Find the angle whose tangent equals a given value — the inverse of the tangent function, commonly written arctan or tan⁻¹.
How it works
For any real number x, arctan(x) returns the angle (in this calculator, in degrees) whose tangent is x. Unlike arcsin and arccos, arctan accepts any real number, not just values between -1 and 1.
What this does not include
This returns only the principal value, between -90° and 90°. Tangent is periodic, so other angles share the same tangent value — this calculator doesn’t list them all.
How to use this calculator
- Enter any real number.
A worked example
arctan(1) = 45°, since tan(45°) = 1.
arctan(0.5) = 26.5651°.
What the variables mean
| Variable | Meaning |
|---|---|
| x | A tangent value, any real number |
| Result | The angle (in degrees) whose tangent equals x |
Edge cases worth knowing
Unlike arcsin and arccos, arctan accepts any real number input — tangent itself is unbounded, so there’s no invalid input range to worry about here, unlike the −1 to 1 restriction on inverse sine and cosine.
arctan always returns a value between −90° and 90° — its defined range — even though tangent repeats infinitely, since arctan picks one consistent angle per input.
Why does arctan accept any number while arcsin and arccos don’t?
Sine and cosine are both limited to values between -1 and 1, so their inverses can only accept inputs in that range — tangent, however, can take on any real value, so its inverse has no such restriction.
What does arctan(1) equal, and why 45°?
Because tan(45°) = 1 exactly — at 45°, the opposite and adjacent sides of a right triangle are equal, so their ratio (the tangent) is 1.
Is arctan used in real-world calculations often?
Yes — finding an angle from a slope (rise over run) is a direct application of arctan, used throughout construction, navigation, and physics.
