arctangent calculator

What this arctangent calculator does

This calculator finds the inverse tangent of a real number. In plain language, you provide a ratio (the tangent value), and it returns the corresponding angle. Results are displayed in both radians and degrees, along with a quick check that applies tan(θ) back to the answer.

Why arctangent matters

Arctangent appears whenever you need to recover an angle from slope-like information. It is common in geometry, navigation, engineering, robotics, computer graphics, and signal processing.

• Right-triangle trig: find angle from opposite/adjacent ratio.
• Coordinate geometry: convert slope to orientation angle.
• Physics: resolve vector direction from components.
• Programming: rotate sprites, aim projectiles, or compute heading.

How to use it

Step 1: Enter x

Type any real number into the input box. Example values include 0, 1, -1, 0.5, or 10.

Step 2: Set precision

Choose how many decimal places you want (from 0 to 12). Higher precision is useful for technical work, while lower precision is easier to read.

Step 3: Calculate

Click Calculate Arctangent. You’ll get:

• The angle in radians,
• The angle in degrees,
• A tangent check to confirm the result.

Key properties of arctangent

Principal value range

The function arctan(x) returns only one main angle for each real input: -π/2 < θ < π/2.

Odd symmetry

arctan(-x) = -arctan(x). Negative input produces a negative angle of equal magnitude.

Large input behavior

As x → +∞, arctan(x) → π/2. As x → -∞, arctan(x) → -π/2. So the output gets close to ±90° but never reaches it.

Common benchmark values

• arctan(0) = 0
• arctan(1) = π/4 = 45°
• arctan(-1) = -π/4 = -45°
• arctan(1/√3) = π/6 = 30°
• arctan(√3) = π/3 = 60°

Tips and pitfalls

• Don’t confuse arctan(x) with 1/tan(x). They are different operations.
• Keep track of degree vs radian mode in your workflow.
• For full directional angle from (x, y) components, use atan2(y, x) in code.

FAQ

Can I enter fractions directly?

This calculator expects numeric decimal input. For fractions, convert first (for example, 1/2 = 0.5).

What if I need quadrant-aware angles?

Use a two-input calculator based on atan2. Arctangent of a single value can’t distinguish all quadrants.

Is this calculator accurate?

It uses JavaScript’s native Math.atan(), which is precise for normal educational and engineering use.