What Is an Arctan Calculator?
An arctan calculator computes the arctangent — the inverse tangent — of a number, returning the angle whose tangent equals that value. Arctan reverses the tangent function: tangent turns an angle into a ratio, and arctan turns a ratio back into an angle. It is widely used in trigonometry, geometry, and physics. Enter a value and the calculator gives the angle in degrees or radians.
How to Use the Calculator
- Enter the value x.
- Choose degrees or radians.
- Calculate — see arctan(x).
What Arctan Means
If tan(θ) = x, then arctan(x) = θ. For example, arctan(1) = 45° because the tangent of 45° is 1. Arctan accepts any real number and returns an angle between −90° and 90°.
Common Arctan Values
| x | arctan(x) |
|---|---|
| 0 | 0° |
| 0.577 | 30° |
| 1 | 45° |
| 1.732 | 60° |
The Principal Range
Because tangent repeats every 180°, arctan returns only the principal value between −90° and 90° (−π/2 to π/2 radians). This makes the inverse well-defined for every input, so each value of x maps to exactly one angle.
Where Arctan Is Used
- Triangles: finding an angle from opposite and adjacent sides.
- Slopes: the angle of a line equals arctan of its slope.
- Coordinates: converting between rectangular and polar forms.
- Engineering: phase angles and directions.
Frequently Asked Questions
What is arctan?
Arctan is the inverse tangent function. It returns the angle whose tangent equals the given value, reversing the tangent operation.
What is arctan of 1?
arctan(1) is 45°, because the tangent of a 45° angle equals 1.
What range does arctan return?
Arctan returns angles between −90° and 90° (−π/2 to π/2 radians), known as its principal value range.
How is arctan used to find an angle?
For a right triangle, the angle equals arctan(opposite ÷ adjacent), and for a line, the incline angle equals arctan(slope).
Is this arctan calculator free?
Yes — it is completely free, requires no signup, and works in degrees and radians.