Terminal Velocity Calculator
Estimate terminal velocity using drag coefficient, cross-sectional area, mass, gravity, and fluid density. Choose a shape preset or custom values.
Terminal Velocity Calculator
Result will appear here...
What the terminal velocity calculator does
A falling object does not keep speeding up forever. The air pushes back harder the faster it goes, until that push matches its weight and the speed levels off. That top speed is the terminal velocity, and this calculator works it out.
You give it the object's mass, the area it presents to the airflow, its drag coefficient, the density of the fluid it falls through, and gravity. A shape menu fills in the drag coefficient for common objects so you do not have to look it up. Below is why terminal velocity exists, the equation behind it, and a worked example.
How to use it
- Pick a shape. Choosing a sphere, baseball, cube, and so on fills in a typical drag coefficient. Pick the closest match, or enter your own.
- Enter the mass and cross-sectional area. The area is the silhouette the object presents to the oncoming air, each with its own unit.
- Check the fluid density and gravity. They start at air at room temperature and Earth's gravity, and you can change either for water or another planet.
- Press Calculate for the terminal velocity, or Reset to clear it.
Why a falling object stops speeding up
When something falls, two forces are in play. Gravity pulls it down with a steady force, its weight. The fluid it moves through pushes back up with a drag force, and unlike weight, drag grows with speed, rising with the square of how fast the object is going.
So at the start, falling from rest, there is no drag and the object accelerates. As it speeds up, drag builds. At some speed the upward drag has grown until it exactly equals the downward weight. Now the forces cancel, there is no net force, and by Newton's first law the object stops accelerating and falls on at a constant speed. That balance point is the terminal velocity.
The equation it uses
The terminal velocity is found by setting the drag force equal to the weight and solving for the speed. The drag force is ½ρv²CdA and the weight is mg, and where they meet:
Vt = √( 2 m g ÷ ( ρ A Cd ) )
Here m is the mass, g is gravity, ρ is the density of the fluid, A is the cross-sectional area facing the flow, and Cd is the drag coefficient. Reading it tells the story: more mass means a higher terminal velocity, while a larger area, a higher drag coefficient, or a denser fluid all bring it down.
Drag coefficient, area, and fluid
The drag coefficient is a single number that captures how slippery a shape is. A streamlined body might sit near 0.04, a smooth sphere around 0.47, and a flat-faced cube above 1. The shape menu sets a typical value for you. Worth knowing is that this number is not perfectly fixed: it shifts a little with speed and flow conditions, so it is the least precise part of the calculation, and the result is best read as a close estimate rather than an exact figure.
The area is the cross-section the object presents head-on to the flow, the shadow it would cast on the ground if the light came from straight ahead. And the fluid density is what makes falling through water so different from air. Water is hundreds of times denser, so the same object reaches a far lower terminal velocity in water than in air, which is why a stone sinks gently rather than plummeting.
Units and precision
The calculator works in SI, so mass goes to kilograms, area to square metres, density to kilograms per cubic metre, and the terminal velocity comes out in metres per second, which you can then read in km/h, mph, knots, and more. Mass, area, density, and gravity each carry their own unit selector, and the default fluid is air at about 1.204 kg/m³.
Results are carried to several significant figures. As noted above, the real uncertainty here is physical, mostly in the drag coefficient, not in the arithmetic, so treat the answer as a solid estimate of the true terminal velocity.
A worked example: a falling baseball
Take a baseball: a mass of about 0.145 kg, a cross-sectional area of roughly 0.0043 m², and a drag coefficient of 0.3275 from the shape menu, falling through air at 1.204 kg/m³.
Putting those in, Vt = √( 2 × 0.145 × 9.81 ÷ ( 1.204 × 0.0043 × 0.3275 ) ) ≈ 41 m/s, which is about 148 km/h or 92 mph. So no matter how far you drop a baseball, it tops out near 90 mph, a useful sense of how air resistance caps a fall.
What makes terminal velocity higher or lower
The equation makes the levers clear, and they match what you see in the world. A heavier object has a higher terminal velocity, because more weight needs more drag to balance it, and more drag means more speed. This is why a skydiver in a tight head-first dive falls faster than one spread out flat: tucking in cuts the area, which raises the terminal velocity, while spreading out does the opposite.
A larger area or a higher drag coefficient lowers the terminal velocity, which is exactly what a parachute does, multiplying the area many times over so the balance is struck at a gentle, survivable speed. And a denser fluid lowers it too. For a typical person falling belly-down through air, terminal velocity lands around 55 metres per second, near 200 km/h, reached after roughly the first 10 seconds or 500 metres of fall.
Questions people ask
What is terminal velocity?
It is the fastest speed a falling object reaches, the point where the upward drag from the air balances the object's weight, so it stops accelerating and falls at a constant speed.
Do heavier objects have a higher terminal velocity?
Yes. For the same shape and size, more mass means a higher terminal velocity, since a larger weight needs more drag, and hence more speed, to balance it. This is different from free fall in a vacuum, where mass does not matter.
What is a skydiver's terminal velocity?
About 55 metres per second, near 200 km/h, in a flat belly-down position. Diving head first cuts the area and pushes it much higher, while a parachute drops it to a few metres per second.
Does it depend on the fluid?
Strongly. A denser fluid gives a lower terminal velocity, so the same object falls far slower through water than through air. Set the fluid density to match what the object is falling through.
Why does a parachute slow you down?
It hugely increases the area facing the airflow, which raises the drag at any given speed. The weight is then balanced at a much lower speed, so terminal velocity drops to something safe to land at.
References
A quick note on where the physics comes from. The drag equation and the terminal velocity that follows from balancing drag against weight are standard fluid mechanics, set out in NASA's Beginner's Guide to Aeronautics and in OpenStax's University Physics. The drag coefficients for common shapes are widely tabulated empirical values. The SI units throughout follow the US National Institute of Standards and Technology.
- NASA Glenn Research Center, Beginner's Guide to Aeronautics, Flight Equations with Drag. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/flight-equations-with-drag/
- OpenStax, University Physics Volume 1, Section 6.4, Drag Force and Terminal Speed. https://openstax.org/books/university-physics-volume-1/pages/6-4-drag-force-and-terminal-speed
- National Institute of Standards and Technology (NIST), Special Publication 811, Guide for the Use of the International System of Units (SI). https://www.nist.gov/pml/special-publication-811
Bibek Lal Karna is a PhD student and graduate teaching assistant at the University of Mississippi, with deep interests in theoretical and gravitational physics. He is also the founder of NRCC and is strongly engaged in scientific teaching and communication. At Eon Tools, he reviews physics tools.