Calculate fall time and impact speed from height. Landmark comparisons, survivability guide, height-time-speed tables, and visual bar chart for famous structures.
Given a drop height, this calculator estimates both the fall time and the impact speed. Under the no-air-resistance model, time scales with the square root of height and impact speed scales with the square root of 2gh.
A 3-meter drop lands in under a second, while a 30-meter drop is only about 2.5 seconds but reaches highway-speed impact. That non-linear scaling is the main reason even modest-looking heights can produce dangerous impacts.
The page also includes landmark comparisons and a height-to-speed table so you can place a height in a more intuitive real-world context.
Height-to-impact calculations are one of the clearest places to see constant-acceleration motion in action. Keeping the time, speed, and landmark comparisons together makes it easier to compare different drop heights without redoing the algebra each time.
Fall Time: t = (−v₀ + √(v₀² + 2gh)) / g For v₀ = 0: t = √(2h/g) Impact Velocity: v = √(v₀² + 2gh) For v₀ = 0: v = √(2gh) Kinetic Energy: KE = ½mv² = mgh Stories: n ≈ h / 3 Where: h = height (m), g = 9.81 m/s² (Earth)
Result: t = 2.47 s, v = 24.3 m/s (87.4 km/h)
A 30 m drop (≈10 stories): t = √(2×30/9.81) = 2.47 s. Impact velocity: v = √(2×9.81×30) = 24.3 m/s = 87.4 km/h. This exceeds highway speed limits.
The relationship between fall height and injury severity is well-documented. At heights below 2 meters, fractures are the primary concern. At 6-10 meters, internal organ injury and multiple fractures become likely. Above 15 meters, the fatality rate increases rapidly. Emergency medical guidelines classify falls above 6 meters (20 feet) as "significant mechanism" trauma, triggering activation of trauma teams.
Height-to-speed calculations are essential in many engineering contexts: determining impact loads on structures, designing crash barriers, sizing energy-absorbing materials, and calculating terminal velocity of falling construction debris. Bridge and building designers must account for dropped tools and materials to protect workers and the public below.
Because speed scales as √h, the first few meters of a fall contribute disproportionately to impact velocity. Falling from 5 m produces 35.5 km/h; doubling to 10 m only increases speed to 50.2 km/h (not 71 km/h). This means low-height falls are more dangerous than intuition suggests — and fall protection matters even at modest heights.
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Impact speed scales as √h. Doubling the height increases speed by √2 ≈ 41%. Quadrupling the height doubles the speed. This square-root relationship means diminishing speed gains at greater heights.
Falls are a leading cause of workplace death and injury. Understanding the relationship between height and impact severity helps justify safety regulations. OSHA requires fall protection at just 6 feet (1.8 m) because even short falls can cause serious injury.
For a human body, air resistance becomes noticeable above about 50 m and dominant above 300 m (where speed approaches terminal velocity ~55 m/s). For dense objects like rocks, vacuum equations work well up to hundreds of meters.
Vesna Vulovic survived a fall from 10,160 m (33,330 ft) in 1972 when her aircraft broke apart. However, she likely remained inside fuselage wreckage that slowed her descent. The tallest open-air survival falls are typically under 50 m.
For an object thrown upward, the maximum height reached is h = v₀²/(2g). This calculator is designed for downward falls, but you can use the height formula inversely to find how high something was thrown given its launch speed.
A building story averages about 3 meters (10 feet) from floor to floor in residential buildings. Commercial buildings may have 3.5-4 m story heights. The 3 m estimate is a useful but approximate rule of thumb.