Inverse Tangent Calculator in Degrees

The inverse tangent function, also known as arctangent, calculates the angle whose tangent is a given number. This calculator provides results in degrees, making it useful for geometry, navigation, and engineering applications.

What is Inverse Tangent?

The inverse tangent function, written as arctan(x) or tan⁻¹(x), is the inverse operation of the tangent function. While the tangent function takes an angle and returns a ratio, the inverse tangent takes a ratio and returns an angle.

Inverse tangent is particularly useful in fields like:

Geometry for calculating angles in right triangles
Navigation for determining bearing angles
Engineering for analyzing slopes and gradients
Computer graphics for 3D transformations

Key Properties

The range of the inverse tangent function is -90° to 90°, meaning it only returns angles in the first and fourth quadrants. For angles outside this range, you may need to use additional trigonometric identities.

How to Use This Calculator

Enter the ratio (opposite/adjacent) in the input field
Click "Calculate" to compute the angle in degrees
Review the result and interpretation
Use the "Reset" button to clear the calculator

The calculator handles both positive and negative values, providing the appropriate angle within the -90° to 90° range.

Formula

Inverse Tangent Formula

θ = arctan(x) × (180/π)

Where:

θ = angle in degrees
x = ratio (opposite/adjacent)
π ≈ 3.141592653589793

The formula converts the result from radians (the native output of most programming languages) to degrees by multiplying by 180/π.

Example Calculation

Let's calculate the angle for a right triangle with opposite side = 4 and adjacent side = 3:

Ratio = opposite/adjacent = 4/3 ≈ 1.333
θ = arctan(1.333) × (180/π) ≈ 53.13°

This means the angle between the hypotenuse and the adjacent side is approximately 53.13 degrees.

FAQ

What is the range of the inverse tangent function?

The inverse tangent function returns values between -90° and 90°, covering the first and fourth quadrants of the unit circle.

How do I calculate angles outside the -90° to 90° range?

For angles outside this range, you can use the atan2 function or add/subtract 180° based on the signs of the x and y coordinates.

What's the difference between arctan and tan⁻¹?

Arctan and tan⁻¹ represent the same mathematical function. The notation depends on the context and the specific mathematical convention being used.