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 height, how long does it take an object to fall, and how fast is it going at impact? These are fundamental questions in physics, engineering, and safety analysis. From a height h, the fall time is t = √(2h/g) and the impact velocity is v = √(2gh), assuming no air resistance.
A ball dropped from 3 meters (one story) hits the ground after 0.78 seconds at 27.7 km/h. From 30 meters (ten stories), it takes 2.47 seconds and lands at 87.6 km/h. The relationship is nonlinear: tripling the height increases impact speed by only √3 ≈ 1.73× but increases fall time by the same factor.
This height-focused calculator includes landmark comparisons (Eiffel Tower, Burj Khalifa), a comprehensive height-to-speed table, and a survivability guide based on impact velocity ranges. 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.
Converting height to fall time and impact speed requires square roots and unit conversions. This calculator provides instant context through landmark comparisons, survivability information, and visual height charts — making it useful for physics education, safety assessments, and engineering design. It also keeps the height, time, and impact speed results in one place so you can compare different drop heights quickly.
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.
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.