Terminal Velocity Calculator
Find the terminal velocity of a skydiver or any object falling through air or water at high speed, then see how long it takes to get there.
🪂 What is Terminal Velocity?
Terminal velocity is the constant speed a falling object reaches when the drag force from the surrounding fluid grows until it exactly balances the object's weight. Before that moment the object accelerates, because gravity pulls harder than drag pushes back. As speed rises, drag rises with it, so the net downward force shrinks. When drag equals weight the net force is zero, the acceleration stops, and the object falls at a steady speed for as long as the conditions stay the same. This page covers the fast, high Reynolds number regime, where drag grows with the square of the speed.
The idea matters in many places. Skydivers and parachutists use it to understand how body position and canopy size change their fall rate. Engineers use it to size parachutes and drop packages, meteorologists use it to reason about how raindrops and hailstones fall, and sports scientists use it to compare balls and projectiles. Terminal speed also explains why a bowling ball and a sheet of paper fall so differently, and why a cat or a person can survive falls that a naive vacuum calculation would call impossible. The formula depends on four things: how heavy the object is, how much fluid it has to push aside (the area), how streamlined it is (the drag coefficient), and how dense the fluid is.
A few distinctions are easy to miss. First, this is not the same as Stokes law. For tiny or very slow particles in a viscous fluid, such as drizzle droplets, dust or silt, drag is proportional to speed instead of its square, and the Stokes law terminal velocity calculator is the right tool. Second, the drag coefficient is not a fixed number for an object: it depends on shape, orientation and the Reynolds number. Third, this calculator ignores buoyancy, which is negligible in air but matters in water. Finally, near and above about Mach 0.3 (roughly 100 m/s in air) compressibility starts to change the drag coefficient, so very fast results are estimates.
This calculator gives you the terminal velocity in three units with a drag equals weight check, and a second mode that models the whole approach from rest: the speed after any time, the percent of terminal speed reached, the distance fallen, and the times to reach 90 and 99 percent of the terminal speed. Each mode has its own chart.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Belly-to-Earth Skydiver at Sea Level
80 kg, Cd = 1.0, A = 0.7 m², sea level air (1.225 kg/m³)
Example 2 — Head-Down Dive (Small Area)
80 kg, Cd = 0.7, A = 0.3 m², sea level air
Example 3 — Raindrop-Like Sphere (3 mm Water Drop)
Sphere of radius 1.5 mm: m = 0.0000141 kg, A = 0.00000707 m², Cd = 0.5, sea level air
Example 4 — Bowling Ball
14 lb ball, about 22 cm across: A = 0.0366 m², Cd = 0.47, sea level air
Example 5 — Parachutist Under an Open Canopy
90 kg with equipment, effective Cd = 1.2, canopy area A = 25 m², sea level air
Example 6 — Speed and Distance After 10 Seconds
The Example 1 skydiver, t = 10 s from rest
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for terminal velocity?
With quadratic drag, terminal velocity is v_t = sqrt(2 m g / (rho Cd A)), where m is mass, g is gravity, rho is fluid density, Cd is the drag coefficient and A is the reference area. It comes from setting weight m g equal to drag 0.5 rho Cd A v squared.
What is the terminal velocity of a skydiver?
It depends on body position, mass and altitude. A common reference value is about 55 m/s (around 200 km/h or 120 mph) belly to earth. Enter your own mass, Cd and area: 80 kg, Cd 1.0 and 0.7 m2 at sea level gives 42.8 m/s with this calculator.
Why does a heavier object fall faster in air?
Weight grows with mass, but drag at a given speed depends on shape and area, not mass. A heavier object of the same shape needs a higher speed before drag equals its weight, so v_t is proportional to the square root of mass for fixed Cd and area.
How does air density change terminal velocity?
Terminal velocity is inversely proportional to the square root of density. In standard atmosphere air at 3000 m (0.909 kg/m3) a given skydiver falls about 16 percent faster than at sea level (1.225 kg/m3), and higher still at 10000 m (0.414 kg/m3).
How long does it take to reach terminal velocity?
The speed follows v(t) = v_t tanh(g t / v_t). It reaches 90 percent of v_t at t = (v_t/g) atanh(0.9), about 1.47 v_t/g, and 99 percent at about 2.65 v_t/g. For a 43 m/s skydiver that is about 6.4 s and 11.5 s.
How far do you fall before reaching terminal velocity?
The distance from rest is s(t) = (v_t squared / g) ln cosh(g t / v_t). Time mode computes it. For 80 kg, Cd 1.0, 0.7 m2 at sea level, a skydiver falls about 300 m in the first 10 seconds, instead of about 490 m with no drag.
What is a typical drag coefficient for a falling person?
Published skydiving estimates use a drag coefficient near 1.0 for a belly-to-earth position and about 0.7 head down. Because the reference area changes with posture too, only the product Cd times A really matters for the speed.
Does this calculator include buoyancy?
No. Buoyancy is ignored, which is fine in air where the object is hundreds of times denser than the fluid. In water or other dense fluids, use the effective weight (weight minus buoyant force) as the mass input for a better estimate.
When should I use Stokes law instead?
Use Stokes law for very small, slow objects such as fog droplets, dust or silt in a viscous fluid, where the Reynolds number is well below 1 and drag is linear in speed. This calculator is for fast, large objects where drag grows with the square of speed.
Is terminal velocity the same as free fall speed?
Free fall in a vacuum has no terminal velocity: speed increases without limit as g t. With air drag the speed levels off at v_t. The calculator shows the vacuum distance 0.5 g t squared next to the real distance for comparison.