在数学以及物理中，拉普拉斯算子或是拉普拉斯算符（英语：Laplace operator, Laplacian）是由欧几里得空间中的一个函数的梯度的散度给出的微分算子，通常写成∇·∇，∇或∆。

这名字是为了纪念法国数学家皮耶-西蒙·拉普拉斯（1749–1827）而命名的。他在研究天体力学在数学中首次应用算子，当它被施加到一个给定的重力位（Gravitational potential）的时候，其中所述算子给出的质量密度的常数倍。经拉普拉斯算子运算为零∆f=0的函数称为调和函数，现在称为拉普拉斯方程，和代表了在自由空间中的可能的重力场。

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇, or ∆. The Laplacian ∆f(p) of a function f at a point p, up to a constant depending on the dimension, is the rate at which the average value of f over spheres centered at p, deviates from f(p) as the radius of the sphere grows. In a Cartesian coordinate system, the Laplacian is given by the sum of second partial derivatives of the function with respect to each independent variable. In other coordinate systems such as cylindrical and spherical coordinates, the Laplacian also has a useful form.