Inverse Tangent (arctan) Calculator
Find θ = arctan(x) in degrees, radians and DMS from a tangent value or an opposite/adjacent ratio, with exact π forms and both angles from 0° to 360°.
The inverse tangent, written arctan(x) or tan⁻¹(x), answers the question "which angle has this tangent?". You need it whenever you know a slope, a rise-over-run or the two legs of a right triangle and want the angle. Enter a decimal, a ratio such as 3/4, or an exact expression like 1/sqrt(3), and the calculator returns the angle in degrees, radians, degrees-minutes-seconds and, where possible, an exact multiple of π.
How to use this tool
- Type the tangent value. For a right triangle, type opposite/adjacent, for example 3/4.
- Read the principal angle in degrees and radians at the top of the results.
- Use the π form when the answer is a standard angle such as π/6 or π/4.
- Check the table for the two angles between 0° and 360° that share this tangent.
Formula
θ = arctan(x), where tan θ = x and -90° < θ < 90°
x is the tangent (opposite ÷ adjacent in a right triangle). Degrees = radians × 180 / π. Because tangent repeats every 180°, all solutions are θ + k·180° for any whole number k.
Example
A ramp rises 3 m over a horizontal run of 4 m, so tan θ = 3/4 = 0.75. The calculator gives θ = arctan(0.75) ≈ 36.8699°, which is 0.643501 rad or 36° 52′ 11.63″. The other angle in a full turn with the same tangent is 216.8699°, in quadrant III.
Frequently asked questions
What is the range of arctan?
The principal value always lies strictly between -90° and 90° (-π/2 and π/2). That is why arctan cannot tell a point in quadrant II from one in quadrant IV; use the arctan2 (atan2) calculator when you know the signs of both coordinates.
Is tan⁻¹(x) the same as 1/tan(x)?
No. tan⁻¹(x) is the inverse function (an angle). 1/tan(x) is the cotangent, cot(x), which is a ratio.
What is arctan of infinity?
As x grows without limit the angle approaches 90° (π/2). Type inf to see this; type -inf for -90°.
How do I enter exact values?
Use sqrt( ) or √ and pi, for example 1/sqrt(3) gives exactly 30°, and 2-sqrt(3) gives 15° (π/12).
Last updated: 2026-10-30