Calculate Free Fall Velocity

Online calculator and formulas for free fall velocity neglecting air resistance

Free Fall Velocity Calculator

Free fall without air resistance

Calculates fall velocity (v), fall time (t) and fall height (h) neglecting air resistance.

Standard gravitational acceleration: 9.80665 m/s²
m/s²
m
Result
Fall time:
Velocity:
Velocity:

Example Calculation

Example: Fall from 100m height
Problem:

An object falls freely from a height of 100 m (without air resistance). What are the fall time and impact velocity?

Given:
  • Fall height h = 100 m
  • Gravitational acceleration g = 9.81 m/s²
  • Find: Fall time t and velocity v
Solution:

1. Calculate fall time:

\[t = \sqrt{\frac{2h}{g}}\]
\[t = \sqrt{\frac{2 \times 100}{9.81}} = \sqrt{20.39} = 4.52 \text{ s}\]

2. Calculate impact velocity:

\[v = \sqrt{2gh}\]
\[v = \sqrt{2 \times 9.81 \times 100} = \sqrt{1962} = 44.3 \text{ m/s}\]
\[v = 44.3 \times 3.6 = 159.5 \text{ km/h}\]
Important notes
Air resistance: In reality, air resistance reduces the velocity
Vacuum: The formulas apply exactly only in a vacuum
Approximation: Good approximation for small heights and heavy objects
Gravity comparison

Earth: 9.81 m/s² | Moon: 1.62 m/s² | Mars: 3.71 m/s²

On the Moon, the same object would fall about 6 times longer!

Formulas for free fall

Free fall is uniformly accelerated motion under the influence of gravity. These formulas apply when air resistance is neglected.

Velocity after time

Velocity of a falling object after time t.

\[v = g \times t\]
v = Fall velocity [m/s]
g = Gravitational acceleration [m/s²]
t = Fall time [s]
Fall height after time

Distance traveled in free fall after time t.

\[h = \frac{1}{2} \times g \times t^2\]
Quadratic relationship between time and fall height.
Velocity after height

Final velocity after falling from height h.

\[v = \sqrt{2 \times g \times h}\]
Most important formula for impact velocities.
Fall time from height

Required time for fall from height h.

\[t = \sqrt{\frac{2h}{g}}\]
Rearrangement of the distance-time relationship for time.
Physical significance
  • All bodies fall equally fast in a vacuum (independent of mass)
  • The acceleration is constant and equals about 9.81 m/s² on Earth
  • Free fall is a special case of uniformly accelerated motion
  • In reality, the motion is influenced by air resistance

Gravitational acceleration of various celestial bodies

Gravitational acceleration varies significantly depending on the celestial body. This directly influences the fall velocity and fall time of objects.

Celestial Body Gravity [m/s²] Ratio to Earth
Earth 9.81 1.0
Moon 1.62 0.17
Mercury 3.70 0.38
Mars 3.71 0.38
Venus 8.87 0.90
Saturn 10.44 1.06
Uranus 8.69 0.89
Neptune 11.15 1.14
Jupiter 24.79 2.53
Sun 274.00 27.9
Pluto 0.62 0.06
Extreme examples

On the Moon:
A fall from 100m takes 11.1s
(on Earth: 4.5s)

On Jupiter:
The same fall takes only 2.8s
(almost twice as fast)

Caution

These values apply to the surface of the respective celestial bodies. Gas giants like Jupiter have no solid surface!


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