Tan-1 Calculator to Degrees

The tan-1 calculator to degrees helps you find the angle whose tangent is a given value, expressed in degrees. This is also known as the inverse tangent or arctangent function. The calculator provides quick results and explains the conversion process.

What is tan-1?

The tan-1 function, also written as arctan, is the inverse of the tangent function. While tan(x) gives you the ratio of the opposite side to the adjacent side of an angle in a right triangle, arctan(x) gives you the angle when you know the ratio.

In trigonometry, the tangent of an angle θ in a right triangle is defined as:

tan(θ) = opposite / adjacent

The inverse tangent function, tan-1(y), returns the angle θ whose tangent is y:

θ = tan-1(y)

This calculator converts the result to degrees, which is the most commonly used angle measurement in everyday applications.

How to use this calculator

Enter the value for which you want to find the inverse tangent in the input field.
Click the "Calculate" button to get the result in degrees.
Review the detailed explanation of the calculation.
Use the "Reset" button to clear the calculator for a new calculation.

Note: The calculator automatically converts the result to degrees. If you need radians, you can use our tan-1 to radians calculator.

Formula

The inverse tangent function is calculated using the following formula:

θ = arctan(y) = tan-1(y) (in radians)

θ (in degrees) = (arctan(y) × 180) / π

Where:

θ is the angle in degrees
y is the value for which you want to find the inverse tangent
π (pi) is approximately 3.14159265359

The calculator uses this formula to provide accurate results in degrees.

Example calculation

Let's find the angle whose tangent is 0.5:

Enter 0.5 in the calculator input field.
Click "Calculate".
The calculator will display the result: approximately 26.565 degrees.

This means that tan(26.565°) ≈ 0.5.

Remember that the range of the arctan function is -90° to +90°, so the calculator will always return a value within this range.

FAQ

What is the difference between tan and tan-1?: The tan function takes an angle and returns a ratio, while the tan-1 (arctan) function takes a ratio and returns an angle.
Why does the calculator return degrees instead of radians?: Degrees are more commonly used in everyday applications and are easier to understand for most users.
What happens if I enter a very large number?: The calculator will still return a valid angle between -90° and +90° because the arctan function has a limited range.
Can I use this calculator for complex numbers?: No, this calculator works only with real numbers. For complex number calculations, you would need a more advanced tool.
Is the result always accurate?: The calculator uses JavaScript's built-in Math.atan() function, which provides accurate results for most practical purposes.