Inverse Tangent (Arctan) Calculator
Calculate the angle (degrees or radians) from a tangent ratio.
What is Inverse Tangent?
The inverse tangent, also known as arctan or tan⁻¹, is the mathematical function that reverses the tangent operation. While the tangent function takes an angle and gives you the ratio of the opposite side to the adjacent side in a right-angled triangle, the arctan function takes that ratio and returns the original angle.
The Arctan Formula
The basic formula for inverse tangent is expressed as:
θ = arctan(opposite / adjacent)
Or simply:
θ = tan⁻¹(x)
Common Arctan Values Table
| Value (x) | Degrees (°) | Radians (rad) |
|---|---|---|
| 0 | 0° | 0 |
| 0.577 | 30° | π/6 |
| 1 | 45° | π/4 |
| 1.732 | 60° | π/3 |
| Infinite | 90° | π/2 |
Practical Examples
Example 1: Roofing Pitch
Suppose a roof rises 5 feet for every 12 feet of horizontal run. To find the angle of the roof slope, you calculate the ratio (5/12 = 0.4167). Using the inverse tangent of 0.4167, the calculator reveals an angle of approximately 22.62°.
Example 2: Physics and Vectors
In physics, if a force is acting with a horizontal component of 10N and a vertical component of 10N, the angle of the resulting vector is arctan(10/10) = arctan(1) = 45°.
How to Use This Calculator
- Enter the decimal value or ratio into the "Input Value" field.
- Click "Calculate Arctan".
- The tool will instantly provide the result in both degrees (common for engineering and construction) and radians (common for advanced mathematics and physics).