Projectile Motion with Air Drag Calculator

This calculator simulates the flight of a projectile including air resistance, giving a far more realistic result than the textbook formulas that ignore drag. In introductory physics, projectile motion is solved assuming a vacuum, where the only force is gravity and the path is a perfect parabola. That is fine for a heavy, slow object over a short distance, but for anything fast, light, or travelling far, air drag matters enormously: it shortens the range, lowers the peak height, and makes the descent steeper than the climb, breaking the neat symmetry of the parabola. Because drag depends on the square of the speed, there is no simple formula, so this tool solves the motion numerically, stepping the projectile forward in tiny time slices and applying gravity and drag at each step. You enter the launch speed, the launch angle, the projectile's mass, and a drag factor that captures its size and shape, and the calculator returns the range with drag, the maximum height reached, the flight time, and, for comparison, the ideal range it would have in a vacuum. The results update as you type, so you can see how increasing the drag or reducing the mass cuts the range. Use it for more realistic physics problems, for understanding ballistics and sports projectiles, or to appreciate just how much air resistance changes the picture. The drag factor combines the air density, drag coefficient and cross-sectional area into a single number, so a larger or less streamlined object has a higher value. The contrast with the vacuum range is often striking: a fast projectile can travel far less than half its ideal range once drag is included, which is why real-world ballistics never matches the simple parabola.

Numerical simulation with drag force = drag factor x speed squared, opposing motion. Drag factor combines air density, drag coefficient and area. Compared with the ideal vacuum range.