Sass math.atan()

Definition and Usage

math.atan($number) returns the arctangent of $number in deg. $number must be unitless (any real slope ratio). Load it with @use "sass:math" on Dart Sass 1.25+.

Syntax

@use "sass:math";

math.atan($number); //=> angle in deg

math.atan(10); // 84.2894068625deg
math.atan(1);  // 45deg
math.atan(0);  // 0deg
math.atan(-1); // -45deg

// Slope from lengths (must cancel units first)
math.atan(math.div(10px, 10px)); // 45deg

// Module API — prefer math.atan after @use "sass:math"

Pattern: build a unitless slope → math.atan for a CSS angle → use math.atan2 when x and y are separate and the quadrant matters.

Slope and Range

Unlike asin/acos, atan accepts any real unitless number:

Related Functions

Load with @use "sass:math". Previous: math.asin(). Next: math.atan2(). Also: math.tan(), math.acos(), math.sin(), math.div().

SCSS Examples

Examples target Dart Sass 1.25+ with @use "sass:math". Open View Compiled CSS for verified output (matches official Sass docs samples).

@use "sass:math";

@debug math.atan(10); // 84.2894068625deg

.basic {
  --ten: #{math.atan(10)};
}

.basic {
  --ten: 84.2894068625deg;
}

@use "sass:math";

.slopes {
  --zero: #{math.atan(0)};
  --one: #{math.atan(1)};
  --neg: #{math.atan(-1)};
}

.slopes {
  --zero: 0deg;
  --one: 45deg;
  --neg: -45deg;
}

@use "sass:math";

.compare {
  --atan-neg: #{math.atan(math.div(1, -1))};
  --atan2: #{math.atan2(1, -1)};
}

.compare {
  --atan-neg: -45deg;
  --atan2: 135deg;
}

@use "sass:math";

.roundtrip {
  --back-num: #{math.tan(math.atan(1))};
  --back-ang: #{math.atan(math.tan(45deg))};
  --asin: #{math.asin(0.5)};
}

.roundtrip {
  --back-num: 1;
  --back-ang: 45deg;
  --asin: 30deg;
}

@use "sass:math";

$slope: 1;

.angle {
  --deg: #{math.atan($slope)};
  transform: rotate(math.atan($slope));
}

.angle {
  --deg: 45deg;
  transform: rotate(45deg);
}

Sass Support

Prefer the module form with Dart Sass 1.25+.

Compile with the Dart Sass CLI.

Key Takeaways

Compile Notes

Practical checklist:

1. @use "sass:math"
2. Pass a unitless slope (cancel length units first)
3. Expect a deg angle (~ -90deg…90deg)
4. Use math.atan2 when quadrant matters
5. Use math.tan for the forward transform