Arctan calculator
Enter any number and get the angle whose tangent it is, in degrees or radians. For example tan⁻¹(1) = 45°.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
What does arctan do?
Arctan (tan⁻¹ or atan) gives the angle that belongs to a tangent. Unlike arcsin and arccos, it works for every number, because a tangent can be any value. The principal value lies between −90° and 90°.
Finding a slope angle
The tangent of a slope angle is rise ÷ run. A road that climbs 12 m over 100 m has a gradient of 0.12, and arctan(0.12) ≈ 6.8°. For a triangle with two known sides, the right triangle calculator also gives the other angle and the hypotenuse.
Examples
| Input | arctan in degrees |
|---|---|
| −1 | −45° |
| 0 | 0° |
| 0.5774 | 30° |
| 1 | 45° |
| 1.7321 | 60° |
| 1000 | 89.94° |
From coordinates to an angle
The point (3, 4) lies at an angle of arctan(4 ÷ 3) ≈ 53.13° above the x-axis. This works for points in the right half of the plane. For points on the left, add 180°, or let the Cartesian to polar converter take care of it.
Gradients and angles
Road signs, wheelchair ramps and roofs use a percentage, a ratio or an angle. They are connected by the arctan: a 1:12 ramp has a gradient of 8.33% and an angle of arctan(1/12) ≈ 4.76°. To go the other way, from an angle to the gradient, use the tangent calculator.
Frequently asked questions
Why does arctan never reach 90°?
The tangent grows without limit as the angle approaches 90°, so arctan approaches 90° for huge inputs without reaching it. arctan(1000) is about 89.94°.
How do I turn a percentage gradient into an angle?
Divide by 100 and take the arctan. An 8% gradient is arctan(0.08) ≈ 4.57°.
Why is the angle of a point in the second quadrant wrong?
Arctan only returns −90° to 90°, so it cannot tell (−3, 4) from (3, −4). The [Cartesian to polar converter](/en/math/cartesian-to-polar) uses both coordinates and gives the right quadrant.
What is the difference between arctan and tan⁻¹?
None. Arctan, atan and tan⁻¹ are three names for the inverse tangent. It is not 1/tan, which is the cotangent.