Arctan Calculator (Inverse Tangent)

The arctan function, mathematically written as arctan(x) or tan^-1(x), is the inverse of the standard tangent function. If you have a right triangle where the tangent of an angle Θ is equal to x (opposing side divided by adjacent side), the arctan function takes x and returns the angle Θ: Θ = arctan(x). In two-dimensional coordinate geometry, when utilizing both X and Y inputs, the calculator evaluates the angle of the vector using the four-quadrant arctangent function (atan2), ensuring the output angle accurately reflects the correct quadrant.

Imagine you are building a wheelchair ramp and need to find the angle of elevation. The rise (opposite side) is 3 meters, and the run (adjacent side) is 4 meters. First, calculate the ratio x = Y / X = 3 / 4 = 0.75. Next, apply the inverse tangent formula: Θ = arctan(0.75). Evaluating this yields approximately 0.6435 radians, which converts to approximately 36.87 degrees. Thus, your ramp rises at a safe angle of nearly 36.9 degrees.

Always double-check whether your application requires output in degrees or radians before proceeding with further calculations. When working with coordinates where both X and Y might be negative, ensure your calculator preserves the signs of both inputs to place the resulting angle in the correct quadrant. Remember that the domain of standard arctan is all real numbers, but its range is strictly restricted between -90° and +90° (-π/2 and +π/2 radians).