Calculate the inverse tangent (arctan) of any value. Supports both atan(x) and atan2(y,x) modes for full 360° angle resolution. Returns degrees, radians, quadrant, and related trig values.
The **Arctan Calculator** computes the inverse tangent (tan⁻¹) of any real number, returning the angle whose tangent equals your input. Unlike arcsin and arccos, arctangent accepts all real numbers — its output smoothly sweeps from −90° to 90°. Switch to atan2(y, x) mode to resolve the full 360° angle using the signs of both components, which is essential for navigation, robotics, and game development.
Arctangent is arguably the most commonly used inverse trig function in applied fields. Programmers use it to calculate the angle of a 2D vector (via atan2). Engineers use it to find phase angles in AC circuit analysis. Surveyors use it to convert rise-over-run into slope angles. Physicists apply it in optics, orbital mechanics, and electromagnetic field calculations.
The single-argument form, atan(x), returns the principal value in (−90°, 90°) and cannot distinguish between opposite quadrants — for example, atan(1) = 45° whether the point is (1, 1) or (−1, −1). The two-argument form, atan2(y, x), solves this by considering the signs of both components, giving a unique angle in (−180°, 180°] that covers all four quadrants. This calculator supports both modes and shows the 0–360° positive equivalent for compass-style applications.
Eight presets cover standard values and both modes, visual bars track angle and trig coordinates, and reference tables list common arctan values and the atan2 quadrant convention.
Arctan Calculator (Inverse Tangent) helps you avoid repetitive setup mistakes when solving trigonometric and coordinate-geometry problems. Instead of recalculating conversions, signs, and edge cases by hand, you can test inputs immediately, inspect intermediate values, and confirm final answers before submitting work or using numbers in downstream calculations. It surfaces key outputs like Angle (degrees), Angle (radians), Angle (0–360°) in one pass.
atan(x): θ = tan⁻¹(x), range (−π/2, π/2). atan2(y, x): θ = the angle from the positive x-axis to the point (x, y), range (−π, π]. Conversion: degrees = radians × 180/π.
Result: 45°
Using value=1, unit=degrees, the calculator returns 45°. This example mirrors the calculator's live computation flow and is useful for checking manual steps and unit handling.
This calculator is tailored to arctan calculator (inverse tangent) workflows, including common input modes, unit handling, and special-case behavior. It is designed for fast checking during homework, exam preparation, technical drafting, and coding tasks where trigonometric consistency matters.
Use the primary result together with supporting outputs to verify direction, magnitude, and validity. Cross-check against known identities or geometric constraints, and confirm that angle ranges, sign conventions, and domain restrictions are satisfied before using the numbers elsewhere.
A reliable way to improve is to solve once manually, then verify with the calculator and explain any mismatch. Repeat this on varied examples and edge cases. The built-in preset scenarios for quick trials, comparison tables for side-by-side validation, visual cues that make trends and quadrants easier to read help you build pattern recognition and reduce sign or conversion errors over time.
atan(x) takes a single ratio and returns an angle in (−90°, 90°). atan2(y, x) takes two separate values and returns the full-circle angle in (−180°, 180°], correctly handling all four quadrants.
The tangent function approaches infinity as the angle nears 90°, so its inverse asymptotically approaches 90° but never equals it for any finite input. This provides clearer practical guidance for reliable use.
Yes. Unlike arcsin and arccos, arctan accepts any real number. Its output is always between −90° and 90° (exclusive).
If atan2 returns a negative angle, add 360° to get the positive equivalent. This calculator shows both representations.
Mathematically undefined, but most programming languages return 0 for atan2(0, 0) by convention. This provides clearer practical guidance for reliable use.
If a slope is given as rise/run = m, the angle of inclination is arctan(m). For example, a 1:1 slope is arctan(1) = 45°.