Arctan Calculator — Inverse Tangent (tan⁻¹)
Calculate the arctangent (inverse tangent) of any value in degrees and radians. Includes atan2(y, x) mode for quadrant-aware results with full unit circle reference. See also our Cosine Calculator and Trigonometry Calculator.
How to Calculate Arctangent
- Choose the mode: standard atan(x) or quadrant-aware atan2(y, x).
- Enter the value (for atan) or y and x coordinates (for atan2).
- Click Calculate to get the angle in both degrees and radians.
- The atan2 mode returns angles from -180 to 180 degrees, identifying the correct quadrant.
Formula
atan(x): Returns angle θ where tan(θ) = x
Range: -90° to 90° (-π/2 to π/2)
atan2(y, x): Returns angle θ of point (x, y) from positive x-axis
Range: -180° to 180° (-π to π)
Conversion: degrees = radians × (180 / π)Example
Calculate atan(1):
tan(45°) = 1, so atan(1) = 45°
In radians: 45° × (π/180) = π/4 = 0.7854 radians
Calculate atan2(-1, -1):
Point (-1, -1) is in the third quadrant
atan2(-1, -1) = -135° = -2.3562 radians
Arctangent Reference Table
| x | atan(x) Degrees | atan(x) Radians |
|---|---|---|
| -∞ | -90° | -π/2 |
| -√3 | -60° | -π/3 |
| -1 | -45° | -π/4 |
| -1/√3 | -30° | -π/6 |
| 0 | 0° | 0 |
| 1/√3 | 30° | π/6 |
| 1 | 45° | π/4 |
| √3 | 60° | π/3 |
| ∞ | 90° | π/2 |
Frequently Asked Questions
What is the difference between atan and atan2?
atan(x) returns angles only in the range -90 to 90 degrees. atan2(y, x) uses both coordinates to determine the correct quadrant, returning angles from -180 to 180 degrees.
When should I use atan2 instead of atan?
Use atan2 when you need to determine the angle of a point in a coordinate system and need the correct quadrant. It is essential in game development, robotics, and navigation.
What is the range of arctangent?
For atan(x), the range is (-90°, 90°) or (-π/2, π/2). For atan2(y, x), the range is (-180°, 180°] or (-π, π].
Is arctan the same as tan⁻¹?
Yes. arctan, atan, tan⁻¹, and inverse tangent all refer to the same function. It finds the angle whose tangent equals the given value.
What is atan(0)?
atan(0) = 0 degrees (0 radians). This is because tan(0°) = 0.