Why does a heavier object fall faster in air?

Weight scales with mass while drag depends on shape and area, so a denser, heavier object needs a higher speed before drag can match its weight. In a vacuum, with no drag, all objects fall at the same rate.

What drag coefficient should I use?

Typical values are about 0.47 for a sphere, 1.0 to 1.3 for a flat-plate or spread-eagle human, and 0.04 or less for a streamlined airfoil. Pick the coefficient that best matches your object orientation.

What fluid density goes in for air?

Use about 1.225 kg/m³ for dry air at sea level and 15 °C. Density drops with altitude and rising temperature, so high-altitude jumps reach higher terminal speeds; water is roughly 1000 kg/m³.

Does this formula assume the object has already reached terminal velocity?

Yes. It gives the equilibrium speed where drag equals weight, not the speed at an arbitrary moment during the fall. Reaching it takes time and altitude as the object accelerates and drag builds up.

Terminal Velocity Calculator

Mass

Cross-Sectional Area

m²

Drag Coefficient

Fluid Density

kg/m³

Terminal Velocity42.78 m/s

In km/h153.99 km/h

In mph95.69 mph

The Terminal Velocity Calculator finds the steady falling speed an object reaches once aerodynamic drag exactly balances its weight. Provide the object mass, its projected cross-sectional area, the drag coefficient for its shape, and the density of the fluid it falls through, and the tool returns the terminal speed in metres per second, kilometres per hour, and miles per hour. At this speed the net force is zero, so the object stops accelerating.

Formula

v = sqrt(2·m·g / (ρ·A·Cd))

m: Mass of the falling object (kg)
g: Gravitational acceleration, 9.80665 m/s²
ρ: Density of the surrounding fluid (kg/m³)
A: Projected cross-sectional area (m²)
Cd: Drag coefficient of the body shape

How it works

Enter the mass in kilograms, the projected frontal area in square metres, the dimensionless drag coefficient, and the fluid density (about 1.225 kg/m³ for air at sea level).
The calculator sets the gravitational pull mg equal to the quadratic drag force ½·ρ·A·Cd·v² and solves for the balancing speed v.
It evaluates v = sqrt(2mg / (ρ·A·Cd)) using standard gravity 9.80665 m/s² and converts the result to km/h and mph.

Worked example

A belly-to-earth skydiver of 80 kg with 0.7 m² frontal area, drag coefficient 1.0, in air of density 1.225 kg/m³.

Numerator = 2 · 80 · 9.80665 = 1569.06.
Denominator = 1.225 · 0.7 · 1.0 = 0.8575.
v = sqrt(1569.06 / 0.8575) = sqrt(1829.81) = 42.78 m/s.

About 42.78 m/s, which is roughly 153.99 km/h or 95.69 mph.

Frequently asked questions

Why does a heavier object fall faster in air?: Weight scales with mass while drag depends on shape and area, so a denser, heavier object needs a higher speed before drag can match its weight. In a vacuum, with no drag, all objects fall at the same rate.
What drag coefficient should I use?: Typical values are about 0.47 for a sphere, 1.0 to 1.3 for a flat-plate or spread-eagle human, and 0.04 or less for a streamlined airfoil. Pick the coefficient that best matches your object orientation.
What fluid density goes in for air?: Use about 1.225 kg/m³ for dry air at sea level and 15 °C. Density drops with altitude and rising temperature, so high-altitude jumps reach higher terminal speeds; water is roughly 1000 kg/m³.
Does this formula assume the object has already reached terminal velocity?: Yes. It gives the equilibrium speed where drag equals weight, not the speed at an arbitrary moment during the fall. Reaching it takes time and altitude as the object accelerates and drag builds up.

Related calculators

Kinetic Energy Calculator Force Calculator Momentum Calculator Density Calculator