Inverse Tangent Calculator (arctan)

Your details

Direct mode: enter the tangent value directly. Triangle mode: enter two side lengths.
Any real number. The function is defined for all real values.
Choose which unit to highlight. The Show Your Work panel always shows both.
Angle (degrees)
45deg

arctan result in degrees, range -90 to 90

Tangent value used1
sin(arctan(x))0.707107
cos(arctan(x))0.707107
45 deg84.1% below · Angle (degrees)

arctan(1.0000) = 45.0000 degrees

  • arctan(1.0000) = 45.000000 degrees = 0.785398 radians.
  • The angle is exactly 45 degrees, which occurs when the tangent equals 1.
  • Verification: tan(45.0000 deg) equals the original value 1.000000.
  • Using the identity sin(arctan(x)) = x/sqrt(1+x^2): sin of this angle is 0.707107.

Next steparctan always returns an angle in the range -90 to 90 degrees (-pi/2 to pi/2 radians). For angles outside that range, you need atan2 with both opposite and adjacent signs.

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