Free Fall Calculator

Free Online Free Fall Calculator with Steps

This free fall calculator instantly finds the time, distance fallen, and final (impact) velocity of any object falling freely under gravity — a dropped ball, a coin, a skydiver before the parachute opens, or any object in an introductory physics free fall problem. Enter whichever value you already know — the height it falls from, the time it falls for, or the velocity it reaches — along with an optional initial velocity and a choice of gravity (Earth, Moon, Mars, or a custom value), and the calculator instantly solves for the rest using the standard constant-acceleration kinematics equations, shows a complete step-by-step solution, and draws a labeled diagram of the fall with real distance and velocity values marked directly on it.

Whether you're a physics student solving a free fall word problem for the first time, checking homework before a test, or just curious how long it would take an object to hit the ground from a certain height, this tool handles a simple drop (starting from rest) as well as an object thrown downward with an initial speed, and always shows exactly how each answer was calculated — not just the final number.

What Is Free Fall in Physics?

Free fall is the motion of an object falling under the influence of gravity alone, with air resistance ignored. Near Earth's surface, every object in free fall accelerates downward at the same constant rate, g ≈ 9.81 m/s², regardless of its mass — a heavier object and a lighter one dropped from the same height, in a vacuum, hit the ground at exactly the same time. This surprising fact was famously (if apocryphally) demonstrated by Galileo, and later confirmed on the Moon by Apollo 15 astronauts, who dropped a hammer and a feather side by side and watched them land together.

Because free fall involves constant acceleration, it's one of the simplest and most common applications of the equations of motion taught in every introductory physics course — and it's the direct one-dimensional case of the more general projectile motion, where an object also moves horizontally at the same time.

Free Fall Formulas

Given an initial (downward) velocity v0, gravitational acceleration g, and time t, the key free-fall equations are:

• Velocity after time t: v = v0 + g·t
• Distance fallen after time t: h = v0·t + ½·g·t²
• Velocity in terms of distance (no time needed): v² = v0² + 2·g·h
• Time to fall a given height (solved from the height formula): t = [−v0 + √(v0² + 2gh)] ÷ g
• Time to reach a given velocity: t = (v − v0) ÷ g
• For a simple drop, v0 = 0, which simplifies these to v = g·t, h = ½g·t², and v = √(2gh).

How to Solve a Free Fall Problem Step by Step

Every free fall problem, however it's phrased, can be solved using the same general approach:

• Step 1 — Identify which value is given: the height fallen, the time of the fall, or the final velocity — and which two you're being asked to find.
• Step 2 — Note the initial velocity: it's 0 for an object simply dropped, or a positive downward value if the object was thrown down.
• Step 3 — Choose the matching formula: h = v0t + ½gt² if solving from time, v² = v0² + 2gh if solving from velocity, or the rearranged quadratic if solving from height.
• Step 4 — Substitute the known values (all converted into meters, seconds, and m/s) and solve for the unknown quantity.
• Step 5 — Use the result to find any remaining quantities — for example, once time is known, velocity follows immediately from v = v0 + g·t.
• Step 6 — Double-check the answer makes physical sense: time and height should always come out positive, and the final velocity should always be greater than or equal to the initial velocity.

Why Every Object Falls at the Same Rate

In free fall (ignoring air resistance), the only force acting on an object is gravity, and Newton's second law tells us that acceleration = force ÷ mass. Since the force of gravity on an object is itself proportional to its mass (F = mg), the mass cancels out of the equation entirely — every object, heavy or light, accelerates downward at exactly the same rate g. This is why a bowling ball and a tennis ball, dropped together from the same height in a vacuum, land at the same instant, even though our everyday experience (where air resistance slows light objects like feathers and paper far more than heavy ones) often suggests otherwise.

