Time of Flight Calculator for Projectile Motion

Time of flight is the elapsed time between a projectile leaving its launch point and reaching the selected ground level. This calculator models ideal projectile motion: gravity is constant, the ground is horizontal, and aerodynamic drag is ignored. Those assumptions isolate the vertical part of motion, because horizontal speed changes range but does not determine when the object reaches the ground. The launch speed and angle are resolved into a vertical velocity using vᵧ = v sin(θ). The vertical position at time t is y(t) = h + vᵧt − gt²/2, where h is initial height and g is gravitational acceleration. Setting y to zero produces a quadratic equation. Its physically meaningful positive root is t = (vᵧ + √(vᵧ² + 2gh)) / g. When launch and landing heights are equal, h is zero and the familiar expression simplifies to t = 2v sin(θ) / g. An elevated launch remains airborne longer because it must cover the initial height before reaching the ground. Use metres, seconds, and metres per second together for consistent SI results. Standard gravity is 9.80665 m/s², while 9.81 m/s² is adequate for most classroom work. Gravity varies slightly with latitude and altitude, and other worlds require different values: about 1.62 m/s² on the Moon and 3.71 m/s² on Mars. The angle is measured upward from horizontal. A negative angle is mathematically possible for a downward launch, although practical trajectories must still begin above ground. Real balls, arrows, and other projectiles experience drag, wind, lift, and spin. Drag generally shortens the ideal flight time for a rising projectile, but its exact effect depends on shape, area, density, and speed. Treat this result as an analytical baseline rather than a substitute for a full trajectory simulation when safety or precision matters. The calculator is especially useful for physics homework, checking experiments, estimating sports trajectories, and comparing how launch angle or platform height changes airtime. Always distinguish time of flight from time to peak. Time to peak is vᵧ/g when the projectile initially moves upward, while total airtime includes the subsequent fall. For a level-to-level trajectory the two halves are symmetric, but an elevated or lowered landing point breaks that symmetry. This calculator solves the complete ground-intersection equation, so it remains valid when the projectile starts above ground.