What the Inverse Tangent Does
The arctan calculator reverses the tangent function: give it any number and it returns the angle whose tangent equals that value. Written as arctan(x), tan⁻¹(x), or atan(x), it turns a ratio back into an angle — the answer always lands in the range (−90°, 90°), or (−π/2, π/2) radians.
tan(θ) = x then arctan(x) = θ, for any real x, with θ ∈ (−90°, 90°).Key Properties
Domain: All Real Numbers
Range (−90°, 90°)
Finding an Angle from a Tangent Value
Enter Any Number
Type any value into the input field — positive, negative, or decimal. There are no domain restrictions for arctangent.
Choose DEG or RAD
Select DEG to see the result in degrees, or RAD for radians.
Read the Angle Instantly
The angle is calculated automatically as you type. The result is shown in the active unit alongside its equivalent in the other unit.
Verify the Result
The calculator confirms the answer with the check tan(result) = input, so you can trust the computed angle.
π or pi (for example π/4) directly in the input box.Arctan Calculator Features
Inverse Tangent of Any Number
Computes arctan for any real input, with no domain limits unlike arcsin and arccos.
Degrees & Radians
Shows the resulting angle in the active unit and its equivalent in the other, with radians formatted as π-fractions.
Output in (−90°, 90°)
Returns the principal angle within the open interval (−90°, 90°).
Built-In Verification
Displays the check tan(result) = input, with real-time calculation as you type.
Common Arctangent Values
| Input | arctan result | Radians |
|---|---|---|
| arctan(0) | 0° | 0 |
| arctan(√3/3) | 30° | π/6 |
| arctan(1) | 45° | π/4 |
| arctan(√3) | 60° | π/3 |
| arctan(∞) | 90° | π/2 |
Frequently Asked Questions
How do I find an angle from a tangent value?
Enter the tangent value into the input box and the calculator returns θ = arctan(x), the angle whose tangent equals that number. Switch DEG or RAD to read the angle in degrees or radians.
Why can arctan accept any number?
Because the tangent function can output any real number (from −∞ to +∞), its inverse can accept any real number as input — there is no domain restriction like the −1 to 1 limit on arcsin and arccos.
What is arctan(1)?
arctan(1) = 45° or π/4 radians, because tan(45°) = 1. Other common values are arctan(√3/3) = 30° and arctan(√3) = 60°.
How do I convert the arctan result from radians to degrees?
Multiply the radian value by 180/π. You don't need to do it by hand — toggle DEG or RAD and the calculator shows both units at once.
What happens as the input approaches infinity?
As input → +∞, arctan → 90°. As input → −∞, arctan → −90°. But the function never actually reaches ±90°, which is why the range is an open interval.
Is tan⁻¹(x) the same as 1/tan(x)?
No. tan⁻¹(x) is the inverse function (arctan), which returns an angle. 1/tan(x) is the cotangent. The superscript −1 here denotes the inverse, not a reciprocal.
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