Tan Inverse Calculator in Degrees

The tan inverse calculator in degrees helps you find the angle whose tangent is a given value. This is also known as the arctangent function. The calculator provides quick and accurate results in degrees, which is useful for trigonometric calculations in geometry, physics, and engineering.

What is Tan Inverse?

The tan inverse function, often written as arctan or tan⁻¹, is the inverse of the tangent function. It takes a ratio (opposite side to adjacent side in a right-angled triangle) and returns the angle whose tangent is that ratio. The result is always between -90° and 90°.

In practical terms, if you know the ratio of two sides of a right triangle, you can use the tan inverse function to find the angle between them. This is particularly useful in fields like navigation, surveying, and engineering where angle calculations are common.

How to Use the Calculator

Enter the value for which you want to calculate the inverse tangent in the input field.
Select the output unit (degrees is the default and recommended for this calculator).
Click the "Calculate" button to get the result.
Review the result and use the "Reset" button to clear the inputs if needed.

Note: The calculator uses the Math.atan() function in JavaScript, which returns values in radians. The result is then converted to degrees for display.

Formula

The formula used in the calculator is:

θ = arctan(x) × (180/π)

Where:

θ is the angle in degrees
x is the input value
π is the mathematical constant pi (approximately 3.14159)

This formula converts the result from radians (the default output of the arctan function) to degrees by multiplying by 180/π.

Examples

Let's look at a few examples to understand how the tan inverse calculator works.

Example 1: Basic Calculation

If you have a right triangle with opposite side = 3 and adjacent side = 4, the ratio is 3/4 = 0.75. Using the calculator:

Enter 0.75 in the input field.
Click "Calculate".
The result will be approximately 36.87°.

This means the angle whose tangent is 0.75 is about 36.87 degrees.

Example 2: Negative Value

If you enter -1, the calculator will return approximately -45°. This makes sense because tan(-45°) = -1.

Example 3: Large Value

For x = 1000, the calculator will return approximately 89.42°. This is because the maximum angle for which tan(θ) is defined is just under 90°.

FAQ

What is the difference between tan and tan inverse?

The tan function takes an angle and returns the ratio of the opposite side to the adjacent side. The tan inverse (arctan) function takes a ratio and returns the angle. They are inverse operations of each other.

Why does the calculator only show results in degrees?

Degrees are the most commonly used unit for angles in everyday applications. Radians are used more in advanced mathematics and physics, but degrees are more intuitive for most users.

What happens if I enter a very large number?

The calculator will return a value close to 90°. This is because the tangent function approaches infinity as the angle approaches 90°, so the inverse function approaches 90° for very large inputs.

Can I use this calculator for negative numbers?

Yes, the calculator accepts negative numbers and returns negative angles. For example, tan⁻¹(-1) = -45°.