Inverse Tangent (arctan) Calculator
The Inverse Tangent (arctan) Calculator finds the angle whose tangent equals a value, and also computes atan2(y, x) for full-circle direction. The formula used is: arctan(x) returns an angle in (-90°, 90°); atan2(y, x) returns an angle in (-180°, 180°].
Formula
arctan(x) returns angle in (−90°, 90°); atan2(y,x) returns angle in (−180°, 180°]
Example Calculation
Inputs
- Value: 1
- X (for atan2): 1
- Y (for atan2): 1
arctan(1) = 45°, while atan2(1, 1) = 45° as well since the point (1, 1) lies in the first quadrant. For (x = -1, y = 1), atan2 would give 135°.
Frequently asked questions
What is arctan?
Arctan, the inverse tangent, returns the angle whose tangent equals the value you enter. It reverses the tangent function.
How is atan2 different from arctan?
atan2(y, x) uses the signs of both x and y to return the correct angle in any of the four quadrants, from -180° to 180°.
What is the output range of arctan?
From -90° to 90° (exclusive). atan2 instead spans the full -180° to 180° range.
When should I use atan2?
Use atan2 to find the direction of a vector or point (x, y), where the quadrant matters, such as in geometry and graphics.
Why does arctan(1) equal 45°?
Because tan(45°) = 1, so the angle whose tangent is 1 is 45°.