Math July 13, 2026 · 8 Min Read

Arctan Calculator – Guide & Formulas

Calculate arctan (inverse tangent) instantly. Enter a tangent value to find the angle in degrees or radians with step-by-step results.

The Arctan Calculator computes the inverse tangent of any real number. Enter a tangent value and instantly receive the angle in both degrees and radians, along with a step-by-step explanation of how the inverse tangent function works.

Key Takeaway

Use the free Arctan Calculator to calculate arctan (inverse tangent) instantly. enter a tangent value to find the angle in degrees or radians with step-by-step results. Get instant results with step-by-step explanations.

How to Use the Arctan Calculator

  1. Enter any real number as the tangent value in the input field.
  2. The calculator instantly computes the arctan result.
  3. View the angle in both degrees and radians.
  4. Review the step-by-step explanation and formula reference.

The Formula

arctan(x) = θ where tan(θ) = x and -π/2 < θ < π/2 (or -90° < θ < 90°)

Variable Definitions

  • arctan(x): The angle whose tangent is x, also written as tan⁻¹(x)
  • x: The tangent value (input), can be any real number
  • θ: The resulting angle in radians (-π/2 to π/2) or degrees (-90° to 90°)
  • tan(θ): The tangent function: opposite/adjacent in a right triangle

Example: Arctan(1)

Find the angle whose tangent is 1.

  1. Step 1: We need to find θ such that tan(θ) = 1.
  2. Step 2: From the unit circle or tangent table, tan(45°) = tan(π/4) = 1.
  3. Step 3: Therefore arctan(1) = 45° or π/4 radians ≈ 0.7854 radians.
  4. Step 4: Verify: tan(45°) = 1 ✓

Frequently Asked Questions

What is arctan?

Arctan (inverse tangent) is the function that takes a tangent value and returns the angle whose tangent is that value. It is written as arctan(x) or tan⁻¹(x) and produces angles between -90° and 90° (exclusive).

What is the domain and range of arctan?

The domain of arctan is all real numbers (-∞, +∞). The range is (-π/2, π/2) in radians or (-90°, 90°) in degrees. The endpoints are excluded because tan(±90°) is undefined.

How is arctan different from 1/tan?

Arctan (tan⁻¹) is the inverse function that returns an angle, while 1/tan is the cotangent function (cot) which returns a ratio. They are completely different operations.

What is arctan(0)?

arctan(0) = 0 radians = 0°. This is because tan(0°) = 0. The angle whose tangent is 0 is zero radians.

What is arctan(1)?

arctan(1) = π/4 radians = 45°. This is because tan(45°) = 1. This is one of the most commonly used arctan values.

What is arctan(∞)?

arctan(∞) approaches π/2 radians = 90°. As the tangent value increases without bound, the angle approaches but never reaches 90°.

Can arctan handle negative inputs?

Yes. Arctan accepts any real number including negative values. For example, arctan(-1) = -45°. The function is odd: arctan(-x) = -arctan(x).

What are common arctan values?

Common values: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°, arctan(1/√3) = 30°, arctan(-1) = -45°, arctan(∞) → 90°.

How do I convert arctan result from radians to degrees?

Multiply the radian result by 180/π to convert to degrees. For example, arctan(1) = π/4 radians × (180/π) = 45°.

What is the atan2 function?

atan2(y, x) is a two-argument variant of arctan that handles all four quadrants. It returns the angle of the point (x, y) from the positive x-axis, ranging from -π to π. It is commonly used in programming and physics.