Projectile Range Calculator

Projectile motion describes an object that is launched and then moves under gravity alone. This projectile range calculator resolves the initial velocity into horizontal and vertical components, determines when the projectile reaches ground level, and reports horizontal range, maximum height, and time of flight. It is useful for physics homework, classroom demonstrations, ballistics concepts, sports analysis, and preliminary trajectory estimates where air resistance can be neglected. The horizontal component is initial speed multiplied by the cosine of the launch angle. Because the ideal model has no horizontal force, that component remains constant throughout the flight. The vertical component is initial speed multiplied by the sine of the angle and changes continuously under downward gravitational acceleration. Flight time comes from solving the vertical position equation for the positive time at which height becomes zero. Horizontal range is then horizontal velocity multiplied by that time. Maximum height is the starting height plus the vertical launch component squared divided by twice gravity. Initial height matters whenever launch and landing elevations differ. The familiar range equation based on speed squared and the sine of twice the angle applies only when the projectile lands at its launch elevation. This calculator uses the more general quadratic solution, so a projectile launched from a platform remains airborne longer and travels farther than an otherwise identical level-ground launch. A horizontal launch is also supported: its vertical component begins at zero, but gravity still produces a finite fall time. The model assumes a flat surface, constant gravitational acceleration, no wind, no lift, and no aerodynamic drag. Those assumptions are often excellent for compact, dense objects moving modest distances, but errors grow for lightweight objects, high speeds, long flights, or strong winds. Real trajectories can also be affected by spin, changing air density, Earth curvature, and rotation. Treat the result as an ideal baseline rather than a substitute for a full ballistic simulation. Use consistent SI units: meters per second for speed, degrees for angle, meters for height, and meters per second squared for gravity. Standard Earth gravity is about 9.81 m/s². Angles are measured above the horizontal, so zero degrees is horizontal and 90 degrees is straight upward. At 90 degrees the ideal horizontal range is effectively zero, while maximum height and flight time remain meaningful.