Terminal Velocity Calculator
Enter an object's mass, frontal area, drag coefficient, and the air density to find its terminal velocity in metres per second — the steady speed where drag balances gravity.
The speed where falling stops accelerating
A falling object speeds up until air resistance matches its weight. From that point on it falls at a constant terminal velocity.
Use SI units
Mass in kilograms, area in square metres, and density in kg/m³ give a terminal velocity in metres per second — divide by 3.6 to read it as km/h.
What is terminal velocity?
The steady speed of a free fall
This terminal velocity calculator finds the maximum speed a falling object reaches once air resistance grows strong enough to cancel out gravity. When something is dropped, gravity pulls it down and it accelerates. The faster it goes, the harder the surrounding air pushes back, until the upward drag force exactly equals the downward weight. At that moment the net force is zero, acceleration stops, and the object keeps falling at one constant speed — its terminal velocity. The value depends on how heavy the object is, how much frontal area it pushes through the air, how streamlined its shape is, and how dense the fluid is. It is the number behind why a skydiver levels off near 53 m/s belly-to-earth and why a feather drifts down so slowly.
Enter the mass, cross-sectional area, drag coefficient, and fluid density to get the terminal velocity in metres per second instantly.
Terminal velocity is reached when the drag force equals the weight. Solving that balance for speed gives the square-root formula below, using standard gravity g = 9.80665 m/s².
v = √(2 × m × g / (ρ × A × Cd))Mass sits inside the square root, so doubling the mass raises the terminal velocity by only about 41% (a factor of √2). The same is true in reverse for area, drag coefficient, and fluid density in the denominator: a larger frontal area or a denser fluid pulls the terminal velocity down, but only by the square root of the change.
Take an 80 kg skydiver falling belly-to-earth, with a frontal area of 0.7 m², a drag coefficient of 1, in air of density 1.225 kg/m³.
Build the numerator
2 × 80 × 9.80665 = 1568.84 — twice the weight term in newtons.
Build the denominator
1.225 × 0.7 × 1 = 0.8575 — density times area times drag coefficient.
Divide and take the square root
1568.84 / 0.8575 = 1829.55, and √1829.55 ≈ 42.78 m/s (about 154 km/h) — the terminal velocity.
The formula is exact for steady drag, but a few real-world points are worth keeping in mind.
Constant drag, constant air, and the right units
This model assumes a fixed drag coefficient and a constant fluid density, whereas real air thins with altitude and the drag coefficient shifts as a body tumbles or changes posture. It ignores lift, wind, and the slow approach to the steady value — an object only nears its terminal velocity after falling a while. Keep units consistent: kilograms, square metres, and kg/m³ in, metres per second out. Divide the result by 3.6 to read it as km/h.