gives the arc tangent of the complex number .

ArcTan[x, y]
gives the arc tangent of , taking into account which quadrant the point is in.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • All results are given in radians.
  • For real , the results are always in the range to .
  • For certain special arguments, ArcTan automatically evaluates to exact values.
  • ArcTan can be evaluated to arbitrary numerical precision.
  • ArcTan automatically threads over lists.
  • ArcTan[z] has branch cut discontinuities in the complex plane running from to and to .
  • If or is complex, then ArcTan[x, y] gives . When , ArcTan[x, y] gives the number such that and .
New in 1
New to Mathematica? Find your learning path »
Have a question? Ask support »