Arcus Tangent Calculator

The arcus tangent function, often denoted as arctan(x) or $\tan^{-1}(x)$, is the inverse of the standard tangent trigonometric function. If you have a number $x$ representing the ratio of the opposite side to the adjacent side in a right triangle, the arcus tangent calculates the corresponding angle $y$ in radians. The core equation is expressed as $y = \text{atan}(x)$. To convert this output into a more intuitive format, the calculator multiplies the radian value by 180 and divides by pi, yielding the final measurement in degrees: $\text{angleInDegrees} = y \times 180 / \pi$.

Let us walk through a practical scenario to see how the formula operates. Suppose you want to find the arcus tangent of an input value $x = 1$. First, apply the core inverse tangent function: $y = \text{atan}(1)$. In mathematical terms, we are asking what angle has a tangent of 1. That angle in radians is $\pi / 4$, or approximately 0.7854. Next, to convert this radian measure into degrees, apply the conversion formula: $0.7854 \times 180 / \pi = 45$ degrees. Thus, an input of 1 yields an angle of exactly 45 degrees.

When working with inverse trigonometric functions, always verify whether your calculator or software expects input in degrees or radians to avoid scaling errors. Remember that the standard arctan function has a range limited to between -90 and 90 degrees (or $-\pi/2$ and $\pi/2$ radians). If you need to calculate angles across all four quadrants based on separate $X$ and $Y$ coordinates, consider using the two-argument arctan function (often written as atan2) to retain proper directional orientation.