Tan⁻¹ Calculator — Inverse Tangent
Enter any real number x to find the angle θ such that tan(θ) = x. Get the result in degrees or radians with a right-triangle visualisation showing the geometric meaning.
Output unit
Principal value — the unique angle in (−90°, 90°) whose tangent equals x
- 1
arctan(x) in radians
arctan(1) = 0.7854 - 2
Convert to degrees
0.7854 × 180 ÷ π = 45
How does this calculator work?
tan⁻¹(x) returns the angle θ in (−90°, 90°) whose tangent equals x. Enter any real number — the output is in degrees or radians. Geometrically it is the base angle of a right triangle with opposite = |x| and adjacent = 1. Key values: tan⁻¹(0)=0°, tan⁻¹(1)=45°, tan⁻¹(√3)=60°.
Formula
How this is calculated
The function tan⁻¹(x) — written arctan(x), atan(x), or tan⁻¹(x) — is the inverse of the tangent function. It returns the unique angle θ in the open interval (−90°, 90°) — equivalently (−π/2, π/2) radians — whose tangent equals x. Unlike arcsin and arccos, arctan accepts any real number because the tangent function has range ℝ.
Geometrically, the result is the angle at the base of a right triangle where the ratio of the opposite side to the adjacent side equals x. The diagram normalises this to an adjacent side of length 1, opposite side of length |x|, and a hypotenuse of √(1 + x²). For x = 1 the triangle is a 45-45-90, giving tan⁻¹(1) = 45°.
As x grows large the angle approaches 90° but never reaches it, because the tangent function approaches infinity as the angle approaches 90°. For negative x the result is the negative of tan⁻¹(|x|), reflecting that the angle falls in the fourth quadrant. The computation uses the IEEE 754 Math.atan() function, which is accurate to within one unit in the last place for all finite inputs.
Frequently asked questions
tan⁻¹(x) is the angle whose tangent equals x. It is also written arctan(x) or atan(x). For example tan⁻¹(1) = 45° because tan(45°) = 1. The superscript −1 means "inverse function", not "1/tan(x)" — that would be cotangent.
The principal value lies in the open interval (−90°, 90°). The function never outputs exactly ±90° because that would require x = ±∞. As x → +∞, tan⁻¹(x) → 90°; as x → −∞, tan⁻¹(x) → −90°.
tan⁻¹(√3) = 60° exactly, because tan(60°) = √3. Other exact values: tan⁻¹(0) = 0°, tan⁻¹(1) = 45°, tan⁻¹(1/√3) = 30°.
Also known as
TG we-Calculate Editorial Team. (2026). Tan⁻¹ Calculator — Inverse Tangent [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tan-1-calculator
TG we-Calculate Editorial Team. "Tan⁻¹ Calculator — Inverse Tangent." TG we-Calculate. 2026. https://we-calculate.com/calculator/tan-1-calculator.
TG we-Calculate Editorial Team, "Tan⁻¹ Calculator — Inverse Tangent," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tan-1-calculator
@misc{wecalculate_tan_1_calculator, title = {Tan⁻¹ Calculator — Inverse Tangent}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tan-1-calculator}}, year = {2026}, note = {TG we-Calculate} }
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