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), it falls a distance d = ½gt² in time t, where g is gravitational acceleration. On Earth (g = 9.81 m/s²), this means an object falls about 4.9 meters in the first second, 19.6 meters in two seconds, and 44.1 meters in three seconds.
The distance increases with the square of time — an accelerating relationship that surprises many people. An object doesn't fall twice as far in twice the time; it falls four times as far. This quadratic scaling has critical implications for everything from construction safety to roller coaster design.
This calculator computes fall distance from time, includes planetary comparisons showing how the same fall differs on Mars or Jupiter, and provides height-equivalent visualizations to contextualize the numbers. 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.
The d = ½gt² formula is simple, but interpreting the results — converting meters to stories, comparing planets, understanding accelerating motion — requires context. This calculator provides immediate visual and tabular comparisons that make the physics intuitive. It also keeps the distance, time, and gravity values together so you can compare one fall scenario with another without changing the setup.
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.
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.