Free Free Fall Calculator
Calculate the time, impact velocity, or drop height of an object falling freely from rest under gravity (g = 9.80665 m/s²), with the exact kinematic formulas shown for every result.
Object dropped from rest, no air resistance, g = 9.80665 m/s². Enter either the drop height or the fall time.
From height: t = √(2h/g), v = √(2·g·h). From time: v = g·t, h = ½·g·t². Multiply m/s by 3.6 for km/h. Air resistance is ignored, so impact speeds for long drops are upper bounds.
Quick answer
For an object dropped from rest (no air resistance), fall time is t = √(2h/g) and impact speed is v = √(2·g·h), where g = 9.80665 m/s². For example, dropping from h = 20 m gives t = √(2·20/9.80665) ≈ 2.020 s and v = √(2·9.80665·20) ≈ 19.81 m/s. If you know the time instead, use v = g·t and h = ½·g·t².
Formula & method
v = g · t and h = ½ · g · t²
- v — Impact velocity (m/s)
- h — Drop height / distance fallen (m)
- t — Fall time (s)
- g — Gravitational acceleration, 9.80665 m/s²
From a known fall time t, the impact speed grows linearly and the distance fallen grows with the square of time.
t = √(2h / g) and v = √(2 · g · h)
From a known drop height h, solve for the time to hit the ground and the impact speed. Note v = g·t holds in both directions.
Examples
- Input
- h = 20 m, dropped from rest
- Result
- t ≈ 2.0196 s, v ≈ 19.806 m/s
- Why
- t = √(2·20/9.80665) = √(4.0789) = 2.0196 s. v = √(2·9.80665·20) = √(392.27) = 19.806 m/s. Check: v = g·t = 9.80665 × 2.0196 ≈ 19.81 m/s.
- Input
- t = 3 s, dropped from rest
- Result
- v = 29.420 m/s, h = 44.130 m
- Why
- v = g·t = 9.80665 × 3 = 29.42 m/s. h = ½·g·t² = 0.5 × 9.80665 × 9 = 44.13 m. So after 3 s the object is moving at about 29.4 m/s (≈106 km/h) and has fallen 44.1 m.
- Input
- h = 100 m, dropped from rest
- Result
- t ≈ 4.5160 s, v ≈ 44.287 m/s
- Why
- t = √(2·100/9.80665) = √(20.394) = 4.516 s. v = √(2·9.80665·100) = √(1961.33) = 44.287 m/s ≈ 159 km/h, ignoring air resistance.
- Input
- t = 1.5 s, dropped from rest
- Result
- v = 14.710 m/s, h = 11.032 m
- Why
- v = g·t = 9.80665 × 1.5 = 14.71 m/s. h = ½·g·t² = 0.5 × 9.80665 × 2.25 = 11.032 m. A reaction-test or two-storey drop lands in roughly this time.
When to use this tool
- Estimating how long an object takes to fall and how fast it lands when dropped from a known height (cliffs, balconies, bridges).
- Physics homework and lab prep involving 1-D kinematics under constant gravity from rest.
- Quick safety or engineering sanity checks where you can neglect air resistance over a short drop.
- Converting between fall time and drop height for reaction-time experiments or simple projectile setups.
Common mistakes
- Forgetting that this model assumes the object starts from rest (initial velocity = 0). If it is thrown down or up, you must add the v₀·t and ½·g·t² terms separately.
- Ignoring air resistance: real objects reach a terminal velocity (about 53 m/s for a skydiver), so the calculated impact speed is only valid in a vacuum or for short, dense drops.
- Mixing units — using feet for height while g is in m/s². Keep everything in SI (metres, seconds) or convert first; the formulas here use metres.
- Using h = g·t² instead of h = ½·g·t². The factor of one-half is essential and halving it doubles your distance error.
Frequently asked questions
What is the formula for free fall velocity?
For an object dropped from rest, the impact velocity is v = g·t (from time) or v = √(2·g·h) (from height), where g = 9.80665 m/s². Velocity increases by about 9.81 m/s for every second of fall.
How long does it take to fall a given distance?
Use t = √(2h/g). For h = 10 m, t = √(2·10/9.80665) = √(2.039) ≈ 1.428 s. For h = 50 m it is about 3.19 s. Time grows with the square root of distance, so quadrupling the height only doubles the time.
Does mass affect how fast something falls?
No. In a vacuum, all objects fall with the same acceleration g regardless of mass — a feather and a hammer hit the ground together. Mass only matters in air, where air resistance and terminal velocity depend on shape, area, and density.
What value of g does this calculator use?
It uses g = 9.80665 m/s², the standard gravity defined by the CGPM. Local gravity varies slightly (about 9.78 at the equator to 9.83 at the poles), but 9.80665 is the accepted reference value for most calculations.
Does this account for air resistance?
No. These equations describe ideal free fall in a vacuum. In real air a falling body decelerates as it approaches terminal velocity (roughly 53 m/s for a belly-down skydiver), so actual impact speeds for long drops are lower than the calculated values.
How do I convert the impact velocity to km/h or mph?
Multiply m/s by 3.6 to get km/h, or by 2.237 to get mph. For example, the 19.81 m/s impact from a 20 m drop equals about 71.3 km/h or 44.3 mph.
Sources & references
- Wikipedia — Equations for a falling body
- HyperPhysics — Free Fall (Georgia State University)
- NIST — Standard acceleration of gravity (gₙ)
External references open in a new tab. We are independent and not affiliated with these organizations.
- ✓ Free to use
- ✓ No sign-up required
- ✓ Runs entirely in your browser — nothing is uploaded.
- ✓ Formula and method shown above
Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
Related tools
- Projectile Motion CalculatorScience & Engineering
- Kinetic Energy CalculatorScience & Engineering
- Potential Energy CalculatorScience & Engineering
- Acceleration CalculatorScience & Engineering
- Momentum CalculatorScience & Engineering
Embed this tool on your site
Free to embed, no sign-up. Paste this code where you want the free fall calculator to appear: