Inverse Tangent Calculator

What is an inverse tangent calculator?

The inverse tangent calculator answers a simple question: “Which angle has this tangent?” You give it a tangent value, and it returns the angle that produces it. The operation is called the arctangent, written $\arctan$ or $\tan^{-1}$, and it is the inverse of the ordinary tangent function.

Where the tangent of an angle gives you a ratio, the arctangent reverses the process and recovers the angle. Because the tangent function repeats every 180°, the arctangent returns the principal value — the single angle in the range $-90°$ to $90°$ (exclusive) that matches your input. The result is shown both in degrees and in radians.

How does it work?

The relationship between an angle and its tangent is:

$\tan(\theta) = x$

Solving for the angle gives the inverse:

$\theta = \arctan(x)$

Unlike inverse sine and inverse cosine, the arctangent accepts any real number: the tangent of an angle grows without bound as the angle approaches $90°$, so there is no domain restriction. Very large inputs simply push the result closer and closer to $\pm 90°$ without ever reaching it.

To convert the radian result to degrees, multiply by $\frac{180}{\pi}$:

$\theta_{\text{deg}} = \arctan(x) \times \frac{180}{\pi}$

Worked examples

• Tangent = 1. The angle whose tangent is 1 is $\theta = \arctan(1) = 45°$ (or $0.7854$ radians). This is the classic 45° angle where the opposite and adjacent sides of a right triangle are equal.
• Tangent = 0. $\arctan(0) = 0°$ — a flat, horizontal line has zero slope and therefore zero angle.
• Tangent ≈ 1.7320508. $\arctan(1.7320508) = 60°$, because $\tan(60°) = \sqrt{3} \approx 1.7320508$.
• Tangent = -1. $\arctan(-1) = -45°$. A negative tangent returns a negative angle, reflecting the line below the horizontal.

Practical notes

The arctangent is one of the most widely used inverse trigonometric functions. It appears whenever you need to recover an angle from a slope or a ratio of two lengths — for example, finding the angle of elevation from a horizontal distance and a height, or computing the direction of a vector from its x and y components.

In programming, the two-argument variant atan2(y, x) extends this idea to all four quadrants, returning angles across the full $-180°$ to $180°$ range. This single-argument calculator covers the principal branch, which is what you need for most geometry and slope problems. For the related inverse functions, see the inverse sine calculator, and to go in the opposite direction from an angle to its functions, use the trigonometry calculator.