Projectile Range Calculator
How far, how high and for how long a projectile travels, from launch speed and angle.
Results
Range
40.789
m
Maximum height
10.197
m
Time of flight
2.884
s
What this tool does
Forty-five degrees gives the longest range on flat ground, and any two angles that add up to ninety degrees land in the same place. Air resistance is ignored, which is fine for a thrown ball over a short distance and badly wrong for anything fast or light.
Formula
R = v² × sin(2θ) ÷ g , H = v² × sin²θ ÷ (2g)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v | Speed | m/s |
t | Launch angle | ° |
gv | Gravitational acceleration | m/s² |
R | Range | m |
H | Maximum height | m |
T | Time of flight | s |
Worked example
- Speed20 m/s
- Launch angle45 °
- Gravitational acceleration9.80665 m/s²
- Range40.789 m
- Maximum height10.197 m
- Time of flight2.884 s
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.