Tan-1 Calculator in Degrees

The tan-1 calculator computes the arctangent of a number in degrees. This inverse trigonometric function finds the angle whose tangent is the given value. The calculator handles both positive and negative inputs and provides the result in degrees.

What is tan-1?

The tan-1 function, also known as arctangent, is the inverse of the tangent function. While tan(x) gives the ratio of the opposite side to the adjacent side in a right-angled triangle, tan-1(y) finds the angle x that satisfies tan(x) = y.

Key properties of tan-1:

Range: -90° to 90° (or -π/2 to π/2 in radians)
Domain: All real numbers
Odd function: tan-1(-x) = -tan-1(x)

Note

The tan-1 function is not the same as the cotangent function (tan-1 is the inverse tangent, while cot is the reciprocal of tan).

How to use this calculator

Enter the value for which you want to calculate the arctangent
Click "Calculate" to compute the result
View the result in degrees
Use the "Reset" button to clear the form

The calculator handles both positive and negative values, returning results in the range -90° to 90°.

Formula

Mathematical Formula

tan-1(y) = x where tan(x) = y and -90° ≤ x ≤ 90°

The calculator uses the built-in JavaScript Math.atan() function, which returns values in radians, then converts them to degrees by multiplying by 180/π.

Example Calculation

Let's calculate tan-1(1):

tan(45°) = 1
Therefore, tan-1(1) = 45°

This matches the calculator's result when you enter 1.

Interpreting the Result

The result represents the angle in degrees whose tangent equals your input value. For example:

tan-1(0.5) ≈ 26.565°
tan-1(-0.5) ≈ -26.565°
tan-1(1) = 45°

Negative inputs return negative angles, while positive inputs return positive angles.

FAQ

What is the difference between tan-1 and tan?: tan(x) gives the ratio of opposite/adjacent sides for angle x, while tan-1(y) finds the angle x where tan(x) = y.
What are the units of the result?: The result is always in degrees, as specified in the calculator.
What happens if I enter a very large number?: The calculator will return a value approaching 90° (for positive inputs) or -90° (for negative inputs).
Is tan-1 the same as cot-1?: No, cot-1 is the inverse cotangent function, which is different from tan-1.
Can I use this calculator for angles outside -90° to 90°?: No, the tan-1 function is only defined for angles in this range. For other angles, you would need to use the atan2 function.