Projectile with Height Calculator
Solve a projectile path that begins above or below the landing level.
Model a launch from a nonzero height
Ground-level projectile formulas assume launch and landing share one elevation, which is wrong for a ball released from a platform, a package leaving a ledge, or any raised launcher. This calculator resolves the initial velocity into horizontal and vertical components, then solves the vertical-position quadratic for the positive landing time. That time drives the horizontal range, while the upward component determines peak height above the landing datum.
With the defaults, a 20 meter-per-second launch at 45 degrees begins 10 meters high under 9.81 meters per second squared of gravity. The positive quadratic root gives 3.47063 seconds aloft, a horizontal range of 49.0822 meters, and a maximum height of 20.1937 meters. Setting the starting height to zero reduces the calculation to the familiar level-ground case.
Read the ideal trajectory carefully
The trajectory is an ideal vacuum model: it treats gravity as constant and ignores drag, lift, wind, spin, terrain, and Earth curvature. Angles are measured from horizontal, and all length and time inputs must use coherent units. Calculations stay in your browser, so private launch parameters are not transmitted. Use numerical simulation or measured drag data when aerodynamic forces materially change the path.
Frequently Asked Questions
How does launch height change projectile range?
Extra starting height usually increases flight time, which lets the unchanged horizontal velocity cover more distance before landing.
Which root of the height equation is used?
The tool selects the nonnegative time root of the vertical quadratic because negative time describes the extrapolated path before launch.
Does this include air resistance?
No. It is a constant-gravity vacuum model, so drag, wind, and spin are outside the calculation.
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