Compute the trajectory of a projectile launched at a given speed and angle from a given height. Get range, max height (apogee), time of flight, impact velocity, and impact angle — for Earth, Moon, Mars, Jupiter, the Sun, or any custom gravity. See the parabola plotted in real time, scrub time-step values, and read the kinematic equations behind every number. 100% client-side, drag-free ideal projectile physics (no air resistance).
m/s
degrees from horizontal
m above ground
m/s²
Path shown to scale. The orange marker is the apogee, the arrowhead is the impact point. Adjust angle / speed / gravity above to see the parabola morph in real time.
10 evenly spaced samples between launch (t=0) and impact, showing position and velocity components.
| t (s) | x (m) | y (m) | vx (m/s) | vy (m/s) | |v| (m/s) |
|---|
Position: x(t) = v₀ cos θ · t · y(t) = h₀ + v₀ sin θ · t − ½ g t²
Velocity: vₓ = v₀ cos θ (constant) · vᵧ(t) = v₀ sin θ − g t
Time of flight (impact on y = 0): tf = (v₀ sin θ + √((v₀ sin θ)² + 2 g h₀)) / g
Range: R = vₓ · tf. When h₀ = 0 this reduces to R = v₀² sin(2θ) / g, peaking at θ = 45°.
Max height: hmax = h₀ + (v₀ sin θ)² / (2 g), reached at t = v₀ sin θ / g.
Impact speed: |vimp| = √(v₀² + 2 g h₀). Impact angle: arctan(vᵧimp / vₓ).
Real-world projectiles experience air drag, Magnus force, and Coriolis effects — this tool models the textbook parabola, not a ballistic-grade prediction.