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Terminal velocity: the top speed of a falling object

Calculate the terminal velocity of a skydiver, ball or any falling object from its mass, drag coefficient, frontal area and altitude.

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Terminal velocity

118.8

Time to reach 99% of terminal velocity
14.3 s
Distance fallen by then
1,850
Air density used
0.905 kg/m³
Standard atmosphere: thinner air at altitude means a higher terminal velocity
Drag coefficient used
1.00

When falling stops getting faster

A falling object speeds up under gravity, but the faster it goes, the harder the air pushes back. Air drag grows with the square of the speed, so at some point it exactly balances the object’s weight. From then on the object falls at a constant speed, its terminal velocity:

vt = √(2 m g ÷ (ρ Cd A))

  • m is the mass, including clothing and equipment.
  • g is gravitational acceleration, 9.81 m/s².
  • ρ is the air density, which falls with altitude.
  • Cd is the drag coefficient, which depends on the shape.
  • A is the frontal area facing the airflow.

How to use the calculator

  1. Enter the mass and choose a shape. Typical drag coefficients are about 1.0 for a skydiver lying flat, 0.7 head down and 0.47 for a sphere. Choose “Other” to enter your own.
  2. Enter the frontal area. A skydiver in the belly-to-earth position presents about 7 to 8 sq ft; head down, only 2 to 3 sq ft.
  3. Enter the altitude. The calculator uses the standard atmosphere to estimate the air density there.

Worked example

A skydiver weighing 200 lb with gear, falling belly to earth (Cd 1.0) with 7.5 sq ft of frontal area at 10,000 ft:

  • Air density: 0.905 kg/m³, about 26% thinner than at sea level.
  • Terminal velocity: 118.8 mph (53.1 m/s).
  • 99% of that speed is reached after about 14.3 seconds, having fallen roughly 1,850 ft.

Tucking into a head-down position cuts both the area and the drag coefficient, and speeds of 150 to 200 mph become possible.

Why size matters

Mass grows with the cube of an object’s size, but area only with the square. A mouse can survive a fall that would kill a person, because its terminal velocity is only a few meters per second. A raindrop of 2 mm reaches about 6.5 m/s (15 mph), while hailstones the size of golf balls fall at 40 to 60 mph.

Limits

  • The formula assumes drag proportional to the square of the speed, which holds for most everyday objects in air. Very small or very slow objects, such as dust or fog droplets, follow Stokes’ law instead.
  • Drag coefficients change with speed, orientation and surface roughness. The values offered are typical, not exact.
  • The air density comes from the International Standard Atmosphere. Hot or humid air is less dense and gives a slightly higher terminal velocity.

Frequently asked questions

What is terminal velocity?

The speed at which air resistance on a falling object equals its weight, so it stops accelerating. It is vt = √(2mg ÷ (ρ Cd A)), where m is the mass, ρ the air density, Cd the drag coefficient and A the frontal area.

How fast does a skydiver fall?

About 120 mph in the belly-to-earth position and 150 to 200 mph head down. The calculator's example, a 200 lb skydiver with 7.5 sq ft of frontal area at 10,000 ft, gives 118.8 mph.

Why is terminal velocity higher at altitude?

Air is thinner higher up, so there is less drag at the same speed. At 10,000 ft the air density is about 0.905 kg/m³, 26% less than at sea level, so terminal velocity is about 16% higher.

How long does it take to reach terminal velocity?

In theory it is approached but never reached. With quadratic drag, a skydiver reaches 99% of terminal velocity after about 14 seconds and roughly 1,850 ft of fall in the default example.

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Results are estimates provided for information purposes. They do not replace professional advice.

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