Projectile Motion Simulator
Simulate projectile motion: enter speed, angle, launch height and gravity to get range, max height, flight time and a trajectory graph.
Launch conditions
Results
- Range (horizontal distance)
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- Maximum height
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- Time of flight
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- Time to apex
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- Horizontal velocity (vx)
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- Vertical velocity (vy)
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- Impact speed
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- Impact angle
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Trajectory
Formulas used
- vx = v·cos θ
- vy = v·sin θ
- t_apex = vy / g
- h_max = h₀ + vy² / (2g)
- t_flight = (vy + √(vy² + 2g·h₀)) / g
- range = vx · t_flight
How it works
Enter the initial speed, the launch angle and the height the projectile starts from, and the simulator solves the standard ideal projectile-motion equations instantly. The speed is split into a horizontal component (vx = v·cos θ) that never changes and a vertical component (vy = v·sin θ) that gravity pulls back down, so the flight time comes from (vy + √(vy² + 2g·h₀)) / g and the range is simply vx multiplied by that time. Switch the gravity selector to the Moon, Mars, Venus or Jupiter — or type your own value — to see how the same launch behaves on another world.
The graph plots height against horizontal distance, marking the apex and the landing point, and the CSV download gives you 100 sampled points (time, x, y, vx, vy) for a lab report or a spreadsheet chart. This is the drag-free textbook model: air resistance, wind and spin are ignored, which matches how the problem is posed in physics classes but slightly overestimates the range of real balls and arrows. Everything is computed in your browser — no upload, no account, no ads.
Frequently asked questions
How do you calculate the range of a projectile?
Split the launch speed into vx = v·cos θ and vy = v·sin θ. The flight time is t = (vy + √(vy² + 2g·h₀)) / g, where h₀ is the launch height, and the range is simply vx × t. When the launch height is zero this simplifies to the familiar range = v²·sin(2θ) / g. The simulator applies these formulas as you type.
What launch angle gives the maximum range?
From ground level with no air resistance, 45° gives the longest range, and any pair of angles adding up to 90° (say 30° and 60°) gives the same distance. If you launch from a height above the ground the optimal angle drops below 45°, because extra hang time is worth more than extra vertical speed — try it by raising the launch height field.
Does the simulator include air resistance?
No. It uses the ideal, drag-free model taught in physics classes, so gravity is the only force acting after launch. Real balls, arrows and bullets fall short of these numbers, especially at high speed. Everything is calculated in your browser — nothing is uploaded — and you can export 100 sampled trajectory points as CSV for a lab report.