Arctan Calculator

Enter any real number to find the angle (in degrees or radians) whose tangent equals it.

How to Use the Arctan Calculator

Enter any real number — positive, negative, large, small, it's all valid input here — pick degrees or radians, and the angle appears.

Arctan is the odd one out among these three inverse functions, and it's worth stating plainly: it's the only one with no domain restriction at all. Sine and cosine are both boxed into the −1-to-1 range, which is why arcsin and arccos have to reject out-of-range values. Tangent has no such ceiling — as an angle approaches 90°, the ratio it represents (opposite over adjacent) grows without bound, so tangent's output covers every real number, and there's simply no "impossible input" for arctan to guard against, unlike its two siblings on this site.

if tan(θ) = x, then arctan(x) = θ, where −90° < θ < 90°

Arctan's principal range looks almost identical to arcsin's −90°-to-90° span, but the endpoints themselves work differently: arctan's range excludes both −90° and 90° outright, because tangent itself is undefined at those exact angles (the adjacent side hits zero, and dividing by zero has no answer). Arcsin's range, by contrast, does include its own endpoints — a small difference easy to miss unless it's pointed out directly.

Arctan shows up any time an angle needs to be recovered from a plain ratio rather than from two separate measurements — finding an angle of elevation from an object's height and distance, or the angle a slope makes from its rise-over-run value. This calculator takes that ratio directly; a rise-and-run version of the same idea lives in the site's dedicated Slope Calculator.