In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime. The field tensor was developed by Arnold Sommerfeld after the four-dimensional tensor formulation of special relativity was introduced by Hermann Minkowski. The tensor allows related physical laws to be written concisely, and allows for the quantization of the electromagnetic field by the Lagrangian formulation described below.

The electromagnetic tensor, conventionally labelled F, is defined as the exterior derivative of the electromagnetic four-potential, A, a differential 1-form:

Therefore, F is a differential 2-form— an antisymmetric rank-2 tensor field—on Minkowski space. In component form,

where ${\displaystyle \partial }$ is the four-gradient and ${\displaystyle A}$ is the four-potential.

SI units for Maxwell's equations and the particle physicist's sign convention for the signature of Minkowski space (+ − − −), will be used throughout this article.

The Faraday differential 2-form is given by

where ${\displaystyle dt}$ is the time element times the speed of light ${\displaystyle c}$.

This is the exterior derivative of its 1-form antiderivative, the covariant form of the four-potential, is