Arctangent Calculator

About this calculator

The arctangent (inverse tangent, written tan⁻¹ or atan) answers the question: given a ratio, what angle produces it? Unlike arcsine and arccosine, which are restricted to inputs between −1 and 1, arctan accepts any real number, because the tangent function itself ranges over all real values. Its output — the principal value — is always confined to the open interval −90° to 90° (−π/2 to π/2 radians), which means a single arctan result can never distinguish a direction in the second or third quadrant on its own.

Engineers and programmers reach for arctan constantly when converting rectangular coordinates or vector components into an angle — finding the slope angle of a roof or ramp from rise over run, computing the phase angle of an electrical circuit from reactance over resistance, or orienting a robot arm from its x and y displacement. Because plain arctan loses quadrant information, most software libraries pair it with the two-argument atan2(y, x) function to recover the full 0°–360° direction; this calculator returns the standard principal-value result in both degrees and radians.