and beverage. Color measurements, additive levels, fermentation tracking.
Materials and thin films. Optical density of coatings and filters.
Education. Introductory chemistry and biochemistry experiments.

Frequently asked questions

What is the difference between absorbance and optical density?

In most lab contexts the terms match. Instruments label the same readout as A or OD. Both equal −log₁₀(T).

Is ε wavelength dependent?

Yes. ε depends on the electronic transitions of the analyte. It changes with wavelength. Methods always specify a wavelength for ε. Many methods use the λ_max that gives the largest ε for a given chromophore.

Can I enter transmittance as percent?

Yes. Enter 56% as 56. The calculator converts it to a fraction for the math and reports the final T as a percent for readability.

What path length should I use?

A standard cuvette equals 1 cm. Microplates use effective path lengths that depend on volume. Many plate readers estimate ℓ from well geometry. If your device reports an effective length then use that value.

What causes nonlinearity at high absorbance?

Stray light dominates at high A values. The Beer-Lambert model expects negligible stray light. A tiny leak past the sample adds a constant baseline at the detector. The readout flattens. Dilution fixes it.

Mini reference card

Core equation: A = ε·c·ℓ
Transmittance: T = 10^−A
Absorbance from T: A = −log₁₀(T)
ε units: M⁻¹·cm⁻¹
Linear range: A ≈ 0.1 to 1.0 for most setups

A dependable Beer-Lambert Law Calculator saves time and reduces transcription mistakes. You type ε, c, and ℓ then absorbance appears in a blink. Or you start with a measured A and get concentration with the same ease. Keep your units consistent and work in the linear range. Your numbers will reward you.