Drop a coin off a bridge and it doesn't fall at a steady speed — it keeps accelerating the whole way down, picking up roughly 22 miles per hour of speed for every second it falls. That's gravity at work, and it's one of the most reliably constant forces in everyday physics, which is exactly why free fall problems are a physics-class staple: the math is simple and the same every time.
How to Use the Free Fall Calculator
Enter the object's initial velocity in meters per second — use 0 if it's simply dropped from rest — and the time it has been falling in seconds. The calculator returns the total distance fallen and the final velocity, given both in meters per second and miles per hour so you can sanity-check the result against a more familiar unit.
The Free Fall Formulas
Distance fallen: d = v₀t + 1/2 g t²
Final velocity: v = v₀ + g t
Here v₀ is initial velocity, t is time, and g is the acceleration due to gravity, 9.80665 meters per second squared — the standard gravity value fixed by international agreement in 1901 and still used today as the reference constant, even though actual gravity varies very slightly by location on Earth. Using the calculator's default example — an object dropped from rest and falling for 3 seconds — distance works out to 0 × 3 + 0.5 × 9.80665 × 3², which is 0.5 × 9.80665 × 9, or about 44.13 meters. Final velocity is 0 + 9.80665 × 3, about 29.42 meters per second, which converts to roughly 65.8 miles per hour.
The Role of Air Resistance
This calculator models idealized free fall in a vacuum, where the only force acting is gravity. Real objects also experience air resistance, which grows stronger as speed increases and eventually balances gravity's pull entirely — at that point the object stops accelerating and falls at a constant terminal velocity. A skydiver in a stable belly-down position reaches a terminal velocity of roughly 120 mph after about 12 seconds of fall, far short of what the pure free-fall formula alone would predict for a longer drop, which is exactly why skydiving is survivable and why this calculator's numbers should be treated as an upper bound on speed and a good approximation only for shorter falls or denser, more aerodynamic objects.
Why Falling Objects Accelerate Instead of Moving at Constant Speed
Gravity applies a constant force to a falling object, and a constant force produces a constant acceleration — meaning velocity increases at a steady rate rather than staying fixed. This is different from how we experience everyday motion, like a car cruising at a constant highway speed, and it's why a long fall ends much faster and harder than a short one: an object dropped for 1 second has fallen only about 4.9 meters and hits at about 9.8 m/s (22 mph), but one dropped for 3 seconds — three times the time — has fallen nine times as far and hits nearly three times as fast.
Galileo's Famous Insight
Before modern physics, it was widely assumed that heavier objects fall faster than light ones. Galileo Galilei is credited with showing that's wrong (at least in the absence of air resistance) — a cannonball and a musket ball dropped from the same height land at the same time, because gravitational acceleration doesn't depend on mass at all. The formulas in this calculator reflect that: mass never appears anywhere in the distance or velocity equations, only initial velocity, time, and the fixed constant g.
