Calculator Inputs
Example Data Table
| Mode | Inputs | Angle (Radians) | Angle (Degrees) | Interpretation |
|---|---|---|---|---|
| atan | x = 0.577350 | 0.523599 | 30.000000° | Positive ratio with a classic 30° result. |
| atan | x = 1 | 0.785398 | 45.000000° | Equal rise and run produce a 45° angle. |
| atan | x = -1.732051 | -1.047198 | -60.000000° | Negative ratio returns a negative principal angle. |
| atan2 | y = 4, x = 3 | 0.927295 | 53.130102° | Vector lies in Quadrant I. |
| atan2 | y = 5, x = -5 | 2.356194 | 135.000000° | Vector lies in Quadrant II. |
Formula Used
Standard inverse tangent
θ = atan(x)
Use this when you already know the tangent ratio, where x = opposite / adjacent.
Directional inverse tangent
θ = atan2(y, x)
Use this when you have vector components. It preserves the correct quadrant or axis direction.
Unit conversions
Degrees = Radians × 180 / π
Grads = Degrees × 10 / 9
Turns = Radians / (2π)
The calculator also verifies the tangent value, estimates slope percentage, and shows a reference angle for better mathematical interpretation.
How to Use This Calculator
- Choose atan(x) when you know the tangent ratio directly.
- Choose atan2(y, x) when you know vector components and need the correct quadrant.
- Enter the value or components, then select the unit you want highlighted.
- Set the number of decimal places for the final display.
- Keep extended metrics enabled if you want slope, π multiple, DMS, and verification details.
- Press Calculate Arc Tangent to show the result above the form, then download CSV or PDF if needed.
FAQs
1. What does arc tangent return?
Arc tangent returns the angle whose tangent equals the entered ratio. This calculator shows that angle in radians, degrees, grads, and turns.
2. When should I use atan2 instead of atan?
Use atan2 when you know both Y and X components. It correctly identifies the quadrant, while atan alone only uses a single ratio.
3. Why are radians and degrees both shown?
Radians are standard in higher mathematics and programming. Degrees are easier for everyday interpretation. Showing both helps with study, checking, and conversion.
4. Can the calculator handle negative inputs?
Yes. Negative ratios produce negative principal angles in atan mode. Negative vector components also work in atan2 mode and affect quadrant placement.
5. Why is atan2(0, 0) not allowed?
A zero vector has no direction, so its angle is undefined. The calculator blocks that case to avoid misleading output.
6. Does arc tangent accept any real input?
Yes for atan. Any real number is valid. For atan2, almost any component pair works except the origin where both values are zero.
7. What does slope percentage mean here?
Slope percentage is the ratio multiplied by 100. For example, a ratio of 0.5 means a 50% slope relative to the horizontal.
8. Why download CSV or PDF results?
Exports are useful for homework records, engineering notes, audit trails, or sharing calculations with classmates, teachers, or coworkers.