What is the core free fall velocity equation?

For an object dropped from rest (v0 = 0), downward velocity is: v = g · t = √(2 · g · h), where g is gravitational acceleration, t is fall time, and h is drop distance.

What is the free fall time of flight formula?

The time required for an object dropped from rest to fall distance h is: t = √(2 · h / g).

What is the free fall distance formula?

The distance fallen after elapsed time t is: h = 1/2 · g · t².

Does the mass or weight of an object affect its free fall acceleration or speed in a vacuum?

No. As demonstrated by Galileo Galilei and Apollo 15 astronaut David Scott's hammer-and-feather lunar test, all objects fall with identical gravitational acceleration regardless of mass (m·a = m·g => a = g).

How do you calculate free fall if the object is thrown downward with initial velocity v0?

With initial downward speed v0: v(t) = v0 + g·t, h(t) = v0·t + 1/2·g·t², and v² = v0² + 2·g·h.

How do you calculate apex height and time for an object thrown vertically upward?

For an object thrown upward with initial speed v0: time to peak apex is t_apex = v0 / g, maximum height gained is h_max = v0² / (2·g), and total round-trip flight time is t_total = 2·v0 / g.

How does gravity on the Moon, Mars, and Jupiter alter free fall times and impact speeds?

On the Moon (g = 1.62 m/s²), fall times are 2.46x longer and impact speeds 2.46x lower than on Earth. On Mars (g = 3.71 m/s²), fall times are 1.63x longer. On Jupiter (g = 24.79 m/s²), fall times are 37% shorter.

How is mechanical energy conserved during free fall?

Initial gravitational potential energy (Ug = m·g·h) converts entirely into kinetic energy (Ek = 1/2·m·v²). At any point, total mechanical energy is constant: E_total = m·g·y + 1/2·m·v² = m·g·h.

How do civil engineers, physics students, and amusement park designers use the Free Fall Calculator?

Amusement park engineers size drop tower brake run lengths, forensic investigators verify cliff fall timelines, and physics students verify kinematic homework problems.

⚡ 100% Free • Classical Vacuum Kinematics & Gravity Solver

Free Fall Calculator

Calculate free fall velocity (v = √(2gh)), fall duration (t = √(2h/g)), drop height (h = 1/2·g·t²), and kinetic energy under Earth, Moon, Mars, and custom gravities with the free Free Fall Calculator.

Free Fall Presets:

Calculation Mode

Drop Height (h) 100.0 m (328.1 ft)

Gravitational Field ($g$)

Object Mass (Optional for Energy) 10.0 kg (22.0 lbs)

Impact Velocity ($v$) 44.3 m/s (99.1 mph)

Fall Time ($t$) 4.52 s

Impact Velocity ($v = \sqrt{2gh}$)

44.3 m/s

99.1 mph • 159.5 km/h • Fall Duration: 4.52 s • Drop Height: 100.0 m

Fall Time ($t$)

4.52 s

Time to impact

Drop Height ($h$)

100.0 m

328.1 ft

Speed in mph & km/h

99.1 mph

159.5 km/h

Kinetic Energy ($E_k$)

9,807 J

Impact energy

Potential Energy ($U_g$)

9,807 J

Conserved energy

Average Fall Speed

22.1 m/s

$v_{\text{avg}} = h / t$

Step-by-Step Free Fall Kinematics & Energy Conservation Derivation

What is Free Fall in Classical Physics and Kinematics?

In classical Newtonian mechanics, free fall is the unconstrained vertical motion of a body acted upon solely by the fundamental force of gravity ($F_g = m g$), with zero opposing aerodynamic drag. In an ideal vacuum, all objects—regardless of their mass, shape, or density—accelerate downward at the exact same constant gravitational acceleration ($g = 9.80665\text{ m/s}^2$ on Earth).

The Core Mathematical Formulas for Classical Free Fall

Free Fall Variable	Formula (from Rest $v_0 = 0$)	Formula with Initial Velocity ($v_0$)
Impact Velocity ($v$)	$$v = \sqrt{2 g h} = g t$$	$$v = \sqrt{v_0^2 + 2 g h} = v_0 + g t$$
Time of Flight ($t$)	$$t = \sqrt{\frac{2 h}{g}} = \frac{v}{g}$$	$$t = \frac{-v_0 + \sqrt{v_0^2 + 2 g h}}{g}$$
Drop Distance ($h$)	$$h = \frac{1}{2} g t^2 = \frac{v^2}{2 g}$$	$$h = v_0 t + \frac{1}{2} g t^2 = \frac{v^2 - v_0^2}{2 g}$$
Kinetic Energy ($E_k$)	$$E_k = \frac{1}{2} m v^2 = m g h$$	$$E_k = \frac{1}{2} m (v_0^2 + 2 g h)$$

Planetary Gravity Comparison: Earth, Moon, Mars & Jupiter

How drop times from a 100-meter height vary across the solar system:

Earth ($g = 9.81\text{ m/s}^2$)

Fall Time: 4.52 s

Impact Speed: 44.3 m/s (99.1 mph)

Moon ($g = 1.62\text{ m/s}^2$)

Fall Time: 11.11 s ($2.46\times$ slower)

Impact Speed: 18.0 m/s (40.3 mph)

Mars ($g = 3.71\text{ m/s}^2$)

Fall Time: 7.34 s ($1.63\times$ slower)

Impact Speed: 27.2 m/s (60.9 mph)

Jupiter ($g = 24.79\text{ m/s}^2$)

Fall Time: 2.84 s ($37\%$ faster)

Impact Speed: 70.4 m/s (157.5 mph)

How to Use the Free Fall Calculator

1 Select Known Kinematic Variable

Choose whether you are solving from Drop Height ($h$), Fall Time ($t$), Final Velocity ($v$), or Initial Launch Speed ($v_0$).

2 Enter Physical Values & Units

Input drop height in meters/feet, time in seconds, or speed in $\text{m/s}$ or $\text{mph}$.

3 Select Gravitational Acceleration

Choose Earth ($9.807\text{ m/s}^2$), Moon, Mars, Venus, or Jupiter.

4 Review Velocity, Duration & Energy

Inspect calculated impact velocity, fall duration, mechanical kinetic energy, and live step-by-step mathematical proofs.

Problems Solved by the Free Fall Calculator

1. Amusement Park Drop Tower Sizing

Calculates exact maximum terminal drop velocities and free-fall durations before magnetic eddy-current brake engagement.

2. Forensic Fall Accident Reconstructions

Determines precise cliff and scaffolding fall impact velocities and elapsed flight times in accident analysis.

3. Physics Kinematics Verification

Instantly verifies homework and laboratory free fall experiments with step-by-step mathematical substitutions.

Key Features of the Free Fall Calculator

4-Way Algebraic Solver

Solves for any variable: Drop Height ($h$), Fall Time ($t$), Impact Velocity ($v$), or Initial Velocity ($v_0$).

Planetary Gravity Engine

Includes precise gravitational fields for Earth, Moon, Mars, Venus, Jupiter, and the Sun.

Conservation of Energy Proofs

Tracks the complete conversion of gravitational potential energy ($U_g = mgh$) into kinetic energy ($E_k = \frac{1}{2}mv^2$).

The Equivalence Principle: Why Free Fall is Pure Weightlessness

Albert Einstein's "happiest thought" and the foundation of General Relativity:

When an object is in free fall, every atom accelerates downward at the exact same rate ($a = g$). Because there is no upward normal contact force from a floor or scale ($F_N = m(g - a) = 0$), an observer inside a freely falling enclosure feels completely weightless. This fundamental equivalence between gravitational acceleration and inertial acceleration led Einstein to formulate General Relativity: gravity is not a traditional mechanical contact force, but the curvature of spacetime. The International Space Station (ISS) is not outside Earth's gravity ($g \approx 8.7\text{ m/s}^2$ in orbit); astronauts float because the station is in perpetual free fall around Earth.

Frequently Asked Questions

Comprehensive answers to common questions about free fall equations, gravity drop formulas, flight durations, and Apollo lunar tests.