麦克斯韦-玻尔兹曼分布是一个概率分布，在物理学和化学中有应用。最常见的应用是统计力学的领域。任何（宏观）物理系统的温度都是组成该系统的分子和原子的运动的结果。这些粒子有一个不同速度的范围，而任何单个粒子的速度都因与其它粒子的碰撞而不断变化。然而，对于大量粒子来说，处于一个特定的速度范围的粒子所占的比例却几乎不变，如果系统处于或接近处于平衡。麦克斯韦-玻尔兹曼分布具体说明了这个比例，对于任何速度范围，作为系统的温度的函数。它以詹姆斯·麦克斯韦和路德维希·玻尔兹曼命名。

这个分布可以视为一个三维矢量的大小，它的分量是独立和正态分布的，其期望值为0，标准差为。如果的分布为，那幺

In statistics the Maxwell–Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used in physics (in particular in statistical mechanics) for describing particle speeds in idealized gases where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. Particle in this context refers to gaseous particles (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium. While the distribution was first derived by Maxwell in 1860 on heuristic grounds, Boltzmann later carried out significant investigations into the physical origins of this distribution.