Inverse Tangent Calculator (arctan)

Find the angle whose tangent equals your input, with quadrant details, degrees and radians.

Enter Values

Result

Angle (degrees)
--
degrees
Angle (radians)
--
radians
Input value--
Quadrant--
Reference angle--
Radians (exact fraction of pi)--
sin of result--
cos of result--
Verification: tan(result)--

Step-by-Step Solution

arctan(x) = theta, where tan(theta) = x

Understanding Inverse Tangent (arctan)

The inverse tangent function, also known as arctan or tan-1, reverses the tangent function. Given a ratio value, it returns the angle whose tangent equals that value. This calculator supports both the standard arctan (single value) and the two-argument atan2(y, x) which accounts for the correct quadrant.

arctan vs atan2

arctan(v)

Standard inverse tangent. Returns angles in (-90 deg, 90 deg). Cannot distinguish between quadrants II/III and I/IV.

Range: (-pi/2, pi/2)

atan2(y, x)

Two-argument form. Returns the full angle in (-180 deg, 180 deg] by considering the signs of both y and x.

Range: (-pi, pi]

Quadrant I

x > 0, y > 0: angle is between 0 and 90 degrees.

0 deg < theta < 90 deg

Quadrant II

x < 0, y > 0: angle is between 90 and 180 degrees.

90 deg < theta < 180 deg

Common Values

  • arctan(0) = 0 degrees
  • arctan(1) = 45 degrees = pi/4 radians
  • arctan(-1) = -45 degrees = -pi/4 radians
  • arctan(sqrt(3)) = 60 degrees = pi/3 radians
  • arctan(1/sqrt(3)) = 30 degrees = pi/6 radians

Applications

The inverse tangent is essential in coordinate conversions (Cartesian to polar), calculating angles in physics (projectile motion, optics), electrical engineering (phase angles), and computer graphics (rotation calculations). The atan2 variant is preferred in programming for its ability to return correct quadrant information.