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Atan Calculator Degrees

Reviewed by Calculator Editorial Team

The ATAN calculator computes the arctangent of a number in degrees. This inverse trigonometric function finds the angle whose tangent is the given value. The calculator provides both the angle in degrees and a visual representation of the tangent relationship.

What is the ATAN function?

The arctangent (ATAN) function, also known as the inverse tangent function, calculates the angle whose tangent is equal to a given number. In other words, if you know the ratio of the opposite side to the adjacent side of a right-angled triangle, ATAN will give you the angle.

Unlike the tangent function, which takes an angle and returns a ratio, the arctangent function takes a ratio and returns an angle. This makes it essential for solving problems involving right triangles and trigonometric relationships.

Note: The ATAN function typically returns values between -90° and 90° (π/2 radians). For values outside this range, you may need to use the ATAN2 function which returns values between -180° and 180°.

How to use the ATAN calculator

Using the ATAN calculator is straightforward:

  1. Enter the tangent value (opposite/adjacent) in the input field.
  2. Click the "Calculate" button to compute the angle in degrees.
  3. View the result, which includes the angle in degrees and a visual representation.
  4. Use the "Reset" button to clear the calculator for new calculations.

The calculator handles both positive and negative values, providing the corresponding angle in the appropriate quadrant.

ATAN formula

The arctangent function is mathematically represented as:

θ = ATAN(x) = arctan(x)

Where:

  • θ is the angle in degrees
  • x is the tangent value (opposite/adjacent)

The formula calculates the angle whose tangent is x. The result is always in the range of -90° to 90°.

Worked examples

Example 1: Basic calculation

If the tangent of an angle is 1, what is the angle in degrees?

Using the ATAN calculator:

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

This makes sense because tan(45°) = 1.

Example 2: Negative value

If the tangent of an angle is -0.5, what is the angle in degrees?

Using the ATAN calculator:

  1. Enter -0.5 in the input field.
  2. Click "Calculate".
  3. The result shows -26.565°.

This indicates the angle is in the fourth quadrant where tangent values are negative.

FAQ

What is the difference between ATAN and ATAN2?

ATAN calculates angles between -90° and 90°, while ATAN2 calculates angles between -180° and 180°. ATAN2 takes both x and y coordinates as inputs, allowing it to determine the correct quadrant for the angle.

Can I use ATAN for angles greater than 90°?

No, ATAN only returns angles between -90° and 90°. For angles outside this range, you should use ATAN2 or adjust your approach to work within the ATAN's range.

What units does the ATAN calculator use?

The ATAN calculator uses degrees for the output angle. The input is a dimensionless tangent value (opposite/adjacent).