Free Fall Calculator – Height, Time and Impact Velocity
The Free Fall Calculator solves the kinematics of an object falling under gravity with no air resistance. Enter any two of the three core quantities — fall height, fall time and impact velocity — and the tool derives the rest, together with average velocity, an optional energy and momentum breakdown, a trajectory table and a step-by-step derivation you can copy into a lab report or homework answer.
What Is Free Fall?
Free fall is motion in which gravity is the only force acting on an object. Because gravity produces a constant acceleration g, the object speeds up by the same amount every second: about 9.80665 m/s of extra speed per second on Earth. The distance covered, however, grows with the square of the elapsed time, which is why a fall that lasts twice as long covers four times the distance.
A famous consequence is that mass does not matter. A bowling ball and a marble released together in a vacuum land at the same instant, because the gravitational force scales with mass exactly as fast as the inertia resisting it. Mass only enters the picture when you ask about impact energy or momentum.
The Free Fall Equations
Taking downward as positive, with v₀ the release velocity, the calculator applies the standard constant-acceleration equations:
h = v₀t + ½gt² — height fallen in time t
v = v₀ + gt — velocity after time t
v² = v₀² + 2gh — velocity after falling height h
t = (−v₀ + √(v₀² + 2gh)) / gFor a pure drop from rest (v₀ = 0) these collapse into the familiar textbook forms h = ½gt², v = gt and v = √(2gh). Every input is converted to SI units before the maths runs, so you can mix feet, seconds and miles per hour freely and still get a consistent answer.
Impact Energy and Momentum
Supplying an object mass unlocks the quantities engineers care about for dropped-object safety assessments: kinetic energy at impact KE = ½mv², gravitational potential energy at release PE = mgh, and momentum p = mv. For a drop from rest the two energies match exactly, which is a neat demonstration of conservation of energy — all the potential energy stored at the release point has been converted into kinetic energy by the time the object lands.
Gravity on Other Worlds
Gravity is not a universal constant; it depends on the mass and radius of the body you are standing on. Selecting a preset repeats the same drop under a different g, which makes it easy to see why the Apollo 15 hammer-and-feather demonstration took so long to finish: with lunar gravity at roughly one sixth of Earth's, a fall takes about 2.5 times longer and ends at about 40% of the impact speed.
Measuring a Well or Cliff With a Stopwatch
The classic field measurement — drop a stone and time the splash — has a subtlety. Your stopwatch reading includes both the fall and the time the sound of the impact takes to travel back up to your ear. The well-depth mode solves T = √(2h/g) + h/c for the depth instead of naively treating the whole reading as fall time, which otherwise overestimates deep wells noticeably.
Accuracy and the Air-Resistance Limit
These equations describe an idealised vacuum. Real falls diverge once drag becomes comparable to weight, and every object eventually reaches a terminal velocity beyond which it stops accelerating — roughly 55 m/s for a skydiver in a belly-to-earth position. As a rule of thumb, results stay close to reality for compact, dense objects falling less than about 50 metres; beyond that, treat the computed impact speed as an upper bound rather than a prediction. The tool flags this automatically whenever your result enters the drag-significant regime, and also warns when a drop is tall enough that g itself can no longer be treated as constant.