arc tangent calculator

How to use this arc tangent calculator

This calculator is designed for quick and accurate inverse tangent calculations. Just enter a value for x, choose whether you want the primary output in radians or degrees, and click Calculate arctan. The tool also shows both units automatically, so you can compare results instantly.

• Step 1: Enter any real number for x.
• Step 2: Choose your preferred unit for the main answer.
• Step 3: Set decimal precision (0 to 15 places).
• Step 4: Click calculate to view the angle and interpretation.

What is arc tangent?

Arc tangent (written as arctan(x) or tan-1(x)) is the inverse of the tangent function. It answers the question: “What angle has tangent equal to x?”

Mathematically:

If tan(θ) = x, then θ = arctan(x).

Unlike tangent, which repeats every 180°, arctan returns a principal angle in a restricted interval so the output is unique.

Output range of arctan

For real input values, arctan returns angles in the range:

-π/2 < θ < π/2 (or -90° to 90°, not including endpoints).

Radians vs degrees

Both units describe the same angle, just in different scales:

• Radians: preferred in calculus, physics, and programming.
• Degrees: common in geometry and practical measurement.

Conversion formulas:

• degrees = radians × 180 / π
• radians = degrees × π / 180

Example arc tangent calculations

Example 1: arctan(1)

If x = 1, then the angle is π/4 radians or 45°.

Example 2: arctan(0.577)

This is close to tan(30°), so the angle is approximately 30° (about 0.5236 rad).

Example 3: arctan(-2)

A negative tangent ratio gives a negative principal angle. Here the result is approximately -63.4349°.

When to use arctan vs atan2

The basic arctan function takes one value (a ratio) and returns an angle in Quadrant I or IV. If you are working with separate coordinates or vector components, use atan2(y, x) instead. It correctly identifies the quadrant and returns angles across a wider range.

• Use arctan(x) when you already have a ratio.
• Use atan2(y, x) when you have numerator and denominator (or y and x coordinates).

Common mistakes to avoid

• Confusing tan-1(x) with 1/tan(x).
• Mixing degree-based and radian-based calculations.
• Expecting arctan to return 120° or 150° directly (principal range is limited).
• Rounding too early during multi-step trigonometry problems.

Real-world applications

Arc tangent appears in many practical fields:

• Finding slope angle from rise/run in construction and civil engineering.
• Determining heading and orientation in robotics and navigation.
• Signal phase analysis in electronics and communications.
• Computer graphics, game physics, and motion tracking.

Quick FAQ

Can arctan output be undefined?

For any real number input, arctan is defined. Every real x has a valid arctan value.

Can arctan ever equal exactly 90°?

No. As x grows very large, arctan gets closer and closer to 90° but never reaches it.

Is this calculator accurate?

Yes. It uses JavaScript's built-in Math.atan(), which is precise for typical educational, engineering, and programming use cases.