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Arctan Calculator in Degrees

Reviewed by Calculator Editorial Team

The arctan calculator in degrees helps you find the angle whose tangent is a given number. This is the inverse of the tangent function, also known as the arctangent or atan function. The calculator converts the result to degrees for easier interpretation.

What is Arctan?

The arctangent function, often written as arctan or atan, 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 mathematics, the arctangent function is defined as:

Arctangent Definition

If tan(θ) = y/x, then θ = arctan(y/x)

This function is particularly useful in trigonometry, navigation, physics, and engineering where you need to determine an angle from known side ratios.

How to Use the Arctan Calculator

Using our arctan calculator in degrees is simple:

  1. Enter the value for which you want to find the arctangent in the input field.
  2. Click the "Calculate" button to compute the result.
  3. The calculator will display the angle in degrees.
  4. Review the explanation of the result and any additional information.

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

Arctan Formula

The arctangent function can be calculated using the following formula:

Arctan Formula

θ = arctan(x) = atan(x) in degrees

Where θ is the angle in degrees and x is the input value.

The result is automatically converted to degrees for easier interpretation. The calculator uses the atan2 function in JavaScript to ensure accurate results across all input ranges.

Worked Examples

Let's look at some examples to understand how the arctan calculator works:

Example 1: Basic Arctan Calculation

Find the angle whose tangent is 1.

Using the calculator:

  1. Enter 1 in the input field.
  2. Click "Calculate".
  3. The result will be 45°.

Explanation: tan(45°) = 1, so arctan(1) = 45°.

Example 2: Negative Value

Find the angle whose tangent is -1.

Using the calculator:

  1. Enter -1 in the input field.
  2. Click "Calculate".
  3. The result will be -45°.

Explanation: tan(-45°) = -1, so arctan(-1) = -45°.

Example 3: Large Value

Find the angle whose tangent is 10.

Using the calculator:

  1. Enter 10 in the input field.
  2. Click "Calculate".
  3. The result will be approximately 84.29°.

Explanation: tan(84.29°) ≈ 10, so arctan(10) ≈ 84.29°.

Frequently Asked Questions

What is the range of the arctan function?

The range of the arctan function is from -90° to 90° (or -π/2 to π/2 radians). This means the function will always return an angle within this range.

How does the arctan calculator handle negative values?

The arctan calculator returns negative angles for negative inputs. For example, arctan(-1) = -45°.

What is the difference between arctan and tan?

The tangent function (tan) takes an angle and returns a ratio. The arctangent function (arctan) takes a ratio and returns an angle. They are inverse functions of each other.

When would I use the arctan calculator?

You would use the arctan calculator when you know the ratio of two sides in a right triangle and need to find the angle. This is common in trigonometry, navigation, physics, and engineering problems.