# padé() Function & Examples

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

Try it yourself:

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## pade(): rational approximation from a series

**pade()** builds a Padé approximation: a ratio of two polynomials chosen to match terms of a power series. Rational approximations can represent poles and often behave better than a truncated polynomial away from the expansion point.

## When it helps

Use Padé approximation for symbolic analysis, control models, and numerical estimates where a Taylor series converges slowly. Select numerator and denominator orders based on the available series and the desired behavior.

## Related functions

Use [derivative()](https://calcul.io/function/derivative/index.md) to obtain series information, [simplify()](https://calcul.io/function/simplify/index.md) to reduce the rational result, [resolve()](https://calcul.io/function/resolve/index.md) to inspect poles, and [numeric()](https://calcul.io/function/numeric/index.md) to compare approximations.

## Caveat

A Padé approximant is not automatically accurate everywhere. Check it near singularities and against the original function over the range you actually need.

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