Calculate free fall distance, time, and velocity. Solve for any variable with optional initial velocity, planetary gravity comparison, and distance-time tables.
Free fall describes the motion of an object under the sole influence of gravity, with no air resistance. Starting from rest, an object near Earth's surface accelerates at g ≈ 9.81 m/s², gaining about 35 km/h of speed every second until air resistance becomes significant.
The fundamental equations of free fall — d = ½gt², v = gt, and v² = 2gd — are among the most important in classical mechanics. Galileo first demonstrated that all objects fall at the same rate (ignoring air resistance) by dropping balls from the Leaning Tower of Pisa, overturning 2,000 years of Aristotelian physics.
This comprehensive calculator solves for any unknown (distance, time, or velocity) given the others, supports initial downward velocity, allows custom gravitational acceleration, and compares results across different celestial bodies. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case.
Free fall problems require selecting the right kinematic equation, handling quadratic solutions for time, and converting between m/s and km/h. This calculator solves any combination, provides distance-time tables, and shows how gravity differs across the solar system — making it invaluable for physics students and engineers. Keep these notes focused on your operational context.
Free Fall Equations (from rest): d = v₀t + ½gt² v = v₀ + gt v² = v₀² + 2gd Solving for time from distance: t = (−v₀ + √(v₀² + 2gd)) / g Specific impact energy: E/m = gd Where: d = distance (m), t = time (s) v₀ = initial velocity (m/s), v = final velocity (m/s) g = gravitational acceleration (9.81 m/s² on Earth)
Result: t = 2.019 s, v = 19.81 m/s (71.3 km/h)
Dropping from 20 m on Earth: t = √(2 × 20 / 9.81) = 2.019 s. Final velocity: v = 9.81 × 2.019 = 19.81 m/s = 71.3 km/h.
Free fall is the simplest gravitational motion: constant downward acceleration with no other forces. The resulting parabolic distance-time relationship (d ∝ t²) means an object covers progressively more distance each second. After 1 s it has fallen 4.9 m; after 2 s, 19.6 m (not 9.8); after 3 s, 44.1 m.
The velocity increases linearly: about 9.81 m/s added per second. After 4 seconds, a dropped object on Earth is moving at ≈ 39 m/s (141 km/h). This relentless acceleration is why even moderate heights can produce dangerous impact speeds.
In practice, air resistance always exists and grows with speed. For a compact, heavy object (bowling ball, rock), free fall equations are accurate for drops of a few meters. For lighter objects or higher drops, air resistance becomes significant. A skydiver reaches terminal velocity (where drag equals gravity) after about 12 seconds of free fall.
Galileo's insight that all objects fall at the same rate was revolutionary. It contradicted Aristotle's claim that heavier objects fall faster, which had been accepted for nearly two millennia. This principle — along with the parabolic trajectory of projectiles — laid the foundation for Newton's laws of motion and the entire field of classical mechanics.
No. In a vacuum, all objects fall at the same rate regardless of mass. This was demonstrated dramatically on the Moon by Apollo 15 astronaut David Scott, who dropped a hammer and feather simultaneously — they hit the ground together.
Free fall by definition assumes no air resistance. For real-world scenarios with drag (skydiving, parachutes), see the free-fall-air-resistance calculator. Free fall equations work well for dense objects over short distances.
Felix Baumgartner jumped from 39 km altitude in 2012, reaching 1,357 km/h (Mach 1.25) during his free fall phase. Alan Eustace later broke the altitude record at 41.4 km in 2014.
Earth's surface gravity varies from about 9.78 m/s² at the equator to 9.83 m/s² at the poles due to Earth's rotation and equatorial bulge. The standard value is g = 9.80665 m/s².
Yes, for downward throws. Set the initial velocity to the throw speed. For objects thrown upward, the equations still work but you need to handle the upward phase separately (this calculator assumes downward motion).
Because objects accelerate during free fall. In the first half of the fall time, the object covers only 25% of the total distance. The remaining 75% is covered in the second half of the time, when the object is moving faster.