Free Fall Calculator

Calculate distance, velocity, and time for objects falling under gravity. Assumes no air resistance.

Free Fall Formulas: Distance (starting from rest): d = ½ × g × t² Distance (with initial velocity): d = v₀ × t + ½ × g × t² Velocity: v = v₀ + g × t v² = v₀² + 2 × g × d Time (from rest): t = √(2d / g) Time (with initial velocity): t = (v - v₀) / g t = [-v₀ + √(v₀² + 2gd)] / g Where: • d = distance fallen (m) • v = final velocity (m/s) • v₀ = initial velocity (m/s) • t = time (s) • g = gravitational acceleration (m/s²) Default: 9.81 m/s² (Earth) Key insights: • All objects fall at same rate (no air resistance) • Velocity increases linearly with time • Distance increases with time squared • Energy: mgh = ½mv² (conservation)
Example 1 (Drop from building): Height = 45 m, v₀ = 0, g = 9.81 m/s² Time = √(2 × 45 / 9.81) = √9.174 = 3.03 s Final velocity = 9.81 × 3.03 = 29.7 m/s (107 km/h) Example 2 (Thrown downward): v₀ = 5 m/s, time = 2 s, g = 9.81 m/s² Distance = 5 × 2 + ½ × 9.81 × 4 = 10 + 19.62 = 29.62 m Final velocity = 5 + 9.81 × 2 = 24.62 m/s Example 3 (Cliff diving): Height = 20 m, v₀ = 0 Time = √(2 × 20 / 9.81) = 2.02 s Impact velocity = 9.81 × 2.02 = 19.8 m/s (71 km/h) Example 4 (First second of fall): Time = 1 s, v₀ = 0, g = 9.81 m/s² Distance = ½ × 9.81 × 1² = 4.905 m Final velocity = 9.81 m/s (35.3 km/h) Example 5 (Moon gravity): Height = 45 m, g = 1.62 m/s² (Moon) Time = √(2 × 45 / 1.62) = 7.45 s Final velocity = 1.62 × 7.45 = 12.1 m/s (Same height takes 2.5× longer on Moon) Example 6 (Skydiving - first 3 seconds): Time = 3 s, v₀ = 0, g = 9.81 m/s² Distance = ½ × 9.81 × 9 = 44.1 m Velocity = 29.4 m/s (106 km/h) (Note: Air resistance starts affecting significantly after this)

What is free fall?

Free fall is motion under gravity alone, with no air resistance. All objects in free fall accelerate at the same rate (9.81 m/s² on Earth) regardless of mass. Galileo demonstrated this principle at the Leaning Tower of Pisa.

Why is gravitational acceleration 9.81 m/s²?

Earth's gravity accelerates objects at approximately 9.81 m/s² (often rounded to 10 m/s² for quick calculations). This value varies slightly with altitude and latitude. At sea level: poles ≈ 9.83 m/s², equator ≈ 9.78 m/s².

Does air resistance affect free fall?

Yes, significantly. This calculator assumes no air resistance (vacuum conditions). Real objects experience drag force that increases with speed until reaching terminal velocity. Light objects (feathers) and high-speed falls show major air resistance effects.

What is terminal velocity?

Terminal velocity is the maximum speed reached when air resistance equals gravitational force, causing zero net acceleration. For skydivers: ~120 mph (53 m/s) belly-down, ~200 mph (89 m/s) head-down. Depends on object shape, size, and air density.

How do I calculate free fall distance?

Distance d = ½gt², where g = 9.81 m/s² and t is time. After 1 second: d = 4.9 m. After 2 seconds: d = 19.6 m. After 3 seconds: d = 44.1 m. Distance increases with time squared.

How do I calculate free fall velocity?

Velocity v = gt (starting from rest), where g = 9.81 m/s² and t is time. Alternatively, v = √(2gh) where h is height fallen. After 1 second: v = 9.81 m/s. After 2 seconds: v = 19.62 m/s. Velocity increases linearly with time.

How long does it take to fall from a given height?

Time t = √(2h/g), where h is height and g = 9.81 m/s². From 10 m: t ≈ 1.43 s. From 100 m: t ≈ 4.52 s. From 1000 m: t ≈ 14.3 s. This assumes starting from rest with no air resistance.

What if the object has initial velocity?

With initial downward velocity v₀: d = v₀t + ½gt² and v = v₀ + gt. With initial upward velocity: object rises, stops, then falls. Maximum height = v₀²/(2g). Total time = 2v₀/g plus any additional fall time.

How does gravity vary on other planets?

Moon: 1.62 m/s² (1/6 Earth), Mars: 3.71 m/s² (0.38 Earth), Jupiter: 24.79 m/s² (2.53 Earth), Sun: 274 m/s² (28 Earth). The calculator allows custom gravity values for planetary calculations.

What are real-world examples of free fall?

Examples: dropped objects, bungee jumping (initial phase), skydiving (before terminal velocity), cliff diving, falling elevators (emergency), Space station astronauts (continuous free fall in orbit), apple falling from tree.

Why do astronauts float in space?

Astronauts in orbit are in continuous free fall toward Earth but moving sideways fast enough that they keep missing it. This creates the sensation of weightlessness. They experience the same gravitational acceleration as their spacecraft.

How accurate is this calculator for real scenarios?

Very accurate for short drops (< 10 m) of dense objects. For longer falls, lighter objects, or high speeds, air resistance becomes significant. For precision: vacuum chambers show perfect agreement; real-world results vary up to 50% for extended falls.