Calculate the inverse tangent of a number using this calculator. This arctan calculator converts a value to its inverse tangent. Simply enter the number you wish to calculate.
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Arc Tan Formula
The calculator uses one of three formulas depending on the input mode:
From x: θ = arctan(x) From sides: θ = arctan(opposite / adjacent) From x,y: θ = atan2(y, x)
- θ — the resulting angle, returned in both radians and degrees
- x — any real number (the tangent value)
- opposite, adjacent — side lengths of a right triangle relative to θ
- atan2(y, x) — two-argument arctangent that uses the signs of x and y to place the angle in the correct quadrant
Plain arctan only returns angles in (−90°, 90°). If you need the full angle from a coordinate, use the atan2 mode. Convert between radians and degrees with θ° = θrad × 180/π.
Reference Tables
Common arctan values you can use to sanity check a result:
| x | arctan(x) in degrees | arctan(x) in radians |
|---|---|---|
| 0 | 0° | 0 |
| 1/√3 ≈ 0.5774 | 30° | π/6 |
| 1 | 45° | π/4 |
| √3 ≈ 1.7321 | 60° | π/3 |
| 10 | ≈ 84.29° | ≈ 1.4711 |
| → ∞ | 90° | π/2 |
For atan2, the quadrant of (x, y) determines the sign and range of the output:
| Point (x, y) | Quadrant | atan2(y, x) |
|---|---|---|
| x > 0, y > 0 | I | 0° to 90° |
| x < 0, y > 0 | II | 90° to 180° |
| x < 0, y < 0 | III | −180° to −90° |
| x > 0, y < 0 | IV | −90° to 0° |
Example
A ramp rises 3 ft over a horizontal run of 8 ft. What angle does it make with the ground?
- tan θ = opposite / adjacent = 3 / 8 = 0.375
- θ = arctan(0.375) ≈ 0.3587 rad
- θ ≈ 20.56°
FAQ
Why does my calculator show a negative angle? Arctan of a negative number is negative. The function is odd: arctan(−x) = −arctan(x). For a positive angle measured counterclockwise, use atan2 or add 180°/360° as appropriate.
When should I use atan2 instead of arctan? Whenever you have both an x and a y component (vectors, slopes between two points, navigation bearings). Plain arctan(y/x) loses the sign information and collapses quadrants II and IV onto I and III.
What if the adjacent side is zero? The ratio is undefined and the angle is exactly 90°. The "From sides" mode will flag this; switch to atan2 mode and enter x = 0 with your y value.
Radians or degrees? Degrees are standard for geometry and construction. Radians are required for calculus and most programming languages. The result panel shows both.
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