Free Fall Calculator

The Physics of Free Fall

Free fall is motion under gravity alone — no air resistance, no other forces. It's one of the oldest studied problems in physics, famously associated with Galileo's (likely apocryphal) Leaning Tower of Pisa experiment showing that heavier and lighter objects, absent air resistance, hit the ground at the same time.

$$h(t) = h_0 + v_0 t - \frac{1}{2} g t^2 \qquad v(t) = v_0 - g t$$

Negative velocity means moving downward. Falling time comes from solving $h(t) = 0$ for $t$ using the quadratic formula, keeping the positive root.

Standard Gravity — Why $g$ Isn't Perfectly Constant

This calculator defaults to $g = 9.8 \, \text{m/s}^2$, the commonly used approximation for Earth's surface gravity (the precise standard value is 9.80665 m/s²). Actual local gravity varies slightly — by roughly 0.5% — with latitude and altitude, since Earth isn't a perfect sphere and is slightly flattened at the poles. For everyday problems this variation is negligible, but it's why more precise scientific work specifies the exact gravitational acceleration for a given location.

Dropped vs. Thrown

Set initial velocity to 0 for a simple drop. A positive initial velocity launches the object upward first — it decelerates, momentarily stops at its peak (at $t = v_0/g$), then falls back down and continues past the release point to the ground. Total falling time is measured from release, so it's longer than a simple drop from the same height.

Why Impact Speed Matters More Than Height Alone

Impact kinetic energy is $KE = \frac{1}{2} m v^2$ — proportional to the square of speed, not height directly. Doubling the drop height only increases impact speed by about 41% ($\sqrt{2}$), but that still means a 100% increase in kinetic energy, which is why even modest increases in fall height meaningfully increase impact severity.

Worked Example: Dropped from 20 Meters

For a simple drop ($v_0 = 0$) from a height of 20 m using $g = 9.8 \, \text{m/s}^2$: falling time is $t = \sqrt{2h_0/g} = \sqrt{40/9.8} \approx 2.02$ s, and impact speed is $v = g t \approx 19.8$ m/s (about 71 km/h). Kinetic energy per kilogram of mass at impact is $\frac{1}{2}v^2 \approx 196$ J/kg — multiply by the object's actual mass in kg to get total impact energy in joules.

How Real Air Resistance Changes the Picture

This calculator's equations assume a vacuum — no drag. In reality, air resistance grows with speed and eventually balances gravity at an object's terminal velocity, after which it stops accelerating entirely. For dense, compact objects falling modest distances (a dropped tool, a ball tossed from a balcony), air resistance is small enough that the vacuum equations stay a good approximation. For light or large-surface-area objects (a sheet of paper, a feather, a skydiver in freefall) or very long falls, drag dominates and these formulas will overestimate both speed and impact energy.

A Brief History of Free Fall Physics

Aristotle's view — that heavier objects fall faster than lighter ones, roughly in proportion to their weight — dominated Western thinking for nearly 2,000 years. Galileo Galilei challenged this in the late 1500s and early 1600s, arguing on theoretical grounds (and reportedly, though this specific account is disputed by historians, via a demonstration from the Leaning Tower of Pisa) that all objects fall at the same rate regardless of mass, in the absence of air resistance. Galileo's careful experiments rolling balls down inclined planes — a way of "diluting" gravity's effect to make it measurable with the timekeeping tools available at the time — let him establish that falling distance increases with the square of time, the same relationship this calculator's equations are built on. Isaac Newton later placed Galileo's empirical findings on a rigorous theoretical footing with his law of universal gravitation in 1687, explaining exactly why gravitational acceleration is independent of an object's mass. The famous confirmation of Galileo's claim in the total absence of air came in 1971, when Apollo 15 astronaut David Scott dropped a hammer and a feather simultaneously on the airless Moon, and they struck the surface at the same instant.

Common Free Fall Mistakes

Assuming heavier objects fall faster is the most persistent misconception, rooted in everyday experience with air resistance rather than gravity itself — in a vacuum, a hammer and a feather fall identically, as the Apollo 15 demonstration showed. Forgetting to account for initial velocity when an object is thrown rather than simply dropped is another common error, since the same time-squared relationship for distance only applies cleanly to objects starting from rest. Mixing up average speed and impact (final) speed is a third — free-falling objects accelerate continuously, so the speed at impact is always higher than the average speed over the whole fall.

Free Fall Terms You Should Know

Standard Gravity (g) — the standardized value of gravitational acceleration near Earth's surface, approximately 9.8 meters per second squared.

Terminal Velocity — the maximum speed a falling object reaches when air resistance grows large enough to balance the force of gravity, after which it stops accelerating.

Kinetic Energy — the energy an object has due to its motion, which for a falling object increases as its speed increases.

Vacuum — a space with no air or other matter to create drag, the idealized condition free-fall equations like these assume.