Inverse Tangent Calculator
Calculate arctan(x) in degrees and radians with principal-angle output. Includes a tangent forward mode to verify your results quickly.
Enter a value and click Calculate to get inverse tangent results.
arctan(x) Formula and Range
Inverse tangent maps a ratio back to an angle. If tan(theta) = x, then theta = arctan(x). The principal angle is in the open interval (-pi/2, pi/2).
Core Identity
theta = arctan(x)
Use this form when you know tangent ratio x and need the corresponding angle.
Principal Angle
-pi/2 < arctan(x) < pi/2
In degrees, that means inverse tangent output is always between -90 deg and 90 deg.
Common Inverse Tangent Values
| x | arctan(x) radians | arctan(x) degrees |
|---|---|---|
| 0 | 0 | 0 |
| 1/sqrt(3) | pi/6 | 30 |
| 1 | pi/4 | 45 |
| sqrt(3) | pi/3 | 60 |
Frequently Asked Questions
What does inverse tangent mean?
Inverse tangent, written as arctan(x) or tan^-1(x), returns the angle whose tangent equals x. Its principal value is always in the range (-pi/2, pi/2), or -90 deg to 90 deg.
What is the difference between tan^-1(x) and 1/tan(x)?
tan^-1(x) means inverse tangent (arctan), which returns an angle. But 1/tan(x) is cotangent and returns a ratio. They are different operations.
Why does arctan only give one angle?
Many angles can share the same tangent value, but inverse tangent returns one principal angle by definition. Additional solutions differ by integer multiples of pi.
How do I convert arctan results from radians to degrees?
Multiply radians by 180/pi. For example, pi/4 radians equals 45 degrees, and arctan(1) returns pi/4 or 45 deg.
Related Calculators
Pythagorean Theorem Calculator
Solve right triangle sides using a² + b² = c².
Rounding Calculator
Round numbers to any place value with explanations.
Significant Figures Calculator
Count sig figs and evaluate math expressions properly.
Circumference Calculator
Calculate circle circumference using radius or diameter.
Share This Calculator
Found this tool helpful?
Help others discover it with one click.
Copy Link
Suggested hashtags: #inverse #tangent #Calculator #FreeTools #AICalculator