About the Projectile Trajectory Calculator
What is the Projectile Trajectory Calculator?
This projectile trajectory calculator traces the full path, not just the end points. It lists the horizontal distance and height at ten equal time steps and draws the curve.
Use it to see how launch angle and speed shape the arc of a ball, javelin or fountain jet.
How to use the Projectile Trajectory Calculator
- Launch Speed (m/s) (sample: 25)
- Launch Angle (°) (sample: 35)
- Launch Height (m) (sample: 1.5)
- Gravity (sample: Earth (9.807 m/s²))
- Press Plot the Trajectory (results also refresh as you type). The result card shows the Horizontal Range, along with Peak height, Time of flight and Angle for maximum range (from ground level).
Formula used
x = v cos θ × t; y = h₀ + v sin θ × t − ½gt²
- h₀ = launch height
- g = gravitational acceleration
The path is a parabola when air resistance is ignored.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Launch Speed (m/s) | 25 |
| Launch Angle (°) | 35 |
| Launch Height (m) | 1.5 |
| Gravity | Earth (9.807 m/s²) |
| Result | Value |
|---|---|
| Horizontal Range | 61.96 m |
| Peak height | 11.98 m |
| Time of flight | 3.03 s |
| Angle for maximum range (from ground level) | 45° |
Tips for using the Projectile Trajectory Calculator
- Lower angles give flatter, faster paths; higher angles give taller, slower arcs.
- For a thrown ball, a launch height of about 1.5–2 m is realistic.