The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient value that is large represents a beam becoming 'attenuated' as it passes through a given medium, while a small value represents that the medium had little effect on loss. The (derived) SI unit of attenuation coefficient is the reciprocal metre (m⁻¹). Extinction coefficient is another term for this quantity, often used in meteorology and climatology. The attenuation length is the reciprocal of the attenuation coefficient.

The attenuation coefficient describes the extent to which the radiant flux of a beam is reduced as it passes through a specific material. It is used in the context of:

The attenuation coefficient is called the "extinction coefficient" or sometimes absorption coefficient in the context of solar and infrared radiative transfer in the atmosphere.

A small attenuation coefficient indicates that the material in question is relatively transparent, while a larger value indicates greater degrees of opacity. The attenuation coefficient is dependent upon the type of material and the energy of the radiation. Generally, for electromagnetic radiation, the higher the energy of the incident photons and the less dense the material in question, the lower the corresponding attenuation coefficient will be.

The attenuation of light as it moves through a thin layer of a homogenous material is proportional to the layer thickness, ${\displaystyle d}$ and the initial intensity, ${\displaystyle I_{0}}$. The resulting intensity is given by $${\displaystyle I(d)=I_{0}e^{-\alpha d}}$$ where ${\displaystyle \alpha }$ is the attenuation coefficient. This formula is known as the Beer-Lambert law. This attenuation coefficient measures the exponential decay of intensity, that is, the value of downward e-folding distance of the original intensity as the energy of the intensity passes through a unit (e.g. one meter) thickness of material, so that an attenuation coefficient of 1 m⁻¹ means that after passing through 1 metre, the radiation will be reduced by a factor of e, and for material with a coefficient of 2 m⁻¹, it will be reduced twice by e, or e². Other measures may use a different factor than e, such as the decadic attenuation coefficient below. The broad-beam attenuation coefficient counts forward-scattered radiation as transmitted rather than attenuated, and is more applicable to radiation shielding. The mass attenuation coefficient is the attenuation coefficient normalized by the density of the material.

The attenuation coefficient of a volume, denoted μ, is defined as

where

Note that for an attenuation coefficient which does not vary with z, this equation is solved along a line from ${\displaystyle z}$=0 to ${\displaystyle z}$ as: