Free Fall Calculator
Time to fall, impact velocity and distance fallen — for Earth, Moon, Mars or any custom gravity.
Formulas
Fall time (with initial velocity u): t = (−u + √(u² + 2gh)) / g
Impact velocity: v = √(u² + 2gh)
Velocity after time t: v(t) = u + g·t
Distance fallen after time t: s(t) = u·t + ½·g·t²
How to use
- Enter the drop height above the landing surface.
- Enter an initial downward velocity (0 for a pure drop from rest).
- Optionally, enter a query time to get velocity and distance fallen at that instant.
- Pick gravity and press Calculate.
Physics behind free fall
In an ideal (vacuum) free fall, the only force on the object is gravity, giving a constant downward acceleration g. Because acceleration is constant, the standard kinematics (SUVAT) equations apply: v = u + gt, s = ut + ½gt², v² = u² + 2gh. Mass does not appear anywhere — the result is independent of mass.
In real life, air resistance adds a drag force that grows with speed. At "terminal velocity" the drag equals gravity and the object stops accelerating. For heavy, small objects falling short distances (a rock from a building), air resistance is negligible and the ideal formulas are very accurate.
Worked example
h = 10 m, u = 0, g = 9.80665 m/s²
t = √(2·10/9.80665) ≈ 1.428 s v = √(2·9.80665·10) ≈ 14.007 m/s
Common mistakes
- Using the wrong sign for u. Downward is positive in this tool.
- Forgetting that a falling body keeps accelerating — v keeps growing until impact.
- Using g = 10 when more precision is required.
Related tools
FAQs
How to calculate free fall time from height?
Drop something from rest and ignore air resistance, and the time to hit the ground is t = √(2h/g), where h is the drop height in metres and g ≈ 9.81 m/s². So a 20 m fall takes √(40/9.81) ≈ 2.02 seconds. The formula comes from h = ½gt² rearranged for t. The relationship is square-root, so doubling the height doesn't double the fall time — it only increases it by about 1.41 times. This is the cleanest free-fall problem and the starting point for almost every kinematics chapter.
How long does it take to fall 100 meters?
Using t = √(2h/g) with h = 100 m and g = 9.81 m/s², you get t = √(200/9.81) ≈ 4.52 seconds. That assumes no air resistance, which is fine for a heavy object dropped a short distance but breaks down for things like feathers or paper. By the time it lands, the object would be moving at v = gt ≈ 44.3 m/s, or roughly 160 km/h. Real falling humans hit terminal velocity around 53 m/s due to drag, so 100 m is just about long enough to start saturating that limit.
How do I use free fall velocity from height calculator?
Drop something from height h with no initial velocity, and the speed at the bottom is v = √(2gh). For h = 50 m, that gives v = √(2 × 9.81 × 50) ≈ 31.3 m/s. Same answer comes from energy conservation: mgh = ½mv², so v = √(2gh). The mass cancels, which is why a feather and a hammer fall the same way in vacuum — Apollo 15 actually demonstrated this on the Moon. Air resistance is what changes things on Earth, and the calculator only handles the idealised case.
How to calculate height from fall time?
If you know how long something fell from rest, the height comes out as h = ½gt² with g = 9.81 m/s². A 3-second drop covers h = 0.5 × 9.81 × 9 ≈ 44.1 m. The relationship is quadratic in time: doubling the fall time quadruples the height covered. This is also the formula behind that classic physics demo where you drop a ruler and the catch distance tells you reaction time. Just remember the formula assumes still air and no initial velocity — anything else needs the full SUVAT toolkit.
Does mass affect free fall time?
In a vacuum, mass has zero effect on fall time. A bowling ball and a marble dropped together hit the floor simultaneously, because gravity gives every object the same acceleration g, regardless of mass. This is the equivalence principle, tested famously by Galileo (perhaps apocryphally from the Tower of Pisa) and confirmed by every careful experiment since. In real air, mass does matter indirectly because heavier objects have more inertia relative to drag, so they reach higher speeds before air resistance balances gravity. But in any free-fall calculator that ignores air, mass simply doesn't enter the formulas.
How do I use free fall calculator with initial velocity?
When the object starts with some initial velocity u (positive for upward, negative for downward), use the kinematic equations s = ut + ½gt² and v = u + gt. Take care with signs: if up is positive, then g is −9.81 m/s². For a ball thrown downward at 5 m/s from a 30 m height: 30 = 5t + 4.9t², solved for t ≈ 2.0 s. The calculator handles the algebra, but you choose the convention. Free-fall problems with initial velocity are just SUVAT problems where the acceleration happens to be gravity.
What gravity value to use for free fall?
Use g = 9.80665 m/s² for the standard acceleration of gravity, though 9.81 m/s² is the everyday working value. Some textbooks round to 9.8 or even 10 m/s² for clean arithmetic in introductory problems — always check what the question expects. Real local g varies slightly: about 9.78 m/s² at the equator, 9.83 m/s² at the poles, due to Earth's rotation and slightly oblate shape. Altitude matters too, but only by tiny amounts unless you're at orbital height. For everyday free-fall problems on Earth's surface, 9.81 m/s² is plenty accurate.