Free Fall Calculator
Determine how far an object falls, its velocity on impact, and the time to reach the ground. Accounts for initial velocity and configurable gravity for different planets.
Free fall is motion under gravity alone, with no other forces acting (especially no air resistance). It's a classic introductory physics scenario because the math is elegantly simple: gravity provides constant acceleration g ≈ 9.81 m/s² on Earth, and standard kinematic equations describe everything. Galileo's famous experiment dropping objects from the Leaning Tower of Pisa demonstrated the key insight: in the absence of air resistance, all objects fall at the same rate regardless of mass.
In reality, air resistance matters for most everyday falls. A feather and a hammer fall together only in a vacuum — David Scott demonstrated this on the Moon in 1971 during Apollo 15. On Earth, terminal velocity (the speed at which air drag equals weight) limits how fast objects can fall. For a human in skydiving position: ~53 m/s (120 mph). For a feather: ~0.3 m/s. For a raindrop: ~9 m/s.
This calculator uses the idealized free-fall equations (no air resistance) appropriate for: short drops, dense objects, vacuum scenarios, and as a starting point for engineering analyses. For more accuracy with air resistance, the math becomes a differential equation requiring numerical solution.
Common applications: physics education, ballistics (initial trajectory analysis), accident reconstruction (height-of-fall calculations), elevator drop simulations, drop tests in engineering, and any situation where gravity is the dominant force during a short period.
Inputs
Downward initial velocity (0 for drop from rest)
Results
Fall Time
3.19 s
Impact Velocity
31.32 m/s
Distance
50.00 m
Free Fall Results
| Parameter | Value |
|---|---|
| Drop Height | 50.00 m (164.04 ft) |
| Fall Time | 3.1928 seconds |
| Initial Velocity | 0.00 m/s |
| Final Velocity | 31.32 m/s |
| Final Velocity (mph) | 70.06 mph |
| Final Velocity (km/h) | 112.76 km/h |
| Average Velocity | 15.66 m/s |
| Gravity Used | 9.81 m/s² |
| Formulas | d = v₀t + ½gt², v = v₀ + gt |
Formula
How to use this calculator
- Choose what to solve for: time/velocity from height, height from time, or velocity from time.
- Enter known values: height, time, or initial velocity.
- Gravity defaults to 9.81 m/s² (Earth). Change for other planets.
- Calculator assumes no air resistance — accurate for short, dense object falls.
- For long falls or light objects, real impact velocity is lower (terminal velocity).
- Energy conservation: v = √(2gh) for drops from rest.
Worked examples
Dropped object from skyscraper
**Scenario:** Object dropped from 300 m (~100-story building). Impact time and speed (no air resistance)? **Calculation:** t = √(2 × 300 / 9.81) = √(61.2) ≈ 7.82 s. v = 9.81 × 7.82 ≈ 76.8 m/s. **Result:** ~7.8 seconds to impact, theoretical speed ~76.8 m/s (172 mph). Real impact speed lower due to air resistance — for a typical dense object: ~50-60 m/s. For a feather or paper: drops to terminal velocity within seconds.
Throwing a ball straight up
**Scenario:** Ball thrown straight up at 25 m/s. How high does it go, and when does it return? **Calculation:** h_max = v₀²/(2g) = 625/19.62 ≈ 31.9 m. Time to peak: t = v₀/g = 25/9.81 ≈ 2.55 s. Total time up and down: 2 × 2.55 ≈ 5.1 s. **Result:** Ball rises ~31.9 m (~10 stories), peaks at 2.55 s, returns to hand 5.1 s after throw. Without air resistance, it returns at the same 25 m/s. Air resistance reduces both height and return speed.
Apollo 15 hammer-feather drop
**Scenario:** Astronaut drops hammer and feather from 1.6 m on Moon (g = 1.62 m/s²). Time to fall? **Calculation:** t = √(2 × 1.6 / 1.62) = √(1.975) ≈ 1.41 s. Both objects fall identically in vacuum. **Result:** Both hit lunar dust at ~1.41 s simultaneously — Galileo's prediction confirmed in 1971. On Earth, the feather would float down over many seconds due to air resistance. The Moon has no atmosphere, so vacuum-free-fall holds perfectly.
When to use this calculator
**Use free-fall calculations for:**
- **Educational physics**: introductory mechanics problems. - **Drop tests**: packaging, electronics, structural engineering. - **Ballistics (initial)**: projectile launch and trajectory. - **Accident reconstruction**: estimating fall heights. - **Geology**: rock-fall analysis. - **Sports**: dive analysis, BASE jumping, parachute timing. - **Space science**: lunar and Mars surface operations.
**When air resistance matters:**
- Light objects (feathers, paper, leaves). - Long falls (terminal velocity reached). - High speeds (drag ∝ v²). - Large cross-sections (parachutes, parafoils).
For these, use terminal velocity instead of free-fall speed, or numerical integration.
**Terminal velocity for humans:**
- Belly-first (spread out): ~53 m/s (120 mph). - Head-down: ~90 m/s (200 mph). - Free-fall world record: Felix Baumgartner (2012) reached 373.5 m/s from 38 km altitude (thin air).
**Skydiving phases:**
1. **Free-fall acceleration**: 0-12 s, reaching terminal velocity. 2. **Terminal velocity fall**: 12 s onward at ~53 m/s. 3. **Parachute deploy**: typically 800-1,000 m altitude. Decelerates from 53 to ~5 m/s in 2-3 s. 4. **Canopy descent**: ~5 m/s (12 mph) under parachute.
**Common applications:**
- **Forensics**: estimating fall height from injury patterns. - **Construction**: hard hat requirements based on potential drop heights. - **Climbing**: dynamic vs static rope behavior in falls (fall factor analysis). - **Drone/UAV**: emergency descent calculations. - **Bomb disposal**: trajectory calculations for safe disposal. - **Sports**: high diving (10 m platform, hits water at ~14 m/s).
**Fall factor (climbing):**
FF = fall distance / rope length
FF = 0.5 → moderate fall. FF = 1.0 → standard. FF = 2.0 → maximum, very dangerous.
Higher fall factors generate higher peak forces despite same fall distance.
**Energy considerations:**
PE = mgh (joules)
Falling 1 m converts: 9.81 J/kg. So 1 kg dropped 1 m delivers ~10 J on impact (about 2 nutritional calories). Sufficient to crack a thin glass.
A 1,000 kg car dropped from 10 m: PE = 98,100 J. Equivalent to ~100 kg TNT at impact — destructive.
**Air resistance models:**
For terminal velocity: v_t ≈ √(2mg / (ρAC_d))
Air density ρ ≈ 1.225 kg/m³ at sea level. Falls steeply with altitude (factor 2 by 5,500 m).
**Variable gravity (Earth):**
g changes slightly with: - **Latitude**: 9.78 at equator, 9.83 at poles (Earth's oblateness and rotation). - **Altitude**: −0.003 m/s² per km above sea level. - **Local geology**: density anomalies cause ~0.001 m/s² variations.
For most calculations, g = 9.81 m/s² is sufficient.
**Software:**
- **Physics simulators**: Algodoo, Universe Sandbox. - **MATLAB/Python (scipy.integrate)**: numerical solutions with air resistance. - **CFD packages**: for complex shape drag calculations. - **Drop test analysis tools** (DataPhysics, Endevco): commercial.
**Pitfalls:**
- **Ignoring air resistance**: significant for long/light falls. - **Using wrong gravity**: lunar or Martian conditions differ. - **Mixing units**: m vs ft, s vs ms. - **Assuming initial velocity is zero**: many problems involve launches. - **Free-fall vs projectile motion**: horizontal velocity component matters too. - **Confusing distance with displacement**: signs and directions matter.
Common mistakes to avoid
- Forgetting air resistance for long falls (significantly reduces impact speed).
- Assuming objects start from rest when they have initial velocity.
- Using wrong gravity (Moon vs Earth vs Mars).
- Mixing units (m vs ft, mph vs m/s).
- Confusing speed with velocity (direction matters in projectile motion).
- Treating terminal velocity as instant (takes 10-15 seconds for humans).
- Forgetting that all objects fall at same rate only in vacuum.
- Using free-fall equations for objects with significant air resistance (parachutes, leaves).