Free Fall Physics Calculator
Solve 1D gravitational free fall kinematics for time of fall, impact velocity, drop height, and kinetic energy under vacuum conditions. Switch between SI Metric (meters, m/s, Joules) and US Customary (feet, ft/s, mph, ft·lbf) units or test gravity on Earth, the Moon, and Mars.
Kinematic & Gravity Parameters
Free Fall Kinematic Solution Impact KE: 1,961.3 J
Impact speed equals 159.43 km/h (99.07 mph or 145.30 ft/s) from a 100.00 m (328.08 ft) drop.
Instantaneous Free Fall Trajectory Table (Time Intervals to Impact)
| Elapsed Time (s) | Distance Fallen | Remaining Height | Velocity (m/s) | Velocity (ft/s) | Speed (mph / km/h) |
|---|
Free Fall Physics Formulas (1D Uniform Acceleration)
In ideal free fall (neglecting atmospheric air resistance), an object accelerates downward at a constant gravitational rate g (standard Earth gravity g₀ = 9.80665 m/s² = 32.17405 ft/s²) regardless of its mass. Taking downward displacement h and downward velocity as positive:
2. Fall Time from Height: t = (v_f − v₀) / g = [ −v₀ + √(v₀² + 2 × g × h) ] / g
3. Drop Height from Time: h = (v₀ × t) + (0.5 × g × t²)
4. Drop Height from Velocity: h = (v_f² − v₀²) / (2 × g)
5. Impact Kinetic Energy: KE = 0.5 × m × v_f² = (0.5 × m × v₀²) + (m × g × h)
Illustrative Example
Scenario (Illustrative): A 2.0 kg steel sphere is dropped from rest (v₀ = 0 m/s) from a 100 m (328.08 ft) tower under standard Earth gravity (g = 9.80665 m/s²):
- Final Impact Velocity (v_f):
√(0² + 2 × 9.80665 × 100) = √1961.33 = 44.29 m/s (145.30 ft/s | 99.07 mph | 159.43 km/h) - Time of Fall (t):
44.2869 / 9.80665 = 4.516 seconds - Average Velocity (v_avg):
(0 + 44.2869) / 2 = 22.14 m/s - Impact Kinetic Energy (KE):
0.5 × 2.0 kg × (44.2869 m/s)² = 1,961.33 Joules (1,446.6 ft·lbf)
How to Use This Free Fall Calculator
- Select Your Known Variable: Choose whether you are starting with a known Drop Height (h), a stopwatch Fall Time (t), or a target Impact Velocity (v_f).
- Choose SI Metric or US Customary Units: Toggle between Metric (
m,m/s,kg) and US Customary (ft,ft/s,lb) in the top right. - Pick a Gravitational Environment: Select Earth Standard (
9.80665 m/s²), Textbook Earth (9.80 m/s²), the Moon, Mars, Jupiter, or enter a custom acceleration value. - Inspect the Step-by-Step Substitution & Table: Review the substituted equations, the parabolic vs. linear trajectory graph, and the 10-step time interval table.
Frequently Asked Questions
Does a heavier object fall faster than a lighter object in free fall?
In a vacuum (pure free fall without air drag), all objects accelerate at the exact same gravitational rate g regardless of their mass—famously demonstrated on the Moon during Apollo 15 when Commander David Scott dropped a 1.32 kg geologic hammer and a 0.03 kg falcon feather from 1.6 meters and both hit the lunar surface simultaneously after 1.40 seconds. Mass only changes the object's impact kinetic energy and momentum, not its vacuum fall time or speed.
How does air resistance (terminal velocity) affect real-world drops in Earth's atmosphere?
For dense, compact objects dropped over short to moderate heights (such as a stone or steel ball dropped under 30 to 50 meters), vacuum kinematics closely match real measurements. Over longer falls or with lightweight objects, aerodynamic drag opposes gravity until the object reaches terminal velocity (roughly 54 m/s or 120 mph for a belly-to-earth skydiver).
Why do some physics textbooks use g = 9.8 m/s² instead of 9.80665 m/s²?
Earth's surface gravity varies slightly with latitude and elevation (from about 9.780 m/s² at the equator to 9.832 m/s² at the poles). International standards define standard gravity as g₀ = 9.80665 m/s², while introductory physics courses often round to 9.80 m/s². You can switch between both in the Gravitational Environment dropdown above.