> ## Documentation Index
> Fetch the complete documentation index at: https://docs.truemath.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Function library

> An index of TrueMath's built-in functions by category — arithmetic, trigonometry, statistics, finance, tables, and more.

TrueMath provides a library of built-in functions you can call from any
[activity](/concepts/activities) equation. Functions take arguments separated by
semicolons and are case-insensitive:

```
round(monthly_payment; 2)
pmt(loan_amount; 0; rate / 12; term * 12)
```

Many functions operate on a [table](/math/types/tables) as well as a single number,
returning a table when given one. Many also accept [unit numbers](/math/types/unit-numbers),
carrying units through the calculation; where a function requires a specific kind of unit —
such as an angle for trigonometry — its page says so.

## Categories

| Category                                                         | Functions                                                                                              |
| ---------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------ |
| [Arithmetic and powers](/math/functions/arithmetic-and-powers)   | `+`, `-`, `*`, `/`, `^`, `mod`, `ch`, `sqrt`, `root`, `ln`, `log`, `alog`, `exp`                       |
| [Trigonometry](/math/functions/trigonometry)                     | `sin`, `cos`, `tan`, `asin`, `acos`, `atan`, `sec`, `csc`, `cot`, and hyperbolic forms                 |
| [Rounding and numeric](/math/functions/rounding-and-numeric)     | `round`, `floor`, `ceil`, `abs`, `sign`, `ipart`, `fpart`                                              |
| [Unit functions](/math/functions/units)                          | `unit`, `unitvalue`                                                                                    |
| [Statistics](/math/functions/statistics)                         | `sum`, `avg`, `min`, `max`, `median`, `stddev`, `variance`, `fact`, `perm`, `comb`, `rand`, and more   |
| [Finance](/math/functions/finance)                               | `pv`, `fv`, `pmt`, `rate`, `periods`, `amortization`, `npv`, `irr`, `effrate`, `nomrate`, and more     |
| [Table functions](/math/functions/tables)                        | `length`, `width`, `item`, `row`, `column`, `subset`, `lookup`, `vlookup`, `rlookup`, `sort`, `append` |
| [Conditionals and logic](/math/functions/conditionals-and-logic) | `if`, `choose`, `loop`                                                                                 |

For operators and the order of operations, see
[Operators and precedence](/math/functions/operators-and-precedence).