Tangent Input

Arctangent Output

Angle in Degrees
45.0000 °
Angle in Radians
0.7854 rad
Multiples of Pi
0.2500 π
Principal Quadrant
Quadrant I

An Arctan Calculator is an advanced mathematical tool that computes the inverse tangent of a given number. Also known as arctangent or tan−1, this function reverses the standard tangent operation, allowing you to find a specific geometric angle when you already know the ratio of the opposite and adjacent sides of a right triangle.

How the Arctan Function Works

While the regular tangent function takes an angle and gives you a numerical ratio, the arctangent function takes that numerical ratio and gives you back the original angle. This is incredibly useful in engineering, physics, and computer graphics when determining trajectories, slopes, or directional vectors.

Equation: θ = arctan(x)

For example, if the opposite side of a triangle is exactly equal to its adjacent side, their ratio is 1. When you input the value 1 into the arctan function, it returns an angle of 45 degrees (or π / 4 radians), confirming the triangle is a perfect isosceles right triangle.

How to Use This Calculator

  • Enter your known value or ratio into the "Enter Value" input box.
  • You can enter any real number, including positive values, negative values, and decimals ranging from negative infinity to positive infinity.
  • The calculator will instantly determine the exact angle and display it prominently in degrees.
  • You can also view the angle converted into standard radians, its fractional relationship to Pi, and the principal quadrant where the angle naturally resides.

Frequently Asked Questions

What is the difference between tangent and arctangent?

Tangent calculates a ratio based on a known angle. Arctangent calculates the unknown angle based on a known ratio. They are exact mathematical opposites of one another.

What are the limits of the arctan function?

Unlike the arcsine and arccosine functions which restrict inputs to values between −1 and 1, the arctan function can accept absolutely any real number. However, the output angle will always strictly fall between −90 degrees and +90 degrees (or −π/2 and π/2 radians).

What does a negative input mean?

Inputting a negative number indicates that the slope of your line is pointing downward. The calculator will output a negative angle, which mathematically places the result in the fourth quadrant (Quadrant IV) of the standard Cartesian coordinate system.