# norm() Function & Examples

Use the norm() arithmetic function in Calcul.io. Review its syntax, edit working examples, understand the result, and explore related math functions.

## norm

#### norm(x)

#### norm(x, p)

Try it yourself:

```calculio
abs(-3.5)
norm(-3.5)
norm(3 - 4i)
norm([1, 2, -3], Infinity)
norm([1, 2, -3], -Infinity)
norm([3, 4], 2)
norm([[1, 2], [3, 4]], 1)
norm([[1, 2], [3, 4]], "inf")
norm([[1, 2], [3, 4]], "fro")
```

---

## Measure vector or matrix size with norm

**norm** calculates a norm: a non-negative measure of vector length or matrix magnitude. The default commonly corresponds to Euclidean length for vectors.

## Example

The norm of `[3,4]` is 5. Use [hypot](https://calcul.io/function/hypot/index.md) for component lengths directly, and [distance](https://calcul.io/function/distance/index.md) for separation between points. Norms support normalization, error measurement, and convergence checks.

## Choices and caveats

Different norm orders measure different properties, so state which norm a formula requires. For complex vectors, conjugation matters; see [conj](https://calcul.io/function/conj/index.md) and [ctranspose](https://calcul.io/function/ctranspose/index.md). Inputs should be numeric and dimensionally meaningful.

[All functions](https://calcul.io/functions/index.md)