Arcus Tangent Calculator — arctan(x)
Find the arctangent (arctan) of any real number. Enter x and instantly get the angle whose tangent equals x, expressed in radians, degrees and gradians, with the arctan curve plotted so you can see where your value falls.
Angle whose tangent equals x — range (−π/2, π/2)
- 1
Degrees
arctan(1) × 180 ÷ π = 45Multiply the radian result by 180/π to convert to degrees. - 2
Gradians
arctan(1) × 200 ÷ π = 50 - 3
Arctangent in radians
arctan(1) = 0.785398
How does this calculator work?
arctan(x) is the angle θ in radians — always between −π/2 and π/2 — such that tan(θ) = x. Any finite real number is valid input. Convert to degrees by multiplying by 180/π. Widely used for slope angles, polar coordinates and inverse-trig problems.
Formula
How this is calculated
The arctangent is the inverse of the tangent function. Given a ratio x (which equals opposite ÷ adjacent in a right triangle), arctan(x) returns the angle θ such that tan(θ) = x. The result is always in the open interval (−π/2, π/2), i.e. (−90°, 90°), which is the principal value branch that makes arctan a well-defined function for all real inputs.
Unlike sine and cosine, the tangent is defined for all finite real numbers (it blows up only at odd multiples of π/2, which are outside arctan's domain), so arctan accepts any real x without restriction. As x → +∞ the angle approaches π/2 (90°) and as x → −∞ it approaches −π/2 (−90°). This makes arctan useful for converting Cartesian coordinates to polar angles, though for the full (−180°, 180°] range you need atan2(y, x) instead.
A practical example: a road rising 1 metre for every 5 metres of horizontal run has an inclination of arctan(1/5) ≈ 11.3°. Engineers, game developers and signal-processing tools constantly use arctan to recover angles from tangent ratios. The verification row confirms accuracy by checking that tan(arctan(x)) ≈ x.
Frequently asked questions
arctan(x) accepts only a ratio and returns angles in (−90°, 90°). atan2(y, x) takes the y and x components separately and returns angles in the full (−180°, 180°] range, placing the result in the correct quadrant. atan2 is preferred in programming for general angles.
The tangent function repeats every 180°, so its inverse must be restricted to one branch to be single-valued. The standard principal-value branch is the interval (−π/2, π/2) in radians, giving a unique angle for every real input x.
Multiply radians by 180/π ≈ 57.2958. For example arctan(1) = π/4 rad ≈ 0.7854 rad = 45°. The calculator shows all three angle units automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Arcus Tangent Calculator — arctan(x) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/arcus-tangent-calculator
TG we-Calculate Editorial Team. "Arcus Tangent Calculator — arctan(x)." TG we-Calculate. 2026. https://we-calculate.com/calculator/arcus-tangent-calculator.
TG we-Calculate Editorial Team, "Arcus Tangent Calculator — arctan(x)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/arcus-tangent-calculator
@misc{wecalculate_arcus_tangent_calculator, title = {Arcus Tangent Calculator — arctan(x)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/arcus-tangent-calculator}}, year = {2026}, note = {TG we-Calculate} }
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