Calculate inverse tangent (arctan) of a slope ratio. Maps any real value input to angles.
The Arctan Calculator is an inverse trigonometric tool designed to compute the angle corresponding to a given tangent value. Arctangent (commonly written as arctan or tan⁻¹) is the inverse of the tangent function. Given an input ratio x, it solves for the angle θ such that tan(θ) = x. The resulting angle can be expressed in degrees or radians.
Unlike arcsin and arccos, the domain of the arctangent function is completely unbounded, accepting any real number input from negative infinity to positive infinity. The range of principal values for arctan is restricted to the interval (−90°, 90°) or (−π/2, π/2 radians), representing the angles where the tangent function is defined.
Arctangent is essential in coordinate geometry and navigation for determining the direction (bearing) of a vector from its coordinate components. For example, the angle of a point (x, y) relative to the origin is calculated as arctan(y / x). In computer programming and game development, the function `Math.atan2(y, x)` is used extensively to calculate rotation angles for characters and cameras. The arctan calculator provides instant decimal angle results, assisting in vector resolution and design layouts.
Understanding Inverse Tangent (arctan / tan⁻¹) and the Unit Circle
In geometry, a trigonometric ratio relates the angles of a right triangle to its side lengths. When extended to all real coordinates, we use the **Unit Circle** (a circle with radius r = 1 centered at the origin).
- Sine (sin θ): represents the vertical projection coordinate (y-coordinate) of the intersection point.
- Cosine (cos θ): represents the horizontal projection coordinate (x-coordinate) of the intersection point.
- Tangent (tan θ): represents the ratio of vertical to horizontal change (y/x). Undefined when the cosine is 0 (90° and 270°).
- Pythagorean Identity: For any angle, the relationship sin²(θ) + cos²(θ) = 1 always holds.
Arctan Domain & Range: The domain of arctan is all real numbers (-∞ < x < ∞). Its range is restricted to (-90°, 90°) ([-π/2, π/2] radians), excluding the endpoints where tangent is undefined.
How it Works & Formula
Calculates the inverse tangent, returning the angle whose tangent is the given value.
Practical Examples
arctan(1) = 45°.
Frequently Asked Questions
Is the domain of arctan limited?
No, arctan accepts any real number input from negative infinity to positive infinity.