Arctangent Calculator Degrees

The arctangent function, also known as the inverse tangent function, calculates the angle whose tangent is a given number. This calculator computes the arctangent in degrees, providing both the principal value and the result in degrees for any real number input.

What is Arctangent?

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

Key properties of the arctangent function:

Domain: All real numbers (-∞, ∞)
Range: (-90°, 90°) in degrees
Principal value: Returns the angle in the range (-90°, 90°)
Periodicity: The function is periodic with a period of 180°

The arctangent function is widely used in trigonometry, navigation, computer graphics, and engineering calculations where angles need to be determined from known ratios.

How to Use the Calculator

Using the arctangent calculator is straightforward:

Enter the value for which you want to calculate the arctangent in the input field.
Select the output unit (degrees is the default).
Click the "Calculate" button to compute the result.
The result will appear in the result panel below the calculator.
Use the "Reset" button to clear the input and result.

Note: The calculator returns the principal value of the arctangent function, which lies between -90° and 90°.

Formula

The arctangent function in degrees is calculated using the following formula:

arctan(x) = atan(x) × (180° / π)

Where:

atan(x) is the arctangent function in radians
180° / π is the conversion factor from radians to degrees

The calculator uses this formula to convert the result from radians to degrees, providing the angle in the more commonly used degree measurement.

Examples

Example 1: Basic Calculation

Calculate the arctangent of 1:

arctan(1) = atan(1) × (180° / π) = 45°

The result is 45 degrees, which matches the known value of arctan(1).

Example 2: Negative Input

Calculate the arctangent of -1:

arctan(-1) = atan(-1) × (180° / π) = -45°

The result is -45 degrees, demonstrating the function's behavior with negative inputs.

Example 3: Large Input

Calculate the arctangent of 10:

arctan(10) ≈ atan(10) × (180° / π) ≈ 84.29°

The result is approximately 84.29 degrees, showing how the function approaches 90° as the input becomes very large.

FAQ

What is the difference between arctangent and tangent?

The tangent function takes an angle and returns a ratio, while the arctangent function takes a ratio and returns an angle. They are inverse functions of each other.

Why does the arctangent function have a range of -90° to 90°?

The arctangent function returns the principal value, which is the angle in the range (-90°, 90°). This is because the tangent function is periodic with a period of 180°, so multiple angles can have the same tangent value.

Can the arctangent function be used to find angles in right triangles?

Yes, the arctangent function is commonly used to find angles in right triangles when the lengths of the opposite and adjacent sides are known. The formula is angle = arctan(opposite/adjacent).