What is the range of arctan?

arctan(x) always returns an angle between −90° and +90° (i.e., −π/2 and +π/2 radians). It can never return a value outside that range, regardless of the input.

What is the difference between arctan and atan2?

arctan(x) takes a single ratio and returns an angle in the range (−90°, 90°). atan2(y, x) takes two separate coordinates, checks their signs, and returns an angle in the full range (−180°, 180°), correctly identifying the quadrant.

Why would I use atan2 instead of arctan?

When you have a vector defined by separate x and y components, dividing y/x loses the sign information needed to determine the correct quadrant. atan2(y, x) preserves that information automatically.

arctan(1) = 45° (or π/4 radians), because tan(45°) = 1.

arctan(0) = 0° (or 0 radians), because tan(0°) = 0.

Can arctan handle very large or very small inputs?

Yes. As x approaches positive or negative infinity, arctan(x) approaches ±90° (±π/2). This tool handles any finite real number input.

Arctangent Calculator

Enter a value to instantly compute its arctangent in both degrees and radians, with optional atan2 mode for full quadrant-aware angle calculation.

Mode

Value of x

Any real number — no restrictions.

Quick values

Enter a value to compute arctan

arctan range reference

arctan(x) ∈ (−90°, 90°) atan2(y,x) ∈ (−180°, 180°]

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Summary

The arctangent (arctan or tan⁻¹) is the inverse trigonometric function that returns the angle whose tangent equals a given value. This calculator computes arctan(x) instantly in both degrees and radians. It also supports atan2(y, x), which uses the signs of both coordinates to determine the correct quadrant, making it ideal for vector angle calculations.

How it works

Select "arctan(x)" mode or switch to "atan2(y, x)" mode using the tab buttons.
In arctan mode, type any real number into the input field.
In atan2 mode, enter the Y coordinate and X coordinate separately.
The calculator instantly displays the angle in both degrees and radians.
Copy either result with one click using the copy buttons.

Use cases

Find the angle of a slope or gradient given rise/run ratio.
Convert a tangent value back to an angle in trigonometry problems.
Compute a bearing or heading from 2D vector components using atan2.
Determine phase angles in electrical engineering and signal processing.
Calculate camera or object rotation angles in game development.
Verify scientific calculator results for inverse tangent functions.
Solve navigation problems that require quadrant-correct angles.
Use in physics for decomposing force vectors into angular form.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu

Arctangent Calculator

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