Last updated: July 31, 2026
Inverse Tangent Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
arctan(x) = tan^-1(x) = Math.atan(x), and degrees = radians × 180/π for any real x.
Where:
- x=Input value(unitless)
- θ=Principal inverse tangent angle(radians or degrees)
- π=Pi constant(unitless)
Worked Examples
Slope of 1
x = 1 produces the well-known 45° angle.
- 1Use x = 1 as the tangent value.
- 2Compute arctan(1) = π/4.
- 3Convert π/4 radians to 45 degrees.
Zero input
A tangent value of 0 maps to the horizontal angle.
- 1Enter x = 0.
- 2Compute arctan(0) = 0.
- 3The degree result remains 0.
Negative slope
Negative tangent values give negative principal angles.
- 1Use x = -1.
- 2Compute arctan(-1) = -π/4.
- 3Convert the radian result to -45 degrees.
Non-finite input check
Infinite values are not accepted as calculator inputs.
- 1A finite real number is required.
- 2Infinity fails the validation step.
- 3The calculator returns an error instead of an angle.
Introduction
The inverse tangent calculator converts any real finite input into its principal angle in radians and degrees. Unlike arcsin and arccos, arctan is defined for every real number, so it is especially convenient for slopes and ratios. The calculator is a quick way to move between tangent values and angles.
What inverse tangent does
Inverse tangent finds the principal angle whose tangent equals the input value.
It reverses the tangent function on a restricted range.
The input is a tangent ratio or slope.
The output is the principal angle.
Every finite real number is allowed.
Results appear in radians and degrees.
It is written as arctan(x) or tan⁻¹(x).
Domain and principal range
Inverse tangent accepts every real number but still returns a bounded principal angle.
All finite real x values are valid.
The principal range is between -90° and 90°.
The endpoints are never reached for finite x.
Large positive x approaches 90°.
Large negative x approaches -90°.
The function stays continuous across all real x.
Radians and degrees
The calculator computes the radian output first and then converts to degrees.
Radians come directly from atan(x).
Degrees use the factor 180/π.
Both units describe the same angle.
Degrees help with intuitive interpretation.
Radians help with calculus and programming.
The display is rounded to six decimals.
Typical inputs
Many users enter slopes, rise-over-run ratios, or tangent values from other steps.
x = 1 gives 45°.
x = 0 gives 0°.
Negative values produce negative angles.
Very large values approach vertical behavior.
Decimals are accepted.
Only finite values are allowed.
How to use the output
The primary degree value is useful for interpretation, while the radian value supports technical work.
Read degrees for geometry and navigation.
Read radians for code and formulas.
Compare the sign with the input sign.
Use the result to recover an angle from a slope.
Check against known special values.
Convert between coordinate interpretations.
Common mistakes
Arctan is straightforward, but a few conceptual errors appear often.
Confusing tan⁻¹(x) with 1/tan(x).
Expecting outputs outside the principal range.
Mixing tangent values with angle values.
Ignoring unit differences.
Entering Infinity instead of a large finite approximation.
Rounding too early in multi-step work.
Applications of inverse tangent
Inverse tangent is widely used whenever a ratio must be interpreted as an angle.
Converting slope to direction angle.
Solving right-triangle problems.
Analyzing vectors and gradients.
Programming geometric logic.
Studying trigonometric graphs.
Checking scientific calculator output.
FAQs
What is the domain of arctan(x)?
The real-valued domain includes every finite real number.
What is the principal range of arctan?
The output lies between -90° and 90°, not including the endpoints for finite inputs.
Why is x = 1 a common example?
Because arctan(1) equals 45°, which is a standard reference angle.
Can the output be negative?
Yes. Negative inputs produce negative principal angles.
Does the calculator show radians and degrees?
Yes. It returns both units for the same principal angle.
Why is Infinity rejected?
The calculator is limited to finite numeric inputs even though arctan approaches a limit as x grows.
What does tan⁻¹(x) mean?
It means inverse tangent, not one divided by tangent.