Free Fall on Earth, the Moon, and Mars

The value of g depends entirely on the mass and radius of the planet or moon in question, which is why the same drop height produces very different fall times and impact velocities depending on where it happens. This calculator includes ready-made gravity presets for Earth (9.81 m/s²), the Moon (1.62 m/s², about one-sixth of Earth's), and Mars (3.72 m/s², about38% of Earth's), plus a custom option for any other value — useful for classroom problems, other planets, or simplified textbook values like g = 10 m/s².

Because gravity is so much weaker on the Moon, an object dropped from the same height falls roughly 2.5 times slower there than on Earth, and lands with a much lower impact velocity — exactly the kind of comparison this calculator makes easy by simply switching the gravity dropdown.

How to Use This Free Fall Calculator

First, choose what you already know from the dropdown: the height or distance the object falls, the total time it falls for, or the velocity it reaches by the end. Fill in that value in your preferred unit, and optionally set an initial (downward) velocity if the object wasn't simply dropped from rest — leave it at 0 for a standard drop. Pick Earth, Moon, or Mars gravity, or switch to Custom to enter any value of g.

The calculator instantly computes the distance fallen, time of fall, final velocity, and average velocity, all backed by a full step-by-step solution and a labeled diagram that marks the object's real distance and velocity at each quarter of the fall, alongside a distance-versus-time chart showing the same values plotted as a curve.

Worked Examples

Example 1 — a ball dropped from a 20 m building (v0 = 0): time to fall = √(2×20/9.81) = 2.02 s. Final velocity = 9.81 × 2.02 = 19.8 m/s.

Example 2 — a coin falls for 3 seconds from rest: distance = ½ × 9.81 × 3² = 44.1 m. Final velocity = 9.81 × 3 = 29.4 m/s.

Example 3 — an object hits the ground at 30 m/s after being dropped from rest: height = 30² ÷ (2×9.81) = 45.9 m, and time = 30 ÷ 9.81 = 3.06 s.

Example 4 — a ball thrown downward at 5 m/s from a 50 m cliff: time = [−5 + √(5² + 2×9.81×50)] ÷ 9.81 ≈ 2.72 s, and final velocity = 5 + 9.81×2.72 ≈ 31.7 m/s.

Free Fall vs. Projectile Motion

Free fall is really just the special, purely vertical case of the more general topic of projectile motion, where an object also has a horizontal velocity component that carries it sideways while gravity pulls it down. In pure free fall, there's no horizontal motion at all — the object moves only up and down (or, more precisely for a drop, only downward) along a single straight line. Anyone who has already mastered free fall calculations has effectively mastered the vertical half of every projectile motion problem too.

Real-World Applications of Free Fall

Free fall calculations show up constantly in physics, engineering, and everyday safety analysis:

• Construction and safety engineering — estimating the impact speed of a falling tool or object to design guardrails and safety nets.
• Skydiving and bungee jumping — modeling the initial seconds of a jump before air resistance or a parachute changes the motion.
• Drop testing — engineers use free fall equations to predict how hard a dropped phone, package, or component will hit the ground.
• Astronomy and planetary science — comparing how objects fall differently on the Moon, Mars, or other planets and moons.
• Elevator and amusement ride design — modeling brief free-fall segments in drop towers and other thrill rides.
• Basic ballistics and target-drop problems — finding how long a dropped object takes to fall a known distance.

Tips for Solving Free Fall Word Problems Faster

Always identify the given quantity first — height, time, or velocity — since that determines which of the three main equations to reach for. Remember that a simple 'dropped' object always starts with v0 = 0, while a 'thrown down' or 'thrown up' object has a nonzero initial velocity (thrown up problems use a negative v0 in the sign convention used here, since upward is opposite to the direction of fall). Keep units consistent — convert everything to meters and seconds before plugging into any formula, since g is defined in m/s². And remember the v² = v0² + 2gh shortcut whenever a problem gives velocity and asks for height, or vice versa, without mentioning time at all — it avoids having to find time as an intermediate step.