> For the complete documentation index, see [llms.txt](https://docs.lottielab.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.lottielab.com/editor/interactivity/formulas.md). # Formulas When choosing an [interaction type](/editor/interactivity/interactions.md#anatomy-of-an-interaction), one of the options is a **Custom formula.** This allows you to create a [*mapping*](/editor/interactivity/interactions.md#mappings) that uses the full power of the scripting engine in Lottielab Interactivity. With a custom formula mapping, you get a text field where you can type in a formula whose result will be used to control the selected parameter (playhead position, blending with another state, or playback speed):

These formulas use a simple expression language. At each frame, the value of the expression is calculated, and the output (typically 0-1) is applied to the selected parameter: * For the "Time (progress)" mapping, 0 means the beginning of the state's segment, and 1 means the end of the state's segment (with intermediate values in-between.) * For the "Playback speed" mapping, the value is directly applied as a speed coefficient (1.0 = normal speed, 0.5 = twice as slow, etc.) * For the "Blend" mapping, the value is applied as the blending coefficient between this state and the other selected state (0.0 = fully display this state, 1.0 = fully display the other state, 0.5 = blend 50/50 between the states, etc.). Lottielab Player also exposes several built-in variables based on user input, and allows you to provide custom variables that can be re-used from the formula. ## Formula language The formula language follows the expression rules of a C-like language. You can use parentheses and specify literal numbers. ### Types All types are floating point numbers. For the purposes of boolean operations, all non-0 numbers are interpreted as truthy (and 0 numbers as falsy). ### Operators These operators are available, from highest to lowest precedence: * Logical negation (`!`) * Exponent/power operation (`^`) * Multiplication and division (`*`, `/`) * Addition and subtraction (`+`, `-`) * Comparisons (`>`, `<`, `>=`, `<=`, `==`) * Logical (`||`, `&&`) * Ternary conditional (`?:`, as in `condition ? a : b`) ## Built-in functions and constants The language provides support for [all functions and constants inside the JavaScript `Math` namespace.](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math) This includes trigonometric functions, constants such as `PI`, logarithms, and others. These functions and constants are available *without the \`Math.\` prefix.* For example, a valid formula can be: `sin(PI * mouse.progress.x)`. ## Built-in variables The Lottielab Player runtime provides several variables that can be used in the formula to respond to user input: * `time`: Time in seconds since this state started. * `time.abs`: Time in seconds since the animation first started. * `playhead`: The current playhead position in this state, in seconds. * `playhead.progress`: The current playhead position in this state, as a * value from 0 to 1 within the segment (0 = start, 1 = end). * `playhead.abs`: Global position of the playhead in seconds. * `mouse.x`, `mouse.y`: The current mouse position, relative to the top-left * of the lottie, in pixels * `mouse.progress.x`, `mouse.progress.y`: The current mouse position, as a value from 0 to 1 within the lottie's bounds (0 = left/top, 1 = right/bottom) * `mouse.abs.x`, `mouse.abs.y`: The current mouse position, relative to the top-left of the whole viewport rather than the lottie itself * `mouse.buttons.left`, `mouse.buttons.right`, `mouse.buttons.middle`: Whether the left, right, or middle mouse buttons are currently pressed ## Custom variables You can use a variable name that doesn't appear in the list above. In this case, the variable is treated as a custom variable, and you should provide the value at runtime using the `interactivity.inputs.set()` [API of the Lottielab player](https://github.com/lottielab/lottie-player/blob/master/INTERACTIVITY.md). Note that, when using custom variables, the Lottielab preview page won't work properly, as it doesn't have a value for this variable. For testing purposes, you can temporarily change the variable name to something like `mouse.progress.x` in order to be able to test the interaction, and then change it back to your custom variable name before export.