Free Fall Calculator

What Is the Free Fall Calculator?

The Free Fall Calculator solves for any of the four key free fall variables: fall time, impact speed, height fallen, and initial velocity. Most free fall tools online only solve one direction (typically finding speed from height), which means you have to rearrange equations manually when the problem gives you a different set of known values. This calculator lets you pick what you want to find, enter what you know, and get all four variables at once with a full step-by-step breakdown. It also includes a gravity selector covering Earth, Moon, Mars, Jupiter, Venus, and Mercury, so you can compare how the same fall plays out under different gravitational fields. According to Khan Academy's kinematics reference, the free fall equations are a direct application of the SUVAT kinematic formulas with acceleration fixed at the local gravitational constant.

The Free Fall Equations

Free fall is governed by three kinematic equations applied with constant downward acceleration g. Taking downward as positive: v = u + g*t gives the impact velocity from initial velocity and time. h = u*t + 0.5*g*t^2 gives the height fallen in terms of initial velocity and time. v^2 = u^2 + 2*g*h connects velocity and height without requiring time. For an object dropped from rest (u = 0), these simplify to v = g*t, h = 0.5*g*t^2, and v = sqrt(2*g*h). The key insight is that all three equations describe the same motion: each one eliminates a different variable, so together they let you solve for any unknown given any two known quantities.

Does Mass Affect Free Fall Speed?

No. In ideal free fall with no air resistance, every object falls at the same acceleration regardless of mass. A 1 kg ball and a 100 kg ball dropped from the same height hit the ground at exactly the same time. This was first argued convincingly by Galileo in the 16th century and has since been verified to extraordinary precision in vacuum drop experiments. The reason is that although a heavier object experiences a larger gravitational force, it also has proportionally more inertia resisting that force, so the resulting acceleration is identical. In the real world with air, the aerodynamic drag force depends on cross-sectional area and drag coefficient, not directly on mass, which creates the observed difference between a feather and a coin falling in air. In a vacuum, both fall identically. Our free fall with air resistance calculator handles the more realistic scenario where drag significantly affects the outcome.

Gravity on Other Planets

Gravitational acceleration varies dramatically across the solar system. Earth has g = 9.81 m/s². The Moon has just 1.62 m/s², about one-sixth of Earth, which is why lunar astronauts could jump so high relative to their effort. Mars has g = 3.72 m/s², which is relevant for mission planners calculating lander descent rates and rover drop tests. Jupiter has the highest surface gravity of any planet at 24.79 m/s², about 2.5 times Earth. The practical effect is striking: a 10-metre fall that takes 1.43 seconds on Earth takes 3.51 seconds on the Moon but only 0.90 seconds on Jupiter. Impact speeds from the same height scale with the square root of g, so Jupiter impact speeds are sqrt(24.79/9.81) = 1.59 times higher than Earth for the same drop. Understanding these differences is essential for spacecraft lander design, extraterrestrial habitat engineering, and mission safety calculations. Our displacement calculator covers the general case of any kinematic displacement problem when you need to work with non-gravitational acceleration scenarios.

Free Fall vs. Terminal Velocity

Free fall acceleration is only truly constant in a vacuum. In the real atmosphere, air resistance creates a drag force that increases with the square of speed. As a falling object speeds up, drag increases until it exactly balances gravity, at which point the object stops accelerating and falls at a constant speed called terminal velocity. For a human in a stable skydiving position, terminal velocity is about 55 m/s (200 km/h). In a streamlined head-down position, it reaches about 90 m/s (320 km/h). For a raindrop, terminal velocity is only about 9 m/s due to the high drag-to-weight ratio of small water droplets. The free fall formulas in this calculator assume no air resistance, which is an excellent approximation for dense, compact objects falling relatively short distances (under 50 metres at typical speeds), but progressively underestimates fall time and overestimates impact speed for long falls or lightweight objects. For practical purposes, a person falling from a 10-storey building reaches about 40 m/s at impact, close to the free fall prediction, because they have not yet reached terminal velocity during the short duration of the fall.

Using Free Fall Calculations in Forensic and Safety Contexts

The relationship between fall height and impact speed is used extensively in workplace safety, forensic engineering, and accident reconstruction. The inverse calculation (finding height from measured or estimated impact speed) allows investigators to check whether a claimed fall height is consistent with observed evidence. The formula h = v^2 / (2*g) makes this straightforward: an impact speed of 10 m/s implies a fall height of 5.1 metres. Safety standards use these relationships to set minimum fall protection requirements: the UK HSE and OSHA both require fall protection for working heights above 2 metres in most contexts, a threshold chosen partly because falls above 2 metres reach impact speeds above 6 m/s (22 km/h) where serious injury risk rises sharply. Understanding the physics of free fall helps engineers design energy-absorbing systems (safety nets, fall arrestors, crumple zones) that reduce peak deceleration forces by extending the stopping distance.

Free Fall vs Weightlessness: A Common Confusion

One of the most frequently asked physics questions is whether astronauts in orbit experience zero gravity. They do not: the ISS is still about 400 km above Earth and experiences approximately 89 percent of Earth surface gravity at that altitude. The reason astronauts float is that they are in continuous free fall around the Earth. Free fall produces weightlessness not because gravity disappears but because everything in the environment falls together, removing the contact forces we experience as weight on the ground. This same principle applies to a dropped object in a lift: if the cable snaps and the lift is in free fall, everything inside floats because the lift floor is falling as fast as the objects inside it. Understanding this distinction is essential for orbital mechanics, spaceflight physiology, and for understanding why the free fall equations apply equally to an apple falling from a tree and to a spacecraft in orbit.

Accuracy and Limitations of the Free Fall Calculator

This calculator uses exact free fall equations with no air resistance: h = ½gt², v = gt, and v² = 2gh. Results are accurate for dense objects falling short distances in air, such as a steel ball dropped from 10 metres (where aerodynamic drag changes the result by under 1%). For light or large-surface objects (leaves, paper, raindrops) or falls over 50 metres, air resistance becomes significant and the drag-free model overpredicts speed and underpredicts fall time. The NASA guide to falling objects and drag explains the drag-dominated regime and when the terminal velocity limit applies. The gravity presets use standard published values: Earth 9.81 m/s², Moon 1.62 m/s², Mars 3.72 m/s², matching the NASA planetary fact sheet surface gravity figures.

The Most Common Free Fall Calculation Mistake

The most common mistake is using the impact speed formula (v = sqrt(2gh)) to find the time of fall, instead of the time formula (t = sqrt(2h/g)). The two formulas look similar but compute different things: one gives you the speed at impact, the other gives you the duration of the fall. A ball dropped from 20 metres hits the ground at 19.8 m/s after 2.02 seconds. Using v = sqrt(2 × 9.81 × 20) = 19.8 incorrectly as a time gives 19.8 seconds, which is 10 times too long. The Physics Classroom free fall equations guide presents all five kinematics equations side by side with the variable each solves for, which eliminates this confusion. Use this calculator to figure out both v and t simultaneously rather than selecting formulas manually.