What do you want to do?

Use a known absorption coefficient or solve for any of the four quantities.

Sample data

Choose what to calculate and replace the example values with your data.

What do you want to calculate?

A = \varepsilon_{\lambda}\,l\,c

Molar absorption coefficientελL·mol⁻¹·cm⁻¹

Use the coefficient for the measurement wavelength.

Optical pathl

Molar concentrationc

Absorbance

0.622A

Absorbance and transmittance

Absorbance: 0.622A
Transmittance: 0.2388
Percent transmittance: 23.88%

Light passing through the sample

Higher absorbance means a smaller fraction of transmitted light.

Transmitted light23.88 %

Of the incident light

Illustrative diagram; the color does not represent the sample spectrum.

Fundamentals & Explanation

Absorbance and transmittance

The instrument compares incident power $P_0$ with transmitted power $P$ . Transmittance is their ratio and decadic absorbance applies a negative logarithm:

T=\frac{P}{P_0}\qquad A=-\log_{10}(T)\qquad T=10^{-A}

$A$ and $T$ are dimensionless. Percent transmittance is $\%T=100\,T$ : for example, $T=0.25$ corresponds to 25%. The logarithm turns ideal attenuation into a linear relationship with optical path length.

Beer–Lambert law and units

At a fixed wavelength, absorbance is proportional to concentration and optical path length. Molar and mass concentrations require coefficients with compatible units:

A=\varepsilon_{\lambda}\,l\,c\qquad A=a^{*}_{\lambda}\,l\,\rho

$\varepsilon_\lambda$ : L·mol⁻¹·cm⁻¹, with $c$ in mol/L.
$a^*_{\lambda}$ : L·g⁻¹·cm⁻¹, with $\rho$ in g/L.
With these coefficients, $l$ is expressed in cm. The coefficients depend on the absorbing species and wavelength $\lambda$ .

For example, $\varepsilon_\lambda=6220\;\mathrm{L\,mol^{-1}\,cm^{-1}}$ , a 1 cm optical path and $c=100\;\mu\mathrm{M}=10^{-4}\;\mathrm{mol/L}$ give $A=0.622$ and approximately 23.88% transmittance.

Assumptions of the ideal model

Radiation with a sufficiently narrow spectral bandwidth.
A homogeneous, non-scattering medium and a known optical path.
A stable absorbing species without interactions that change its coefficient.
A linear instrument response and appropriately treated blank.

Independent species can contribute additively, $A_{total}=\sum_i A_i$ . Distinguishing the components of a mixture requires additional measurements and a suitable model.

Causes of deviation

Stray light compresses high absorbances; broad spectral bandwidth combines different coefficients. Turbidity adds scattering, while chemical equilibria, association, or pH changes may alter the absorbing species. Consequently, no universal absorbance interval guarantees linearity for every instrument and method.

Calibration, interpolation, and dilution

Standards are fitted by ordinary least squares with a free intercept. Standards and sample must share wavelength, optical path length and blank treatment. Concentration is estimated from absorbance and corrected for dilution:

A=m\,c+b\qquad \hat c=\frac{A_s-b}{m}\qquad c_0=\hat c\,FD

$m$ is the slope, $b$ the intercept and $A_s$ the sample absorbance. Concentrations use the same unit as the standards; quantification requires $m>0$ .

The dilution factor $FD$ is the ratio of final volume to aliquot volume in a simple dilution. Bringing 1 mL of sample to a final volume of 10 mL gives $FD=10$ . $\hat c$ refers to the measured aliquot and $c_0$ to the original sample.

Interpolation occurs only when $\hat c$ lies between the minimum and maximum standards. Outside that domain, extrapolation extends the line mathematically but adds uncharacterized uncertainty.

Residuals, R², and intercept

Residuals $e_i=A_i-\hat A_i$ are differences between measured and predicted absorbances. They help examine curvature, changes in scatter and points away from the general pattern. A high R² does not by itself validate linearity, matrix effects, blank treatment or precision.

If the 95% confidence interval for the intercept excludes zero, the blank or matrix may contribute. The fit alone does not identify the cause.

Detection and quantification limits

The limit of detection (LOD) refers to the lowest detectable concentration; the limit of quantification (LOQ), to the lowest quantifiable concentration with suitable precision and accuracy. With residual standard deviation $s_{y/x}$ and slope $m>0$ :

LOD_{est}=3.3\frac{s_{y/x}}{m}\qquad LOQ_{est}=10\frac{s_{y/x}}{m}

These estimates depend on the calibration range and experimental design. Confirmation requires samples of known concentration near the limits and evidence of suitable precision and accuracy; fitting a line alone does not demonstrate that performance.

Scope and references

OD600 primarily depends on scattering. For nucleic acids, A260 can estimate concentration with appropriate factors and corrections; A260/A280 is an indicator of purity. That ratio alone does not determine concentration.

UV-Vis Spectrophotometry (Beer–Lambert)

Sample data

Absorbance

Light passing through the sample

Fundamentals & Explanation

Absorbance and transmittance

Beer–Lambert law and units

Assumptions of the ideal model

Causes of deviation

Calibration, interpolation, and dilution

Residuals, R², and intercept

Detection and quantification limits

Scope and references

Absorbance and transmittance

Beer–Lambert law and units

Assumptions of the ideal model

Causes of deviation

Calibration, interpolation, and dilution

Residuals, R², and intercept

Detection and quantification limits

Scope and references