Arctan Calculator
Find the angle whose tangent is a given value, returned in degrees or radians — the quickest way to turn a slope into an angle.
How to use it
- Enter the tangent value — any real number is valid.
- Choose degrees or radians for the answer.
- For a gradient, enter rise ÷ run to get the slope angle.
Examples
| arctan(1) | 45° |
| arctan(0.5) | 26.565° |
Arctan reverses tangent: given a rise-over-run ratio (or any opposite-over-adjacent ratio), it returns the angle. It's the most commonly reached-for inverse trig function in practice because slope, gradient and bearing problems almost always start with two lengths rather than a hypotenuse.
Worked example — road gradient sign
A road drops 15 m over a horizontal distance of 150 m. The gradient as a percentage is 15 ÷ 150 = 10%, and the actual angle below horizontal is arctan(0.1) ≈ 5.71°. Road signage almost always quotes the percentage rather than the angle, but they describe the same slope — arctan is what converts between them.
Unlike arcsin and arccos, no input limit
Because tangent itself is unbounded, arctan accepts any real number, positive or negative, and always returns an angle strictly between −90° and 90° — it never has an 'invalid input' case the way arcsin and arccos do outside −1 to 1.
Questions people ask
How do I convert a percentage gradient to an angle?
Divide the percentage by 100 and take the arctangent. A 10% gradient is arctan(0.1) = 5.71°.
Is anything sent to a server?
No. Every calculation runs in your browser, so nothing you type is uploaded and the page keeps working offline once it has loaded.
Last updated 17 August 2026