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How to use
This calculator uses the ideal projectile model with constant downward acceleration and uniform horizontal motion, allowing initial height and custom g. It uses a cancellation-resistant impact-time formula for downward launches from a height.
- Choose SI or imperial units.
- Enter launch speed, an angle from -90° to 90°, non-negative initial height and positive gravity.
- Calculate velocity components, flight time, range, maximum height, and impact speed and angle.
How it is calculated
Example
Example: 20 m/s at 45° from ground level with g=9.80665 gives about 2.884 s flight time, 40.79 m range and 10.20 m maximum height.
Important notes
The model neglects air resistance, wind, spin, Earth curvature and changing g. It is an educational/idealized physics model, not a ballistic or safety-critical engineering tool.
Worked examples and interpreting results
Launch speed 20 m/s, angle 30°, initial height zero and assumed gravity 10 m/s² give flight time 2 seconds and range about 34.641 metres.
| Case | Calculation | Result |
|---|---|---|
| Flight time | 2 × 20 × sin(30°) ÷ 10 | 2 s |
| Horizontal range | 20 × cos(30°) × 2 | 34.641016 m |
How to check the result
Select SI and gravity 10 to reproduce this example. The model ignores air resistance and assumes constant gravity with landing at reference height zero.
Frequently asked questions
Does 45° always maximize range?
Only in the ideal model when launch and landing heights are equal. A different initial height changes the optimum.
What does a negative angle mean?
The initial vertical component points downward; from zero height, impact is immediate in this model.
Why can real motion differ from this model?
Air resistance, wind, object shape and spin alter flight time, range and impact speed. Differences usually grow for light objects, large frontal areas and high speeds.