Quick answer
Inverse tangent returns the angle whose tangent is x: θ = arctan(x). arctan(1) = 45°, or 0.7854 radians.
Enter a value. The calculator returns the angle in degrees and radians.
Related tools: Tangent Calculator: tan of an angle in degrees or radians. Inverse Sine Calculator: arcsin (inverse trigonometric function) with the result in degrees and radians. Inverse Cosine Calculator: arccos (inverse trigonometric function) with the result in degrees and radians.
How to use the Inverse Tangent Calculator
- Enter value (between -1e+300 and 1e+300).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Value | A number | ≥ -1e+300, ≤ 1e+300 |
Formula and method
Formula
θ = arctan(x)
IEEE-754 double precision; shown to at most 6 decimal places.
Principal value of the inverse function. asin/atan return −90°…90° and acos returns 0°…180°.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Value = 1.
| Result | Value |
|---|---|
| arctan(1) | 45° |
| Radians | 0.785398 |
Example 2
Inputs: Value = 0.
| Result | Value |
|---|---|
| arctan(0) | 0° |
| Radians | 0 |
The first line is the headline result (arctan(1)). Below it the inverse Tangent Calculator lists radians, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Range
arctan accepts any real number and returns an angle strictly between −90° and 90°. Large values approach 90°: arctan(1000) ≈ 89.94°.
Slope to angle
A slope of rise ÷ run converts to an angle by arctan: a 25% grade is arctan(0.25) = 14.04°. For coordinates in all four quadrants, use atan2 on y and x to get the right quadrant.
Slopes and quadrants
arctan(1) = 45°. A road grade of 10% is arctan(0.10) ≈ 5.71°, and arctan(0.5) ≈ 26.57°.
The result is between −90° and 90°. For a point such as (−1, 1), arctan(−1) gives −45° although the true direction is 135°, so use atan2 to keep the quadrant.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Value: entering "abc" shows "Value must be a number." beside that field and no result.
Choosing between the Inverse Tangent Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Tangent Calculator](/math/tangent-calculator/) | angle and unit | tan(45°) |
| [Inverse Sine Calculator](/math/inverse-sine/) | value | arcsin(0.5) |
| [Inverse Cosine Calculator](/math/inverse-cosine-calculator/) | value | arccos(0.5) |
| [Inverse Trigonometry Calculator](/math/inverse-trigonometry-calculator/) | function and value | Angle |
| [Trigonometry Calculator](/math/trigonometry-calculator/) | angle and unit | sin |
Background: trigonometry
In a right triangle, sin θ is the opposite side over the hypotenuse, cos θ the adjacent side over the hypotenuse and tan θ the opposite over the adjacent. Their reciprocals are cosecant, secant and cotangent. At 30° the values are sin = 0.5, cos = 0.866025 and tan = 0.577350.
Check the angle unit before you calculate: degrees convert to radians by multiplying by π/180, so 30° is about 0.5236 rad. Some values are undefined, for example tan 90°, because the cosine is zero there and the ratio would divide by zero.
Assumptions and limitations
- Value must be between -1e+300 and 1e+300
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for value to confirm this.
Frequently asked questions
What is arctan(0)?
arctan(0) = 0°, a horizontal line with no slope.
What is arctan(√3)?
arctan(√3) = 60°, since tan 60° = √3.
Is there a limit on the input?
Practically none: arctan accepts any real number up to about 10³⁰⁰ and always returns an angle below 90°.
What angle does a 10% grade make?
arctan(0.10) ≈ 5.71°.
Why is arctan not enough for coordinates?
It cannot tell which quadrant the point is in. Use atan2(y, x) for the full direction.
What does the Inverse Tangent Calculator calculate?
arctan (inverse trigonometric function) with the result in degrees and radians. It returns arctan(1) and Radians.
What formula does the Inverse Tangent Calculator use?
θ = arctan(x). Principal value of the inverse function.
What do I need to enter in the inverse Tangent Calculator?
You enter Value.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Value must be between -1e+300 and 1e+300.
What is an example of a inverse Tangent result?
With value 1, the arctan(1) is 45°.
Related calculators
- Tangent Calculator — tan of an angle in degrees or radians.
- Inverse Sine Calculator — arcsin (inverse trigonometric function) with the result in degrees and radians.
- Inverse Cosine Calculator — arccos (inverse trigonometric function) with the result in degrees and radians.
- Inverse Trigonometry Calculator — Arcsine, arccosine or arctangent in degrees and radians.
- Trigonometry Calculator — All six trigonometric functions of an angle.
- SOHCAHTOA Calculator — Find the other two sides of a right triangle from one side and an acute angle.
Sources
- Standard trigonometric definitions on the unit circle (NIST DLMF §4.14)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.