Inverse Tangent Calculator
Calculate arctan (tan⁻¹) of any real number — get the result in both degrees and radians.
How it works
- 1Enter any real number — arctan is defined for all real numbers, so there are no restrictions.
- 2The calculator applies arctan and converts the result from radians to degrees with deg = rad × 180 ÷ π.
- 3Results are shown simultaneously in degrees (−90° to 90°) and radians (−π/2 to π/2).
Use cases
- Computing the angle of a slope or gradient when the rise-over-run ratio is known.
- Converting a tangent ratio back to an angle in navigation, physics, and engineering.
- Verifying inverse-trig identities and checking calculator results in coursework.
Frequently asked questions
Why does arctan accept any real number when arcsin and arccos do not?
Tangent produces every real number across its domain, so its inverse maps all of ℝ back to angles. Sine and cosine are bounded in [−1, 1], restricting their inverses.
What is the principal range of arctan?
arctan returns angles in (−90°, 90°), equivalently (−π/2, π/2) radians — the standard branch where the function is continuous and increasing.
How is arctan different from atan2?
arctan takes a single ratio and returns an angle in (−90°, 90°). atan2(y, x) uses the signs of both components to return a full-circle angle in (−180°, 180°].
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