Projectile Motion Calculator
Find how far and how high a launched object travels.
Your numbers
Your results
Range (m)
Range (m)
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Maximum height (m)
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Time of flight (s)
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Impact speed (m/s)
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Projectile Motion Calculator by TheCalcTools
How the Projectile Motion Calculator works
Enter the launch speed, angle above horizontal, launch height and gravity.
The speed splits into horizontal and vertical parts.
The vertical motion decides the flight time, and the horizontal speed times that time gives the range.
The formula
t = (v sin θ + √((v sin θ)² + 2gh)) ÷ grange = v cos θ × t
Worked example
Using the default values shown in the calculator:
| Launch speed (m/s) | 20 |
|---|---|
| Launch angle (°) | 45 |
| Launch height (m) | 0 |
| Gravity (m/s²) | 9.80665 |
- Launch at 20 m/s and 45° from the ground.
- Time of flight = 2.884 s.
- Range = 40.79 m and maximum height = 10.20 m.
Result:
| Range (m) | 40.79 |
|---|---|
| Maximum height (m) | 10.20 |
| Time of flight (s) | 2.884 |
| Impact speed (m/s) | 20.00 |
Frequently asked questions
What angle gives the longest range?
45° from level ground. When launching from a height the best angle is a little lower.
Does it include air resistance?
No. Drag shortens range substantially for fast or light objects, so real flights fall short of these values.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.