Calculator Form
Choose a physics angle mode, enter known values, and submit to evaluate the angle and related quantities.
Example Data Table
| Mode | Inputs | Key Output | Physics Meaning |
|---|---|---|---|
| Trig evaluation | 45°, degrees | sin(θ)=0.7071, cos(θ)=0.7071 | Useful for wave phase and force resolution. |
| Vector direction | x=3, y=4 | Direction ≈ 53.13° | Finds direction of resultant displacement or force. |
| Slope / incline | Rise=5, Run=12 | Angle ≈ 22.62° | Evaluates ramp or incline orientation. |
| Projectile launch | vx=20, vy=15 | Launch angle ≈ 36.87° | Connects velocity components with launch direction. |
| Refraction | n₁=1.5, n₂=1.0, θ₁=30° | θ₂ ≈ 48.59° | Tracks light bending between media. |
Formula Used
1) Trig evaluation
Convert units with radians = degrees × π / 180 and degrees = radians × 180 / π. Then evaluate sin(θ), cos(θ), tan(θ)=sin(θ)/cos(θ), and reciprocal ratios where defined.
2) Vector direction
Use θ = atan2(y, x) to evaluate direction safely in all quadrants. Magnitude is √(x² + y²). Bearing from north is 450° − θ, then normalized to 0°–360°.
3) Slope angle
Incline angle comes from θ = atan2(rise, run). Percent grade is (rise / run) × 100, when run is not zero.
4) Projectile launch
Launch speed is √(vx² + vy²). Launch angle is θ = atan2(vy, vx). Time to peak is vy / g, and rise to peak is vy² / (2g).
5) Refraction
Snell’s law is n₁ sin(θ₁) = n₂ sin(θ₂). If (n₁ / n₂) sin(θ₁) > 1, refraction is impossible and total internal reflection occurs.
All inverse-angle operations use quadrant-aware forms where needed, which is important in physics graphs and vector-based systems.
How to Use This Calculator
- Select the angle mode that matches your physics problem.
- Enter the known values in the visible input fields.
- Choose the number of decimal places for the output.
- Press Evaluate Angle to show the result above the form.
- Review the summary cards, detailed table, and Plotly graph.
- Use the CSV or PDF buttons to export your result.
FAQs
1) What does this evaluating angles calculator cover?
It handles angle evaluation for trigonometric ratios, vector direction, incline geometry, projectile launch direction, and optical refraction in one page.
2) Why is atan2 used instead of plain arctan?
atan2 reads both x and y signs, so it returns the correct quadrant. That makes vector and motion angles much safer to interpret.
3) Why are some trig values marked undefined?
Some ratios require division by zero at special angles. For example, tan(90°) and sec(90°) are undefined because cos(90°)=0.
4) What is a reference angle?
A reference angle is the smallest positive angle between the terminal side and the x-axis. It helps compare equivalent trig patterns across quadrants.
5) How is bearing different from direction angle?
Direction angle is measured from the positive x-axis. Bearing is measured clockwise from north, which is common in navigation and field measurements.
6) Can this calculator detect total internal reflection?
Yes. When Snell’s law predicts no real refracted angle, the tool reports total internal reflection and shows the reflection case instead.
7) Why is the projectile graph shown as a vector?
The angle comes directly from launch velocity components. Showing the vector makes the angle source clear before any full trajectory analysis is added.
8) When should I use degrees versus radians?
Degrees are common for classroom geometry and lab setup. Radians are preferred in advanced physics, calculus, oscillations, and many programming workflows.