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Calculate free fall velocity after falling any distance, time to fall a given height, or distance fallen in a given time. Uses g = 9.81 m/s² standard gravitational acceleration with optional initial velocity support.
Free fall is motion under gravity alone — no air resistance. All objects fall with the same acceleration g = 9.81 m/s² regardless of mass (Galileo's principle). After t seconds of free fall from rest: v = gt, d = ½gt². Impact velocity from height h: v = √(2gh).
Free fall describes the motion of an object falling solely under the influence of gravity, with no air resistance. Galileo Galilei (1589-1592) demonstrated the revolutionary principle that all objects fall at the same rate regardless of their mass — a 1 kg ball and a 100 kg ball dropped simultaneously hit the ground at the same time (in vacuum). This contradicted Aristotle's 2000-year-old belief that heavier objects fall faster.
Standard gravitational acceleration at Earth's surface: g = 9.80665 m/s² (defined standard). Commonly used: g = 9.81 m/s². The value varies slightly: equator (9.78 m/s²) vs poles (9.83 m/s²), due to Earth's rotation and equatorial bulge. At 100km altitude (edge of space): g ≈ 9.52 m/s² — gravity barely diminishes at this scale.
| Time/Height | Velocity | Distance | Speed |
|---|---|---|---|
| 1 s | 9.81 m/s | 4.9 m | 35.3 km/h |
| 2 s | 19.6 m/s | 19.6 m | 70.6 km/h |
| 3 s | 29.4 m/s | 44.1 m | 105.8 km/h |
| 5 s | 49.1 m/s | 122.6 m | 176.8 km/h |
| 10 s | 98.1 m/s | 490.5 m | 353.2 km/h |
| Eiffel Tower (330m) | 80.5 m/s | 8.2 s fall | 289.8 km/h |
| Terminal vel. (skydiver) | — | — | ~54 m/s (195 km/h) |
Gravitational acceleration varies by planet. Impact velocity from 10m height on different worlds: Earth (g=9.81): v = √(2×9.81×10) = 14.0 m/s. Moon (g=1.62): v = √(2×1.62×10) = 5.7 m/s. Mars (g=3.72): v = √(2×3.72×10) = 8.6 m/s. Jupiter surface (g=24.79): v = √(2×24.79×10) = 22.3 m/s. This is why lunar rovers fall slowly and why landing on Mars requires special deceleration techniques (parachutes work poorly in thin atmosphere — hence the Curiosity rover's sky crane system).
Galileo's discovery that all objects fall at the same rate (equivalence of gravitational and inertial mass) was later elevated by Einstein to a fundamental principle: the Equivalence Principle — the basis of General Relativity. In an accelerating elevator or rocket (no windows), you cannot tell the difference between acceleration and gravity by any local experiment. This thought experiment led Einstein to realize gravity is not a force but a curvature of spacetime. The Apollo 15 astronaut David Scott demonstrated this on the Moon in 1971, simultaneously dropping a hammer and feather on live TV — both hit the surface at the same time, confirming Galileo in vacuum.
Construction safety calculations use free fall physics. A tool dropped from scaffold height h: impact velocity v = √(2gh). From 10m: v = 14.0 m/s = 50.4 km/h. From 50m: v = 31.3 m/s = 112.7 km/h. Kinetic energy at impact: KE = ½mv² = mgh. A 0.5 kg wrench from 10m: KE = 0.5 × 9.81 × 10 = 49.1 J — equivalent to being hit by a baseball bat. This is why hard hats and tool tethers are mandatory on construction sites. Elevator safety: counterweight and governor brakes stop freefall. Emergency brakes engage when cable snaps — brake springs compress against guide rails, decelerating at 3-5g.
Always ensure units are consistent before calculating. This calculator uses SI units (International System): meters (m) for distance, kilograms (kg) for mass, seconds (s) for time, Newtons (N) for force, Joules (J) for energy, Watts (W) for power, and Pascals (Pa) for pressure. When converting from other unit systems (imperial, CGS), convert all values before entering them into the calculator.
Physics calculations directly inform engineering safety standards. Stopping distance calculations (kinetic energy / braking force) set speed limits and vehicle safety requirements. Pressure calculations determine pipe and vessel wall thickness in plumbing and industrial equipment. Torque specifications on fasteners prevent structural failures. Centripetal acceleration limits guide road curve design and roller coaster safety. Every safety standard in transportation, construction, and consumer products has physics calculations at its foundation.