Calculate how far an object falls in a given time under gravity. Distance-time tables, planetary comparisons, height equivalents bar chart, and energy analysis.
When an object is dropped with no air resistance, the fall distance follows d = 1/2 gt^2. On Earth, that means about 4.9 meters in the first second, 19.6 meters in two seconds, and 44.1 meters in three seconds.
The square-of-time relationship is the important part: doubling the time does not double the distance, it quadruples it. That is why free fall becomes much more dramatic than intuition suggests.
This calculator computes distance from time, then compares the result across different gravities and height-equivalent references so the numbers are easier to picture.
Free-fall distance is one of those formulas that is easy to write down but easy to underestimate in practice. Keeping the distance, time, and gravity values together makes it easier to compare scenarios and to turn meters into something people can actually picture.
Distance: d = v₀t + ½gt² Final Velocity: v = v₀ + gt Average Velocity: v̄ = d / t Kinetic Energy: KE = ½mv² Potential Energy: PE = mgh Where: d = distance (m), t = time (s) v₀ = initial velocity (m/s), g = 9.81 m/s² (Earth) m = mass (kg)
Result: 44.15 m (144.8 ft)
d = ½ × 9.81 × 3² = ½ × 9.81 × 9 = 44.15 m. Final velocity: v = 9.81 × 3 = 29.43 m/s (106 km/h). This is about 14.7 stories.
This deceptively simple formula encapsulates one of physics' most important relationships. The factor of ½ comes from the integration of constant acceleration: velocity increases linearly (v = gt), and distance is the area under the velocity-time curve — a triangle with area ½ × base × height = ½ × t × gt = ½gt².
Construction workers, firefighters, and safety engineers use fall distance calculations daily. OSHA requires fall protection for any work at heights above 6 feet (1.83 m) — corresponding to a fall time of just 0.61 seconds and an impact speed of 6 m/s (21.6 km/h). At 10 stories (30 m), the impact speed reaches 88 km/h, making survival unlikely without a deceleration system.
Galileo measured free fall by rolling balls down inclined planes to slow the motion enough for manual timing. His discovery that d ∝ t² (published in 1638) was one of the first quantitative laws of physics and directly inspired Newton's formulation of the laws of motion 50 years later.
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Because velocity increases linearly with time (v = gt), and distance is the integral of velocity. Each second the object is moving faster than the last, so it covers more ground. The cumulative effect produces a quadratic (t²) distance relationship.
A typical building story is about 3 meters (10 feet). So a 30-meter fall is about 10 stories, a 50-meter fall about 16-17 stories. The calculator includes a stories estimate for easy comparison.
For dense, compact objects (rocks, metal balls) over moderate distances (up to ~50 m), the vacuum approximation is quite accurate (within a few percent). For lighter objects or longer falls, air resistance becomes significant.
If the object is thrown downward at speed v₀, total distance is d = v₀t + ½gt². The initial velocity term adds a linear component to the quadratic free-fall distance. Enter any downward speed in the initial velocity field.
For fall from rest, 25% of the distance is covered in the first half of time, and 75% in the second half. This dramatically illustrates how acceleration works and why the d ∝ t² relationship matters practically.
Without air resistance, there is no limit. With air resistance, a skydiver at terminal velocity (~55 m/s belly-down) falls about 55 meters per second indefinitely. Felix Baumgartner fell over 36,000 meters total during his stratosphere jump.