ATAN2 Calculator

Enter Calculation

X Coordinate:

Y Coordinate:

Results

Angle (Degrees)

45

X Coordinate	1.0
Y Coordinate	1.0
Angle (Radians)	0.785398
Magnitude	1.4142

What the ATAN2 Calculator Does

This calculator takes a point's X coordinate and Y coordinate and returns the angle of that point measured from the positive x-axis, expressed in both degrees and radians. It also reports the point's magnitude — its straight-line distance from the origin. Unlike a plain arctangent of y/x, the atan2 function uses the signs of both X and Y to place the angle in the correct quadrant, so it works correctly all the way around the full circle.

atan2(Y, X) returns the angle theta from the positive x-axis to the point (X, Y).

How to Use It

• X Coordinate: the horizontal position of your point (can be negative or zero).
• Y Coordinate: the vertical position of your point (can be negative or zero).

Enter both values and the calculator outputs three results: the angle in degrees, the same angle in radians, and the magnitude.

The Formula

The tool computes:

• Angle (radians) = atan2(y, x)
• Angle (degrees) = atan2(y, x) converted with toDegrees
• Magnitude = √(x² + y²)

The atan2 result ranges from −180° to +180° (−π to +π radians). Positive angles are counter-clockwise above the x-axis; negative angles are clockwise below it. The magnitude formula is simply the Pythagorean distance from (0, 0) to (x, y).

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atan2 returns angles from -180 to +180 degrees, with the correct quadrant.

Worked Example

Suppose X = 3 and Y = 4.

• Angle (radians) = atan2(4, 3) ≈ 0.9273
• Angle (degrees) = 0.9273 × (180/π) ≈ 53.13°
• Magnitude = √(3² + 4²) = √25 = 5

So the point (3, 4) sits about 53.13° above the positive x-axis, at a distance of 5 units from the origin.

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Frequently Asked Questions

Why use atan2 instead of atan(y/x)? Plain atan only returns values between −90° and +90° and can't tell the difference between quadrants — for example (1, 1) and (−1, −1) would give the same answer. atan2 uses both signs, so it correctly distinguishes all four quadrants.

What does the calculator return for X = 0? It still works. For (0, 5) you get +90°; for (0, −5) you get −90°. The function handles the vertical case without dividing by zero.

How do I convert a negative angle to 0–360°? If the degree result is negative, add 360. For instance, −90° becomes 270°.

Related calculators

• Arctan Calculator — angle from a tangent value.
• Arcsin (Inverse Sine) Calculator — angle from a sine value.
• Arccos (Inverse Cosine) Calculator — angle from a cosine value.
• Tangent Calculator — tangent of an angle.