Physics · Classical Mechanics · Kinematics
Free Fall Calculator
Calculates the velocity, distance fallen, and time of flight for an object in free fall under gravity.
Calculator
Formula
v is the final velocity (m/s), v₀ is the initial velocity (m/s, positive downward), g is gravitational acceleration (m/s²), t is time elapsed (s), and d is the distance fallen (m). The three kinematic equations allow any unknown to be solved when two other quantities are known.
Source: Halliday, Resnick & Krane — Physics, 5th Edition; NIST standard gravitational acceleration g = 9.80665 m/s².
How it works
Free fall describes the motion of an object accelerating solely under gravity, with no thrust or significant aerodynamic drag. Near Earth's surface, gravitational acceleration is treated as constant at g = 9.80665 m/s² (the internationally defined standard value). This constant acceleration makes free-fall problems tractable with three linked kinematic equations that relate initial velocity, final velocity, elapsed time, and distance fallen.
The three governing equations are: v = v₀ + gt (velocity–time), d = v₀t + ½gt² (displacement–time), and v² = v₀² + 2gd (velocity–displacement). Given any two known quantities — for example time of fall or distance fallen — and an initial velocity, all remaining unknowns can be determined. This calculator accepts either time or distance as the known input and solves for the complementary set of outputs including final velocity and kinetic energy per unit mass at impact.
Practical applications span a wide range of fields: aerospace engineers model rocket stage separation and payload drops; safety engineers calculate impact velocities for fall-protection design; geologists estimate the depth of a shaft by timing a dropped stone; and physics educators use free-fall experiments as a foundational demonstration of Newton's laws. On other planets or the Moon, simply adjusting the gravitational acceleration input (e.g., 1.62 m/s² for the Moon, 3.72 m/s² for Mars) adapts all calculations instantly.
Worked example
Problem: A ball is dropped from rest from the top of a 44.1 m building. Find the time of fall and the impact velocity using Earth's standard gravity.
Step 1 — Identify knowns: Initial velocity v₀ = 0 m/s, distance d = 44.1 m, g = 9.80665 m/s².
Step 2 — Solve for time using v² = v₀² + 2gd first, then t:
v² = 0 + 2 × 9.80665 × 44.1 = 864.83 m²/s²
v = √864.83 = 29.41 m/s
Step 3 — Solve for time using v = v₀ + gt:
t = (v − v₀) / g = 29.41 / 9.80665 = 3.000 s
Step 4 — Verify distance:
d = ½ × 9.80665 × 3² = 0.5 × 9.80665 × 9 = 44.13 m ✓
Result: The ball takes 3.00 seconds to fall and strikes the ground at 29.41 m/s (≈ 105.9 km/h). Kinetic energy at impact per kilogram of mass = ½ × 29.41² ≈ 432.1 J/kg.
Limitations & notes
This calculator assumes no air resistance, meaning results are exact only in a vacuum. In practice, aerodynamic drag reduces terminal velocity and extends fall time, especially for light or large-surface-area objects. The standard gravitational acceleration of 9.80665 m/s² is an internationally defined constant; actual surface gravity varies from roughly 9.764 m/s² at the equator to 9.832 m/s² at the poles due to Earth's rotation and oblateness. For heights exceeding several kilometres, the decrease in g with altitude becomes non-negligible and requires an extended gravitational model. The distance-mode solver assumes the object is always moving downward (positive d); for upward throws with negative initial velocity, users should use the time-mode and compute the apex separately. Finally, relativistic effects are entirely negligible for any terrestrial free-fall scenario.
Frequently asked questions
What is free fall in physics?
Free fall is the motion of an object under the influence of gravitational force alone, with no other forces such as air resistance or thrust acting on it. Near Earth's surface, this produces a constant downward acceleration of approximately 9.81 m/s², causing speed to increase linearly with time and distance to increase with the square of time.
How long does it take an object to fall 100 metres?
Using d = ½gt² and solving for t gives t = √(2d/g) = √(200/9.80665) ≈ 4.52 seconds, assuming the object starts from rest and air resistance is neglected. The impact velocity would be approximately 44.3 m/s (about 159 km/h).
Does mass affect free fall time?
No — in the absence of air resistance, all objects fall at the same rate regardless of mass. This was famously demonstrated by Galileo and later confirmed by Apollo 15 astronaut David Scott on the Moon using a hammer and feather. Mass affects impact force and kinetic energy, but not the time or velocity of free fall.
How do I use this calculator for the Moon or Mars?
Simply change the gravitational acceleration input to the appropriate planetary value: 1.62 m/s² for the Moon, 3.72 m/s² for Mars, or 24.79 m/s² for Jupiter's surface. All three kinematic equations scale directly with g, so the calculator handles any body in the solar system without modification.
What is terminal velocity and why isn't it included here?
Terminal velocity is the constant speed an object reaches when aerodynamic drag equals gravitational force, which stops further acceleration. This calculator models idealised free fall without drag, so it does not compute terminal velocity. A separate drag-force calculator is needed to model realistic atmospheric falls for objects like skydivers or meteorites.
Last updated: 2025-01-15 · Formula verified against primary sources.