What Is Free Fall and How Does This Calculator Work?
Free fall is the motion of an object accelerating under gravity alone, with no other forces — including air resistance — acting on it. In true free fall every object accelerates at the same rate regardless of its mass, which is why a hammer and a feather dropped together on the Moon (with no atmosphere) hit the ground at the same instant, as demonstrated live by Apollo 15 astronaut David Scott in 1971.
The kinematic equations for free fall from rest — first derived by Galileo Galilei in his 1638 work Two New Sciences — are: h = v₀t + ½gt² for height, and v = v₀ + gt for velocity, where h is the distance fallen, v₀ is the initial downward velocity, t is elapsed time, v is the velocity at time t, and g is standard gravity (9.80665 m/s² on Earth). Combining the two eliminates time to give v² = v₀² + 2gh, which this calculator uses to solve for velocity directly from a known height.
Real falling objects rarely reach the ground in a true vacuum, though — air resistance pushes back against them, growing with the square of their speed until it exactly cancels gravity. At that point the object stops accelerating and falls at a constant speed called its terminal velocity, calculated as v_t = √(2mg ÷ (ρ·Cd·A)), where m is mass, ρ is air density, Cd is the object's drag coefficient, and A is its cross-sectional area facing the airflow.
How to Use This Free Fall and Terminal Velocity Calculator
Switch between the two modes depending on whether you want an idealized physics-class answer or a real-world falling speed:
- Free Fall (Vacuum): Enter either the height an object falls from or the time it falls for, plus an optional initial velocity, and get impact velocity, fall time, and fall height — assuming no air resistance.
- Terminal Velocity (Air): Pick a preset object — skydiver, baseball, raindrop, cat, feather — or enter your own mass, drag coefficient, and cross-sectional area to find the maximum speed that object can reach falling through air.
- Unit System: Toggle between metric (m, m/s) and US customary (ft, mph) units at any time.
- Air Density: Defaults to 1.225 kg/m³, the standard value at sea level and 15°C; lower it for high-altitude calculations, since thinner air raises terminal velocity.
This calculator works in both metric and US customary units, and expresses the vacuum-fall result set to the same standard gravity (9.80665 m/s²) used worldwide in physics and engineering curricula, regardless of unit system.
How Terminal Velocity Differs Between Falling Objects
Terminal velocity depends on the ratio of an object's weight to its air resistance, so shape and size matter as much as mass. A skydiver reaches a much higher terminal velocity than a cat of similar relative build because the skydiver's streamlined, weight-forward posture produces less drag per kilogram than a small animal's splayed body shape.
| Object | Approx. Terminal Velocity | Why |
|---|---|---|
| Skydiver (head-down) | ~280 km/h (175 mph) | Minimal frontal area in a tracking dive |
| Skydiver (belly-to-earth) | ~195 km/h (120 mph) | Standard stable freefall position |
| Baseball | ~120 km/h (74 mph) | Dense, small, moderately smooth sphere |
| House cat (splayed) | ~100 km/h (60 mph) | Relaxed limbs roughly double drag area |
| Large raindrop (5 mm) | ~32 km/h (20 mph) | Tiny mass relative to its surface area |
| Feather | ~7 km/h (4 mph) | Almost no mass per unit of drag area |
A 1987 study published in the Journal of the American Veterinary Medical Association (Diamond & Whitney) found that cats falling from higher floors of buildings often had fewer injuries than those falling from lower floors, once they had time to relax into a splayed posture and reach their lower terminal velocity — a phenomenon veterinarians call "high-rise syndrome."
Frequently Asked Questions About the Free Fall Calculator
What is the formula for free fall velocity?
In a vacuum, an object's velocity after falling for time t is v = v₀ + gt, where v₀ is its initial velocity and g is standard gravity (9.80665 m/s²). If you know the height fallen instead of the time, use v = √(v₀² + 2gh), which this calculator applies directly.
How is terminal velocity calculated?
Terminal velocity is v_t = √(2mg ÷ (ρ·Cd·A)), where m is mass, g is gravity, ρ is air density, Cd is the object's drag coefficient, and A is its cross-sectional area. It is the speed at which upward air resistance exactly balances downward gravity, so acceleration drops to zero.
How fast do skydivers actually fall?
A skydiver in a standard belly-to-earth position typically reaches a terminal velocity of about 195 km/h (120 mph) after roughly 12 seconds and 450 meters of fall. Switching to a head-down tracking position reduces drag enough to exceed 280 km/h (175 mph).
Why do heavier objects fall at the same rate as lighter ones — but not always in real life?
In a vacuum, gravitational acceleration doesn't depend on mass, so a bowling ball and a feather fall identically — this was famously confirmed on the airless Moon during Apollo 15. In air, though, terminal velocity depends on the ratio of weight to drag, so a dense, compact object like a bowling ball reaches a much higher terminal velocity than a lightweight, spread-out object like a feather before air resistance catches up.
How accurate is this free fall and terminal velocity calculator?
The Free Fall mode uses the exact kinematic equations for constant acceleration and is exact given the inputs. The Terminal Velocity mode uses the standard quadratic-drag model, which is very accurate for objects moving fast enough that air resistance dominates (like skydivers or baseballs) but the preset drag coefficients and areas are representative averages — a real object's exact shape, orientation, and altitude will shift the result somewhat.