Free Fall Calculator

Quick Presets

Solve For

Initial Velocity v₀

m/s

Distance h

Time t

s

Final Velocity vf

Gravity g

m/s²

Select what to solve for, fill in the known values, and get instant results.

What Is Free Fall?

Free fall is the motion of a body subject only to gravitational force — with no air resistance, no thrust, and no other forces. In a vacuum, Galileo's principle holds: all objects fall at the same rate regardless of mass, with constant acceleration g ≈ 9.81 m/s² near Earth's surface.

Real-world falls in air are modified by drag — as the object speeds up, air resistance increases until it equals gravity, at which point the object reaches terminal velocity and stops accelerating.

h = ½gt²

Distance from rest

vf = gt

Final velocity from rest

g = 9.81

m/s² on Earth

Free Fall Equations (Vacuum)

Equation	Solves for	Requires
h = v₀t + ½gt²	Distance h	v₀, t, g
vf = v₀ + gt	Final velocity vf	v₀, t, g
vf² = v₀² + 2gh	vf (no t needed)	v₀, h, g
t = (−v₀ + √(v₀²+2gh))/g	Time t	v₀, h, g

Air Resistance & Terminal Velocity

When air drag is included, the drag force is Fd = ½ρCdAv². At terminal velocity, Fd = mg, giving:

vt = √(2mg / (ρ·Cd·A))

The velocity as a function of time (starting from rest) is:

v(t) = vt · tanh(g·t / vt)

For a typical skydiver (m = 75 kg, Cd = 1.0, A = 0.7 m²) terminal velocity ≈ 55 m/s (198 km/h). In head-down dive position (Cd ≈ 0.3, A ≈ 0.3 m²), it can exceed 90 m/s.

Fall Time Reference Table

Height	Fall Time (Earth)	Impact Speed	Fall Time (Moon)
1 m	0.45 s	4.4 m/s	1.11 s
5 m	1.01 s	9.9 m/s	2.49 s
10 m	1.43 s	14.0 m/s	3.51 s
50 m	3.19 s	31.3 m/s	7.86 s
100 m	4.52 s	44.3 m/s	11.12 s
1 km	14.28 s	140 m/s	35.15 s

* Vacuum, starting from rest

Worked Examples

Example 1 — Drop from 100 m (Earth, vacuum)

Given: h = 100 m, v₀ = 0, g = 9.81

t = √(2h/g) = √(20.39) = 4.52 s

vf = g·t = 9.81×4.52 = 44.3 m/s

Example 2 — Eiffel Tower (330 m)

Given: h = 330 m, v₀ = 0, g = 9.81

t = √(660/9.81) = 8.20 s

vf = 9.81×8.20 = 80.4 m/s (289 km/h)

Example 3 — Moon 100 m drop

Given: h = 100 m, g = 1.62 m/s²

t = √(200/1.62) = 11.12 s

vf = 1.62×11.12 = 18.0 m/s

Example 4 — Skydiver terminal velocity

m=75kg, Cd=1.0, A=0.7m², ρ=1.225

vt = √(2×75×9.81/(1.225×1.0×0.7))

vt ≈ 54.9 m/s (197 km/h)

Frequently Asked Questions

Free fall is motion under gravity alone, with no other forces (like air resistance) acting on the object. In a vacuum, all objects fall with the same acceleration g ≈ 9.81 m/s² on Earth, regardless of their mass. The key equations are h = ½gt² and vf = gt (starting from rest).

In a vacuum (true free fall), mass has no effect — all objects fall at the same rate. Galileo demonstrated this at the Leaning Tower of Pisa. In air, heavier dense objects fall faster because they have more weight relative to their air resistance, but mass itself is not the determining factor.

Terminal velocity is the maximum speed reached when gravity equals air resistance. At this point acceleration becomes zero. For a human skydiver it is about 55 m/s (200 km/h) in spread-eagle position. Formula: vt = √(2mg/(ρCdA)).

A feather has very low mass but a relatively large cross-sectional area, giving it a low terminal velocity. Air resistance slows it quickly. In a vacuum (no air), a feather and a rock fall at exactly the same rate — proven by astronaut David Scott on the Moon in 1971.

In a vacuum on Earth (g = 9.81 m/s²), starting from rest: t = √(2h/g) = √(200/9.81) ≈ 4.52 seconds. The impact speed would be vf = g×t ≈ 44.3 m/s (159 km/h).

Starting from rest in a vacuum on Earth: vf = g×t = 9.81 × 3 ≈ 29.4 m/s (106 km/h). The distance covered is h = ½×g×t² = ½×9.81×9 ≈ 44.1 m.

Switch to Advanced mode and enter the object's mass (kg), drag coefficient Cd (0.47 for a sphere, ~1.0 for a skydiver spread-eagle), cross-sectional area A (m²), and air density ρ (1.225 kg/m³ at sea level). The calculator uses v(t) = vt×tanh(g×t/vt).

Use g = 9.81 m/s² for most Earth calculations. For high-precision work, g varies from 9.764 m/s² at the equator to 9.832 m/s² at the poles. Use the planet presets for Moon (1.62), Mars (3.71), or Jupiter (24.79 m/s²).

Step-by-Step Solution