Arctan in Degrees Calculator

The arctangent function (also called inverse tangent) calculates the angle whose tangent is the given ratio. This calculator computes the arctangent in degrees, providing both the principal value and the result in the range of -90° to 90°.

What is Arctan?

The arctangent function, often written as arctan or tan⁻¹, is the inverse of the tangent function. While the tangent function takes an angle and returns a ratio of the opposite side to the adjacent side in a right triangle, the arctangent function takes a ratio and returns the angle.

In practical terms, if you know the ratio of the opposite side to the adjacent side in a right triangle, you can use the arctangent function to find the angle. This is particularly useful in fields like engineering, physics, and navigation where angle calculations are common.

The principal value of arctan(x) is the angle θ in the range of -90° to 90° whose tangent is x. For values outside this range, you may need to adjust the result based on the quadrant of the original triangle.

How to Use the Calculator

Enter the value for which you want to calculate the arctangent.
Click the "Calculate" button to compute the result.
View the result in degrees, which will be displayed in the result box.
Use the "Reset" button to clear the input and result.

The calculator will handle all calculations for you, providing an accurate result in degrees. The formula used is clearly displayed on the page for your reference.

Formula

The arctangent function in degrees can be calculated using the following formula:

arctan(x) = atan(x) * (180/π)

Where:

x is the ratio of the opposite side to the adjacent side in a right triangle.
atan(x) is the arctangent function in radians.
180/π is the conversion factor from radians to degrees.

This formula converts the result from radians to degrees, providing the angle in the more commonly used degree measurement.

Examples

Let's look at a few examples to understand how the arctangent function works.

Example 1: Basic Calculation

If the ratio of the opposite side to the adjacent side is 1, the arctangent is:

arctan(1) = atan(1) * (180/π) ≈ 45°

This makes sense because a right triangle with equal opposite and adjacent sides is a 45-45-90 triangle.

Example 2: Negative Value

If the ratio is -1, the arctangent is:

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

This result is negative because the angle is in the fourth quadrant of the unit circle.

Example 3: Larger Value

If the ratio is 0.5, the arctangent is:

arctan(0.5) = atan(0.5) * (180/π) ≈ 26.565°

This result is approximately 26.565 degrees, which is the angle whose tangent is 0.5.

FAQ

What is the difference between arctan and tan?: The tangent function (tan) takes an angle and returns a ratio, while the arctangent function (arctan) takes a ratio and returns an angle. They are inverse functions of each other.
Why does the calculator show results in degrees?: Degrees are a more commonly used unit of measurement for angles in everyday applications, making the results more intuitive and easier to understand.
What is the range of the arctan function?: The principal value of arctan(x) is in the range of -90° to 90°. For values outside this range, you may need to adjust the result based on the quadrant of the original triangle.
Can I use this calculator for negative values?: Yes, the calculator accepts negative values and will return the corresponding angle in the range of -90° to 90°.
Is the arctan function the same as the inverse tangent function?: Yes, the arctan function and the inverse tangent function are the same. They both refer to the function that returns the angle whose tangent is the given ratio.