Arctan Calculator — Inverse Tangent
Find the angle whose tangent equals a given value. Enter any real number x and get arctan(x) in both degrees and radians, plus the complementary arccot(x).
Principal value in the range (−90°, 90°)
- 1
Apply inverse tangent
arctan(1) = 0.785398 radReturns the principal value in (−π/2, π/2) radians. - 2
Convert radians to degrees
0.785398 × (180 ÷ π) = 45
这个计算器是如何工作的？
arctan(x) is the inverse tangent: it returns the angle θ in (−90°, 90°) whose tangent equals x. It accepts any real number and is widely used in physics and engineering to convert a ratio (y/x) into a direction angle. The complementary arccot(x) = 90° − arctan(x).
公式
How this is calculated
The arctangent function is the inverse of the tangent function. Unlike arcsin and arccos, arctan accepts any real number as input because the tangent function spans all of ℝ. It returns the unique angle θ in the open interval (−π/2, π/2) — that is (−90°, 90°) — such that tan(θ) = x. As x → +∞ the angle approaches 90°; as x → −∞ it approaches −90°, giving the characteristic S-shaped curve with horizontal asymptotes.
To convert between radians and degrees, multiply radians by 180/π. The arccotangent is the complementary inverse: arccot(x) = 90° − arctan(x) when x > 0. More precisely, for all finite x, arctan(x) + arccot(x) = π/2 radians (90°), analogous to the arcsin/arccos identity.
The calculator uses the built-in Math.atan(), which follows the IEEE 754 standard. The plot shows the arctan curve for x in [−10, 10] — note that the curve flattens sharply toward ±90° as x grows large, which is the hallmark of the arctangent function.
常见问题
The principal value of arctan is the open interval (−90°, 90°) — it never actually reaches ±90°, only approaches them as x → ±∞.
arctan(1) = 45° (π/4 radians), because tan(45°) = 1. Likewise arctan(−1) = −45° and arctan(√3) = 60°.
arctan accepts any real number (not just [−1, 1]), because the tangent function covers all of ℝ. Its output range (−90°, 90°) is open, while arcsin and arccos have closed output ranges.
也称为
TG we-Calculate Editorial Team. (2026). Arctan Calculator — Inverse Tangent [Online calculator]. TG we-Calculate. https://we-calculate.com/zh/calculator/arctan-calculator
TG we-Calculate Editorial Team. "Arctan Calculator — Inverse Tangent." TG we-Calculate. 2026. https://we-calculate.com/zh/calculator/arctan-calculator.
TG we-Calculate Editorial Team, "Arctan Calculator — Inverse Tangent," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/zh/calculator/arctan-calculator
@misc{wecalculate_arctan_calculator, title = {Arctan Calculator — Inverse Tangent}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/zh/calculator/arctan-calculator}}, year = {2026}, note = {TG we-Calculate} }
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