In optics, **absorbance** or **decadic absorbance** is the *common logarithm* of the ratio of incident to *transmitted* radiant power through a material, and **spectral absorbance** or **spectral decadic absorbance** is the common logarithm of the ratio of incident to *transmitted* spectral radiant power through a material.^{[1]} Absorbance is dimensionless, and in particular is not a length, though it is a monotonically increasing function of path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for absorbance is discouraged.^{[1]}
In physics, a closely related quantity called "optical depth" is used instead of absorbance: the *natural logarithm* of the ratio of incident to *transmitted* radiant power through a material. The optical depth equals the absorbance times ln(10).

The term absorption refers to the physical process of absorbing light, while absorbance does not always measure absorption: it measures attenuation (of transmitted radiant power). Attenuation can be caused by absorption, but also reflection, scattering, and other physical processes.

## Mathematical definitions

### Absorbance

**Absorbance** of a material, denoted *A*, is given by^{[1]}

- $A=\log _{10}{\frac {\Phi _{\text{e}}^{\text{i}}}{\Phi _{\text{e}}^{\text{t}}}}=-\log _{10}T,$

where

- $\mathrm{\Phi}}_{\text{e}}^{\text{t}$
**Absorbance** of a material, denoted *A*, is given by^{[1]}

- $A=\log _{10}{\frac {\Phi _{\text{e}}^{\text{i}}}{\Phi _{\text{e}}^{\text{t}}}}=-\log _{10}T,$

where

- $\Phi _{\text{e}}^{\text{t}}$$\Phi _{\text{e}}^{\text{t}}$ is the radiant flux
*transmitted* by that material,
- $\Phi _{\text{e}}^{\text{i}}$dimensionless quantity. Nevertheless, the
**absorbance unit** or **AU** is commonly used in ultraviolet–visible spectroscopy and its high-performance liquid chromatography applications, often in derived units such as the milli-absorbance unit (mAU) or milli-absorbance unit-minutes (mAU×min), a unit of absorbance integrated over time.^{[2]}
Absorbance is related to optical depth by

- $A={\frac {\tau }{\ln 10}}=\tau \log _{10}e\,,$

where *τ* is the optical depth.

### Spectral absorbance

**Spectral absorbance in frequency** and **spectral absorbance in wavelength** of a material, denoted *A*_{ν} and *A*_{λ} respectively, are given by^{[1]}

- $A}_{\nu}={\mathrm{log}}_{10}\frac{{\mathrm{\Phi}}_{\text{e},\nu}^{\text{i}}}{{\mathrm{\Phi}}_{\text{e},\nu}^{\text{t}}$
Absorbance is related to optical depth by

where *τ* is the optical depth.

### Spectral absorbance

**Spectral absorbance in frequency** and **spectral absorbance in wavelength** of a material, denoted *A*_{ν} and *A*_{λ} respectively, are given by^{[1]}

- $A}_{\nu}={\mathrm{log}}_{10}\frac{}{$
**Spectral absorbance in frequency** and **spectral absorbance in wavelength** of a material, denoted *A*_{ν} and *A*_{λ} respectively, are given by^{[1]}

- $$
where

- Φ
_{e,ν}^{t} is the spectral radiant flux in frequency *transmitted* by that material,
- Φ
_{e,ν}^{i} is the spectral radiant flux in frequency received by that material,
*T*_{ν} is the spectral transmittance in frequency of that material,
- Φ
_{e,λ}^{t} is the spectral radiant flux in wavelength *transmitted* by that material,
- Φ
_{e,λ}^{i} is the spectral radiant flux in wavelength received by that material,
*T*_{λ} is the spectral transmittance in wavelength of that material.

Spectral absorbance is related to spectral optical depth by

- $A_{\nu }={\frac {\tau _{\nu }}{\ln 10}}=\tau _{\nu }\log _{10}e\,,$
- $A_{\lambda }={\frac {\tau _{\lambda }}{\ln 10}}=\tau _{\lambda }\log _{10}e\,,$

where

*τ*_{ν} is the spectral optical depth in frequency,
*τ*_{λ} is the spectral optical depth in wavelength.

Although absorbance is properly unitless, it is sometimes reported in "arbitrary units", or AU. Many people, including scientific researchers, wrongly state the results from absorbance measurement experiments in terms of these made-up units.^{[3]}

## Relationship with attenuation
=
τ
ν
ln

### Attenuance

Absorbance is a number that measures the *attenuation* of the transmitted radiant power in a material. Attenuation can be caused by the physical process of "absorption", but also reflection, scattering, and other physical processes. Absorbance of a material is approximately equal to its *attenuance*^{[clarification needed]} when both the absorbance is much less than 1 and the emittance of that material (not to be confused with radiant exitance or emissivity) is much less than the absorbance. Indeed,

- $\mathrm{\Phi}}_{\text{e}}^{\text{t}}+{\mathrm{\Phi}}_{\text{e}}^{\text{att}}={\mathrm{\Phi}}_{\text{e}}^{\text{i}}+{\mathrm{\Phi}}_{\text{e}}^{$
## Relationship with attenuationattenuance^{[clarification needed]} when both the absorbance is much less than 1 and the emittance of that material (not to be confused with radiant exitance or emissivity) is much less than the absorbance. Indeed,
- $\mathrm{\Phi}}_{\text{e}}^{\text{t}$
where

- Φ
_{e}^{t} is the radiant power transmitted by that material,
- Φ
_{e}^{att} is the radiant power attenuated by that material,
- Φ
_{e}^{i} is the radiant power received by that material,
- Φ
_{e}^{e} is the radiant power emitted by that material,

that is equivalent to

- $T+{\text{ATT}}=1+E,$

where

*T* = Φ_{e}^{t}/Φ_{e}^{i} is the transmittance of that material,
- ATT = Φ
_{e}^{att}/Φ_{e}^{i} is the *attenuance* of that material,
*E* = Φ_{e}^{e}/Φ_{e}^{i} is the emittance of that material,

and according to Beer–Lambert law, *T* = 10^{−A}, so

- $<$
that is equivalent to

- ${\text{ATT}}\approx A\ln 10,\quad {\text{if}}\ E\ll A.$