How this calculator works
Tangent is one-to-one between its asymptotes at -90° and 90°. Arctangent uses this interval and accepts any finite real ratio. Larger positive ratios give steeper positive angles, approaching 90° without reaching it. Negative ratios produce negative principal angles. Adding 180° preserves tangent, giving the second solution in a full turn. For a coordinate pair with a negative horizontal component, use atan2 rather than arctan(y/x) to retain the quadrant.
Formula
y=arctan x means tan y=x with -π/2<y<π/2. tan θ=x has θ=y+kπ. The endpoints ±π/2 are limits, not finite-input outputs.
Worked example
arctan(1)=45° and arctan(-1)=-45°. A rise/run ratio of 0 gives 0°. A ratio of √3 gives 60° and has another tangent-equation solution at 240°.
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Frequently asked questions
Can the input exceed one?
Yes. Unlike sine and cosine, tangent is unbounded. For example arctan(√3)=60°.
Does arctan infinity equal 90° here?
Infinity is not a finite input. The limit approaches 90°, but the principal branch excludes that endpoint.
Is arctan(y/x) enough to find a direction?
It loses the signs of x and y separately. Use an atan2-based direction calculation when the quadrant matters.