How to Use Projectile Motion Calculator
The Projectile Motion Calculator helps you analyse any launch scenario in seconds.
- Initial Velocity — Enter v₀ and choose the unit: m/s, km/h, or ft/s. The Projectile Motion Calculator converts to SI internally.
- Launch Angle — Type the angle in degrees (0–90°). Use 45° for maximum range on flat ground.
- Initial Height — Set the height above the landing surface (default 0 m). A non-zero value extends flight time.
- Gravity — The Projectile Motion Calculator defaults to 9.80665 m/s², but you can override it for other planets or custom scenarios.
- Query Time — Optionally enter a time t ≤ T to see the exact x, y position and velocity components at that instant.
The Projectile Motion Calculator updates all results in real time as you type.
Formula & Theory — Projectile Motion Calculator
The Projectile Motion Calculator decomposes motion into independent horizontal and vertical components.
x(t) = v₀·cos(θ)·t
y(t) = h₀ + v₀·sin(θ)·t − ½·g·t²
T = [v₀·sin(θ) + √(v₀²·sin²(θ) + 2·g·h₀)] / g
H = h₀ + v₀²·sin²(θ) / (2g)
R = v₀·cos(θ)·T
| Symbol | Meaning |
|---|---|
| v₀ | Initial speed (m/s) |
| θ | Launch angle (degrees) |
| h₀ | Initial height (m) |
| g | Gravitational acceleration (m/s²) |
| T | Total flight time (s) |
| H | Maximum height (m) |
| R | Horizontal range (m) |
The Projectile Motion Calculator assumes no air resistance, a flat surface, and constant gravity — the standard assumptions of introductory physics.
Air Resistance
Real-world trajectories differ from the idealised model because of drag forces. The Projectile Motion Calculator provides the theoretical baseline; for engineering applications with significant drag, computational fluid dynamics tools are more appropriate.
Use Cases for Projectile Motion Calculator
The Projectile Motion Calculator is useful across many fields:
- Physics education — Verify textbook problems and build intuition for how angle, speed, and gravity interact.
- Sports science — Estimate the optimal launch angle for throwing events such as shot put, javelin, or basketball free throws.
- Engineering estimation — Quickly size water-jet paths, ballistic trajectories, or fireworks burst positions.
- Game development — Calculate realistic parabolic arcs for character jumps and projectile weapons.
- Astronomy — Substitute g with the surface gravity of other planets (e.g., 3.72 m/s² for Mars) to compare flight behaviour using the Projectile Motion Calculator.