Free Fall with Initial Velocity Calculator

This calculator works out how far an object falls and how fast it is moving after a given time, when it starts with an initial downward velocity rather than from rest. Ordinary free-fall problems assume an object is simply dropped, starting at zero speed, but often an object is already moving downward when the clock starts, thrown down, falling off a moving vehicle, or continuing from an earlier phase of motion. This calculator handles that general case using the standard equations of motion under constant gravitational acceleration. It accounts for both the distance covered by the initial velocity and the additional distance from gravity's acceleration over the time. You enter the initial downward velocity, the time elapsed, and the gravitational acceleration, which defaults to 9.81 metres per second squared for Earth, and the calculator returns the distance fallen, the final velocity, and that velocity in kilometres per hour. The results update as you type. Use it for physics study, for kinematics problems, or to understand falling motion. The distance fallen is the initial velocity times the time, plus one half of gravity times the time squared, the standard displacement equation. The final velocity is the initial velocity plus gravity times the time. The first term in the distance reflects how far the object would travel at its initial speed alone, while the second is the extra distance gravity adds as it accelerates the object. This calculation ignores air resistance, so it is most accurate for dense, compact objects over modest distances and times, where drag is small; for light objects or long falls, air resistance becomes significant and the object approaches a terminal velocity instead. Setting the initial velocity to zero recovers the simple dropped-from-rest case, where distance is just one half of gravity times time squared. This is one of the most fundamental calculations in mechanics, describing motion under constant acceleration.

Distance = u t + ½ g t². Final velocity = u + g t. Ignores air resistance, so best for dense objects over modest falls. Set u = 0 for a dropped object.