**Feel like "cheating" at Calculus?** Check out our **Practically Cheating Calculus Handbook**, which gives you hundreds of easy-to-follow answers in a convenient e-book.

The **Del Operator** (also called the *Nabla operator* or the *vector differential operator*) is a mathematical operator (actually a collection of partial derivative operators) commonly used in vector calculus to find higher dimensional derivatives. An “operator” is similar to a function (Green, 1998).

Although it’s defined as a vector, it doesn’t have magnitude and so isn’t a “true” vector.

By itself, it doesn’t actually have any meaning at all (much like a lonely multiplication or addition symbol). It only has a meaning when combined with a scalar function or vector function.

## Del Operator Uses

The del operator is used in various vector calculus operations. Depending on what expression the operator appears in, it may denote gradient of a scalar field, divergence of a vector field, curl of a vector field, or the Laplacian operator:

**Gradient**: ∇ f**Divergence**(the operator equivalent of a scalar product of two vectors): ∇ x E**Curl**(the vector product equivalent of divergence): ∇ · E**Laplacian**: ∇ · ∇f = ∇^{2}f

The del operator can be applied to a scalar function or a vector function. ∇ · F is a scalar function, and ∇ x F is a vector function.

## References

Green, K. (1998). The Del Operator. Retrieved January 8, 2020 from: http://citadel.sjfc.edu/faculty/kgreen/vector/block2/del_op/del_op.html

Hyperphysics. Vector Calculus.

Ida, N. (2007). Engineering Electromagnetics. Springer.

**CITE THIS AS:**

**Stephanie Glen**. "Del Operator (Nabla operator)" From

**CalculusHowTo.com**: Calculus for the rest of us! https://www.calculushowto.com/del-operator-nabla/

**Need help with a homework or test question?** With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!