Free Fall Calculator
From a single fall time, get how far an object has dropped and how fast it is moving — the two numbers behind every dropped object, drop tower, and falling-body problem.
One input, two answers
Enter the fall time and the calculator returns the distance fallen (½ × g × t²) and the velocity (g × t) at once.
No air resistance
The formulas assume a vacuum — real falling objects are slowed by drag and eventually reach a terminal velocity.
What is free fall?
Time in, distance and velocity out
Free fall is motion under gravity alone, with air resistance ignored. Near Earth's surface gravity gives every falling object the same acceleration, the standard gravity g = 9.80665 m/s², so the only thing you need to know is how long the object has been falling. The distance it has dropped is distance = ½ × g × t², and the speed it has reached is velocity = g × t. That makes the fall time the one input you need for dropped-object problems, impact-speed estimates, and ride design.
Enter the fall time in seconds to get the distance fallen and the velocity instantly.
Two short formulas, both built from the fall time (t) and the fixed acceleration of gravity (g).
distance = ½ × g × t²The distance is half the gravity times the time squared (½ × g × t²). The velocity is just the gravity times the time (g × t). Because the time is squared in the distance formula but not in the velocity formula, distance grows far faster than speed: doubling the fall time doubles the velocity but quadruples the distance.
Suppose an object falls freely for 3 seconds, that is t = 3 s.
Distance fallen
½ × 9.80665 × 3² = 44.129925 m — about 44 metres dropped.
Velocity
9.80665 × 3 = 29.41995 m/s — about 106 km/h at that instant.
Cross-check
The average speed over the fall is 44.129925 ÷ 3 ≈ 14.71 m/s — exactly half the final velocity, as expected for constant acceleration.
The two outputs answer two different practical questions. The distance (about 44 m after 3 seconds) is how far the object has physically dropped — it tells you the height it would clear or the depth it has reached. The velocity (about 29.42 m/s here) is how fast it is moving at that instant — what matters for impact force. The key insight is that distance grows with the square of the time: an object falls much farther in its third second than in its first. In the first second it drops about 4.9 m, but between the second and third second it covers more than 24 m, because it is already moving fast. This idealised model ignores air resistance, so real skydivers never keep accelerating forever — drag balances gravity and they level off at a terminal velocity of roughly 55 m/s. Gravity also changes with location: on the Moon g is only about 1.62 m/s², so the same fall would be far slower and shorter. That square-law growth is exactly why long falls are so much more dangerous than short ones.
The formulas are exact for free fall in a vacuum, but a couple of practical points are worth keeping in mind.
Air resistance and gravity vary
This tool computes idealised free fall in a vacuum, so it ignores air resistance. In real air, drag grows with speed until it balances gravity and the object stops accelerating at its terminal velocity — so for long falls or light objects the real speed is well below what the formula predicts. The value of g also varies slightly with latitude and altitude, and is very different on other bodies (about 1.62 m/s² on the Moon). Keep the time in seconds so the distance comes back in metres and the velocity in metres per second.