Arcus Tangent Calculator (arctan)
The Arcus Tangent Calculator (arctan, the Latin name for inverse tangent) finds the angle whose tangent equals a given value, in radians and degrees. The formula used is: arctan(x) = the angle whose tangent is x, in the range (-90°, 90°).
Formula
arctan(x) = inverse tangent
- The Arcus Tangent Calculator updates instantly as you change the input value.
- Formula: arctan(x) = the angle whose tangent is x
- Input definitions: • Value: any real number; tangent is defined for all of them
- 'Arcus tangent' is simply the traditional name for the inverse tangent (arctan).
- The result is the principal value, an angle from -90° to 90° (exclusive).
- Radians are converted to degrees by multiplying by 180/π.
Example Calculation
Inputs
- Value: 1
arctan(1) = π/4 ≈ 0.7854 radians, which equals 45°, because tan(45°) = 1.
Frequently asked questions
What is arcus tangent?
It is the traditional name for the inverse tangent (arctan) — the angle whose tangent equals the value you enter.
What input range is allowed?
Any real number. Tangent is defined for all values, so there is no restriction on the input.
What is the output range?
The principal value runs from -90° to 90° (-π/2 to π/2 radians), not including the endpoints.
How do I convert the answer to degrees?
Multiply the radian result by 180/π. This calculator shows both radians and degrees.
Why does arctan(1) equal 45°?
Because tan(45°) = 1, so the angle whose tangent is 1 is 45°.