s
Please enter a valid fall time (seconds).
Time the object has been falling (seconds)
Select the planetary body or enter Earth standard
kg
Enter mass to calculate kinetic energy at impact
💡 Free fall assumes no air resistance — valid in a vacuum and for short real-world drops. Results show distance, velocity, and optionally kinetic energy at impact.
Distance Fallen
—
Was this calculator helpful?
Sources & Methodology
Formulas verified against NIST Standard Reference Data and NASA planetary gravity constants.
NIST — Standard Acceleration of Gravity (g)
Official NIST value of standard gravity: gₙ = 9.80665 m/s². Used as reference for Earth standard value.
NASA — Planetary Fact Sheet
Surface gravity values for Moon (1.62 m/s²), Mars (3.72 m/s²), and Jupiter (24.79 m/s²) sourced from NASA NSSDC.
Methodology: Distance: d = (1/2) × g × t². Velocity at impact: v = g × t. Kinetic energy (if mass provided): KE = (1/2) × m × v². All calculations assume free fall from rest (initial velocity = 0) with no air resistance. Metric values converted to feet using 1 m = 3.28084 ft.
⏱ Last reviewed: April 2026
How to Calculate Free Fall Distance
Free fall distance is the vertical distance an object travels when dropped from rest under the influence of gravity alone, with no air resistance. It is one of the most fundamental calculations in physics and engineering, used in everything from amusement park ride design to structural safety analysis, skydiving, and space mission planning.
The Free Fall Distance Formula
d = (1/2) × g × t²
Where:
d = distance fallen (meters)
g = gravitational acceleration (9.81 m/s² on Earth)
t = fall time (seconds)
Example: An object falls for 4 seconds on Earth:
d = 0.5 × 9.81 × 4² = 0.5 × 9.81 × 16 = 78.48 meters
d = distance fallen (meters)
g = gravitational acceleration (9.81 m/s² on Earth)
t = fall time (seconds)
Example: An object falls for 4 seconds on Earth:
d = 0.5 × 9.81 × 4² = 0.5 × 9.81 × 16 = 78.48 meters
Reference: Free Fall Distance by Time on Earth
| Time (s) | Distance (m) | Distance (ft) | Velocity (m/s) | Velocity (mph) |
|---|---|---|---|---|
| 0.5 | 1.23 | 4.0 | 4.9 | 11.0 |
| 1 | 4.91 | 16.1 | 9.81 | 21.9 |
| 2 | 19.62 | 64.4 | 19.62 | 43.9 |
| 3 | 44.14 | 144.8 | 29.43 | 65.8 |
| 4 | 78.48 | 257.4 | 39.24 | 87.8 |
| 5 | 122.63 | 402.3 | 49.05 | 109.7 |
| 10 | 490.5 | 1,609 | 98.1 | 219.4 |
| 15 | 1,103.6 | 3,620 | 147.2 | 329.1 |
Why Distance Grows with the Square of Time
The t² term in the formula is key: falling for twice as long means falling four times as far, not twice as far. This is because gravity continuously accelerates the object — velocity increases linearly (v = g×t), but distance is the integral of velocity over time, giving the squared relationship. In the first second an object falls 4.9 m; in the next second it falls 14.7 m (because it was already moving at 9.81 m/s when the second second started).
Free Fall on Other Planets
The same formula applies on any planetary body — just substitute the local gravitational acceleration. On the Moon (g = 1.62 m/s²), an object dropped for 3 seconds falls only 7.3 meters, versus 44.1 meters on Earth. On Jupiter (g = 24.79 m/s²), that same 3-second fall covers 111.6 meters — 2.5 times farther than Earth despite the same time. This calculator supports Earth, Moon, Mars, and Jupiter.
Practical Uses of Free Fall Distance Calculations
- Safety engineering — calculating whether a falling object would harm workers below, and what safety nets or barriers are needed
- Skydiving and BASE jumping — estimating altitude lost during freefall before parachute deployment
- Structural inspection — determining impact velocity and energy when objects fall from scaffolding or cranes
- Amusement park ride design — calculating drop heights and timing for free-fall attractions
- Physics education — demonstrating Galileo's principle that all objects fall at the same rate regardless of mass
💡 Pro Tip: The formula d = ½gt² assumes the object starts from rest (zero initial velocity) and there is no air drag. For objects with an initial downward velocity, use d = v₀t + ½gt². For real-world drops from significant heights, terminal velocity (around 53 m/s for a human) limits actual fall distance.
Frequently Asked Questions
The free fall distance formula is d = (1/2) x g x t squared, where d is the distance in meters, g is gravitational acceleration (9.81 m/s squared on Earth), and t is the fall time in seconds. For example, after 3 seconds: d = 0.5 x 9.81 x 9 = 44.1 meters.
An object in free fall drops 4.905 meters (about 16.1 feet) in the first second on Earth. The calculation is d = 0.5 x 9.81 x 1 = 4.905 m. Note this is the total distance after 1 full second — the object is accelerating continuously throughout that second.
In 2 seconds, a free-falling object drops 19.62 meters (about 64.4 feet). The calculation is d = 0.5 x 9.81 x 4 = 19.62 m. Because distance grows with t squared, 2 seconds of fall covers exactly four times the distance of 1 second of fall.
In 3 seconds of free fall on Earth, an object drops 44.145 meters (about 144.8 feet, or nearly the height of a 14-story building). The formula gives d = 0.5 x 9.81 x 9 = 44.145 m. A skydiver falls this distance in the very first 3 seconds of a jump.
No — in a vacuum, all objects fall the same distance in the same time regardless of mass. Galileo famously demonstrated this at the Leaning Tower of Pisa. The free fall formula contains no mass term. In real air, heavier or more aerodynamic objects fall slightly faster because air resistance has less effect relative to their weight, but the ideal formula does not account for this.
The standard value of Earth's gravitational acceleration is g = 9.81 m/s squared (32.174 ft/s squared). The precise NIST value is 9.80665 m/s squared. Many textbooks use 9.8 or even 10 m/s squared for simplicity. This calculator defaults to 9.81 m/s squared, with a precise option of 9.807 m/s squared.
Rearrange the formula to solve for time: t = square root of (2d / g). For example, if you need to know how long it takes to fall 100 meters: t = sqrt(2 x 100 / 9.81) = sqrt(20.39) = approximately 4.51 seconds. Use the Free Fall Time Calculator on this site for that calculation.
The impact velocity in free fall is v = g x t, where t is the total fall time. After 3 seconds: v = 9.81 x 3 = 29.43 m/s (about 65.8 mph). Alternatively, you can find velocity from distance using v = square root of (2 x g x d). This calculator shows impact velocity for every calculation.
The Moon's surface gravity is only 1.62 m/s squared — about 16.5% of Earth's. After 3 seconds, an object falls only 7.3 meters on the Moon, versus 44.1 meters on Earth. This is why astronauts appear to bounce slowly on the Moon — every motion, including falling, takes much longer.
Kinetic energy at impact is KE = (1/2) x m x v squared, where m is object mass in kilograms and v is impact velocity in m/s. For a 70 kg person after 3 seconds: v = 29.43 m/s, KE = 0.5 x 70 x 866.1 = 30,313 joules (about 7.2 kilocalories). This calculator computes kinetic energy when you enter the object mass.
Related Calculators