Calculator Inputs
Trajectory Plot
Example Data Table
| Case | Speed (m/s) | Range (m) | Max Height (m) | Estimated Angle (°) |
|---|---|---|---|---|
| Bridge inspection launcher | 40 | 120 | 18 | 30.32 |
| Test pad projectile | 55 | 210 | 40 | 37.31 |
| Field calibration shot | 48 | 160 | 28 | 34.99 |
| Prototype range study | 62 | 250 | 52 | 39.76 |
Formula Used
The calculator applies standard projectile motion equations with constant gravitational acceleration and no air resistance.
For equal launch and landing heights, the main relation is:
R = (v² × sin(2θ)) / g
Rearranging gives:
θ = 0.5 × asin((R × g) / v²)
When velocity components are known, the angle becomes:
θ = atan(vy / vx)
When range and maximum height are known together:
θ = atan((4H) / R)
Additional values come from:
vx = v × cos(θ)
vy = v × sin(θ)
t = (vy + √(vy² + 2gh₀)) / g
Hmax = h₀ + vy² / (2g)
How to Use This Calculator
Choose the calculation mode that matches your available data.
Enter consistent units for speed, distance, height, and time.
Set gravity if your engineering context uses another value.
Pick low or high angle when speed and range allow two paths.
Submit the form to view angle, range, time, speed, and chart.
Download the result table as CSV or PDF for reports.
Use the example table to compare your values with sample cases.
Frequently Asked Questions
1. What does trajectory angle mean?
Trajectory angle is the launch angle above the horizontal. It controls how steeply the object rises and strongly affects range, time, and maximum height.
2. Why are there sometimes two valid angles?
For the same launch speed and range, one low angle and one high angle can reach the same target distance. Their flight paths differ greatly.
3. Does this calculator include air resistance?
No. It uses ideal projectile equations with constant gravity and no drag. Real-world results may vary when aerodynamic effects are significant.
4. Which units should I use?
Use any consistent unit system. This page is labeled for meters, seconds, and meters per second, so mixed units should be avoided.
5. What is the best mode for engineering work?
Use the mode that matches measured inputs. Component-based mode is useful for simulation outputs, while speed-range mode is useful for planning tests.
6. Why does the calculator show an impossible case?
Some combinations cannot produce a real launch angle. For example, the requested range may be too large for the given launch speed and gravity.
7. Can I use this for nonzero launch height?
Yes, but only in modes that explicitly include height. The speed-range and range-height shortcuts assume equal launch and landing height.
8. What do CSV and PDF downloads contain?
They include the visible result table after calculation. This makes it easier to store, share, or attach computed values in engineering documentation.