Math

Direction of the Vector Calculator

Find the direction angle of a 2D vector.

Calculated Output

Direction (°) 53.13

Magnitude 5

Formula: θ = atan2(y, x)

Step-by-Step Breakdown

1. Values used:

2. x component = 3

3. y component = 4

5. Direction = 53.13°

6. Magnitude = 5

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The math behind it

θ = atan2(y, x), reported from 0° to 360° measured counter-clockwise from the positive x-axis.

Vector (3, 4) → direction ≈ 53.13°, magnitude 5.

Why use atan2 instead of atan?

atan2 uses both components to give the correct quadrant for the angle.