# Calibration operators

> For the complete documentation index, see [llms.txt](https://docs.oriondata.io/llms.txt)

Arithmetic, trigonometric and logarithmic calibration operators and their input conventions.

Operators are grouped into three categories: arithmetic, trigonometric, and exponential and logarithmic.

## Arithmetic operators

Arithmetic operators perform standard mathematical operations on the left and right sides of an expression.

| Operator | Result       | Notes                                                   |
| -------- | ------------ | ------------------------------------------------------- |
| +        | left + right | Addition                                                |
| −        | left − right | Subtraction                                             |
| ×        | left × right | Multiplication                                          |
| /        | left / right | Division                                                |
| ^        | left ^ right | Exponentiation. Left is the base, right is the exponent |

## Trigonometric operators

Trigonometric operators apply a function to the right side and multiply the result by the left side. The right side must be an angle expressed in radians.

The result of any trigonometric step is: left × op(right)

To obtain the pure function result without a scalar multiplier, set the left side to a **Value** of 1.

| Operator | Result               | Constraint on Right Side                                                          |
| -------- | -------------------- | --------------------------------------------------------------------------------- |
| sin      | left × sin(right)    | Angle in radians                                                                  |
| cos      | left × cos(right)    | Angle in radians                                                                  |
| tan      | left × tan(right)    | Angle in radians                                                                  |
| arcsin   | left × arcsin(right) | Right must be between -1 and 1 (inclusive)                                        |
| arccos   | left × arccos(right) | Right must be between -1 and 1 (inclusive)                                        |
| arctan   | left × arctan(right) | No constraint                                                                     |
| arctan2  | arctan2(left, right) | Left is the y coordinate, right is the x coordinate. No scalar multiplier applies |

### Note on arctan2

**arctan2** does not follow the standard left × op(right) pattern. The left side is treated as the y coordinate and the right side as the x coordinate. Setting the left side to 1 does not produce a pure function result in the same way as other trigonometric operators.

## Exponential and logarithmic operators

Exponential and logarithmic operators apply a function to the right side and multiply the result by the left side, following the same scalar pattern as trigonometric operators.

The result of any exponential or logarithmic step is: left × op(right)

To obtain the pure function result without a scalar multiplier, set the left side to a **Value** of 1.

| Operator | Result           | Notes                                                                     |
| -------- | ---------------- | ------------------------------------------------------------------------- |
| exp      | left × _e_^right | Right is the exponent. The base is Euler’s number                         |
| log_e    | left × ln(right) | Right is the input number. Natural logarithm                              |
| logb(n)  | log_left(right)  | Left is the base, right is the input number. No scalar multiplier applies |

### Note on logb(n)

logb(n) does not follow the standard left × op(right) pattern. The left side defines the logarithm base and the right side is the input number. Setting the left side to 1 does not produce a meaningful result in the same way as other operators in this category.

## Summary

Calibration action steps support three categories of operators: arithmetic, trigonometric, and exponential and logarithmic. Trigonometric and exponential and logarithmic operators follow a scalar pattern where the result is left x op(right), meaning the left side acts as a multiplier. Setting the left side to 1 returns the pure function result. The exceptions to this pattern are arctan2, where the left side is the y coordinate, and logb(n), where the left side is the logarithm base.

## Next Steps

- Review the action side types that can be used on either side of an operator expression: see [Action step types reference](https://docs.oriondata.io/portal/calibrations/reference/action-step-types-reference/)
- Learn how steps are chained within a group: see Working with calibration groups
- Explore practical examples of operators in use: see Common calibration patterns

## Related articles

- [Calibration action step types](https://docs.oriondata.io/portal/calibrations/reference/action-step-types-reference/)
- [Calibration conditions](https://docs.oriondata.io/portal/calibrations/reference/calibration-conditions-reference/)
- [Calibration aggregates](https://docs.oriondata.io/portal/calibrations/reference/aggregates-reference/)
- Common calibration patterns