Find Central Angle Using Coordinate Point Calculator
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Calculate the angle θ formed at the origin (0,0) by a line segment connecting the origin to a given coordinate point (x,y).
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The horizontal position of the point (positive = right, negative = left).
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The vertical position of the point (positive = up, negative = down).
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I (+,+), II (-,+), III (-,-), IV (+,-)
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Acute angle with x-axis (0° to 90°)
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Angle in standard position (0° to 360°)
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How It Works
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The central angle θ is calculated using the arctangent function (atan2) which correctly handles all four quadrants.
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θ = atan2(y, x)
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The reference angle α is calculated as:
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α = atan(|y / x|)
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The final angle is adjusted based on the quadrant:
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- Quadrant I: θ = α
- Quadrant II: θ = 180° – α
- Quadrant III: θ = 180° + α
- Quadrant IV: θ = 360° – α
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