Free Fall Calculator
Our mechanics calculator computes fall accurately. Enter measurements for results with formulas and error analysis. See charts, tables, and visual results.
Formula
h = ½gt² | v = gt | v² = 2gh | KE = ½mv²
Free fall kinematics: distance fallen equals half of gravitational acceleration times time squared. Velocity equals g times time. These equations assume no air resistance and constant gravitational acceleration. Impact kinetic energy equals half mass times velocity squared.
Worked Examples
Example 1: Dropped Object from Building
Problem: A ball is dropped from the top of a 50m building on Earth. How long does it take to hit the ground, and what is the impact velocity? The ball has mass 0.5 kg.
Solution: h = 50m, v₀ = 0, g = 9.81 m/s²\nFall time: t = √(2h/g) = √(100/9.81) = 3.193 s\nImpact velocity: v = gt = 9.81 × 3.193 = 31.32 m/s\nConverted: 31.32 × 3.6 = 112.8 km/h\nKinetic energy: KE = ½mv² = 0.5 × 0.5 × 31.32² = 245.2 J\nPotential energy: PE = mgh = 0.5 × 9.81 × 50 = 245.3 J ✓
Result: t = 3.19s | v = 31.3 m/s (112.8 km/h) | KE = 245.2J
Example 2: Free Fall on Mars
Problem: How far does an object fall in 5 seconds on Mars (g = 3.72 m/s²) if thrown downward at 2 m/s?
Solution: t = 5s, v₀ = 2 m/s, g = 3.72 m/s²\nDistance: d = v₀t + ½gt² = 2×5 + 0.5×3.72×25 = 10 + 46.5 = 56.5m\nFinal velocity: v = v₀ + gt = 2 + 3.72×5 = 20.6 m/s\nConverted: 20.6 × 3.6 = 74.2 km/h
Result: d = 56.5m | v = 20.6 m/s (74.2 km/h)
Frequently Asked Questions
What is free fall?
Free fall is the motion of an object falling under the sole influence of gravity, with no air resistance or other forces acting on it. In free fall, all objects accelerate at the same rate regardless of mass — this was famously demonstrated by Galileo and later confirmed by Apollo 15 astronauts dropping a hammer and feather on the Moon. On Earth, free fall acceleration (g) is approximately 9.81 m/s² (32.2 ft/s²). The basic kinematic equations are: distance = ½gt², velocity = gt, and v² = 2gh (for objects starting from rest). Free fall is an idealization; real falling objects experience air resistance.
How do you calculate fall time from height?
For an object dropped from rest (v₀ = 0) from height h: Time = √(2h/g). For example, dropping from 100m on Earth: t = √(2×100/9.81) = √20.39 = 4.52 seconds. With an initial downward velocity v₀: use the quadratic formula on h = v₀t + ½gt², giving t = [-v₀ + √(v₀² + 2gh)] / g. Common fall times on Earth: 1 second = 4.9m, 2 seconds = 19.6m, 3 seconds = 44.1m, 5 seconds = 122.6m, 10 seconds = 490.5m.
What is the difference between free fall and terminal velocity?
Free fall assumes no air resistance — the object continuously accelerates at g. In reality, air resistance (drag) increases with speed. Terminal velocity is reached when drag force equals gravitational force, so acceleration becomes zero and speed remains constant. Terminal velocities vary greatly: skydiver (belly-down) ≈ 53 m/s (190 km/h), skydiver (head-down) ≈ 90 m/s (320 km/h), baseball ≈ 42 m/s (150 km/h), tennis ball ≈ 31 m/s (110 km/h), raindrop ≈ 9 m/s (32 km/h). Free fall calculations are accurate for short falls, dense objects, or vacuum conditions.
How accurate are the results from Free Fall Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.
How do I interpret the result?
Results are displayed with a label and unit to help you understand the output. Many calculators include a short explanation or classification below the result (for example, a BMI category or risk level). Refer to the worked examples section on this page for real-world context.