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Projectile Motion Calculator

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).

1. Inputs

m/s

degrees from horizontal

m above ground

m/s²

2. Results

Range
horizontal distance to impact
Time of flight
launch → impact
Max height (apogee)
above ground
Time to apogee
when vy = 0
Range at apogee
Initial vₓ
v₀ · cos θ
Initial vᵧ
v₀ · sin θ
Impact speed
√(vₓ² + vᵧ²) at landing
Impact angle
below horizontal
Launch KE per kg
½ v₀²

3. Trajectory

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.

4. Time-step table

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)

Formulas (idealized, drag-free)

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.