卡方分布（chi-square distribution, χ²-distribution）是概率论与统计学中常用的一种概率分布。k个独立的标准正态分布变量的平方和服从自由度为k的卡方分布。卡方分布是一种特殊的伽玛分布，是统计推断中应用最为广泛的概率分布之一，例如假设检验和置信区间的计算。

由卡方分布延伸出来皮尔森卡方检定常用于： (1)样本某性质的比例分布与母体理论分布的拟合优度；(2)同一母体的两个随机变量是否独立；(3)二或多个母体同一属性的同质性检定。（详见皮尔森卡方检定）

In probability theory and statistics, the chi-squared distribution (also chi-square or χ²-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, e.g., in hypothesis testing or in construction of confidence intervals. When it is being distinguished from the more general noncentral chi-squared distribution, this distribution is sometimes called the central chi-squared distribution.