The **differential element** or just **differential** of a quantity refers to an infinitesimal change in said quantity, and is defined as the limit of a change in quantity as the change approaches zero.

Differentials are useful in the definitions of both derivatives and integrals; for example, the derivative of with respect to is defined as

When transforming coordinates, the value of a differential element is computed using the determinant of the Jacobian matrix.

## Formulae for differential elements

### Line elements

- (scalar line element)
- (tangential vector element)
- (normal vector element)

### Area elements

- (two-dimensional Cartesian coordinates)
- (polar coordinates)

### Surface elements

- (scalar surface element)
- (normal vector surface element)

### Volume elements

- (three-dimensional Cartesian coordinates)
- (cylindrical coordinates)
- (spherical coordinates)