Projectile Trajectory Generator

What this generator does

Splits the flight into equal time steps and computes the position at each, then compares the final position against the range formula, the highest point against the apex formula, and each height against its mirror image on the far side of the apex.

How to use this tool

1. Enter the launch speed and the angle above horizontal.
2. Read the range, the apex height and the flight time.
3. Try two angles that add to ninety degrees and compare their ranges.
4. Look at the trajectory: the descent mirrors the climb exactly.

Understanding the controls

Launch speed

In units per second. Range grows with the square of speed, so doubling it quadruples the distance.

Launch angle

Between 1 and 89 degrees above horizontal. Forty-five gives the greatest range; anything above it trades distance for height.

Common use cases

• Checking a projectile motion answer against a traced trajectory
• Showing that complementary angles give the same range
• Producing trajectory data for a graph or a worksheet
• Teaching why forty-five degrees maximises range
• Comparing apex height against range for the same launch speed

How this generator works

Horizontal velocity is constant and vertical velocity falls steadily under gravity, so the position at any time follows directly. The flight time is twice the time to reach the apex, and the trajectory is sampled over exactly that interval. Before display the simulated landing point is compared against the closed-form range, the highest sampled point against the apex formula, and every sampled height against the height at the mirrored time — the path must be symmetric, and a step size or arithmetic error breaks that symmetry first.

Randomness and fairness

Nothing here is random. A speed and an angle determine the entire flight.

For how randomness is produced across the whole site, see how Generate Random works.

Limitations and good to know

• No air resistance, so real projectiles fall short of these ranges — often dramatically for light or fast objects.
• Launch and landing are at the same height; a hill or a cliff changes the flight time and the range.
• Gravity is fixed at 9.81 units per second squared, matching Earth at sea level.
• Spin, lift and wind are all outside the model, which is why this suits classroom problems better than ballistics.

Privacy and your data

The trajectory is computed in your browser and your inputs are never transmitted, stored or included in analytics.