Terminal Velocity Calculator
Find how fast a falling object stops speeding up, once air drag balances gravity. Enter mass (kg or lb), cross-sectional area (m² or ft²), a drag coefficient, and air density to get terminal velocity in m/s, mph, and km/h.
Example: with Mass 80 · Mass unit kg (kilograms) · Cross-sectional area 0.5 · Area unit m² (square meters) · Drag coefficient (Cd) Skydiver, belly-to-earth (1.0) → Terminal velocity: 50.61 m/s (113.2 mph).
- In mph and km/h113.2 mph / 182.2 km/h
- Comparable toBelly-to-earth skydiver range (about 120 mph)
Computed by the calculator below using its default values. Change any input to see your own numbers.
Terminal velocity v = √(2mg / (ρ·A·Cd)). It climbs with mass and drops with area, drag coefficient, and air density — which is why a spread-eagle skydiver falls slower than a head-down one.
What terminal velocity actually is
As an object falls, gravity pulls it down while air pushes back with a drag force that grows with the square of speed. Early in the fall gravity wins and the object accelerates. But drag climbs fast, and at some speed the two forces cancel. From then on the net force is zero, acceleration stops, and the object coasts at a steady speed — its terminal velocity.
Setting drag equal to weight and solving gives v = √(2mg / (ρ·A·Cd)). Heavier objects fall faster because weight scales with mass, while the drag they must overcome depends on their frontal area and shape, not their mass.
Why shape and posture change the number
The drag coefficient Cd and the cross-sectional area A capture how bluff or streamlined an object is and how much of it faces the wind. A skydiver belly-to-earth presents a large area with a Cd near 1.0 and settles around 120 mph. Tuck into a head-down dive and both area and Cd drop, so terminal velocity climbs past 150 mph.
Air density matters too. It falls with altitude, so the same skydiver reaches a higher terminal speed high up than near the ground. That is why speed records are set by jumping from the stratosphere, where thin air offers little resistance.
How it’s calculated
v = √(2·m·g / (ρ·A·Cd)) in SI: mass in kg, g = 9.80665 m/s², air density ρ in kg/m³ (1.225 at sea level, 15 °C), area A in m². Pounds convert at 1 lb = 0.45359237 kg; 1 ft² = 0.09290304 m². Preset drag coefficients: skydiver belly-to-earth 1.0, head-down 0.7, smooth sphere 0.47. Result shown in m/s, then mph (÷0.44704) and km/h (×3.6).
Assumes constant air density and a constant drag coefficient. It ignores lift, spin, Mach and compressibility effects, and the drop in density with altitude, so real high-altitude speeds run higher.
Terminal velocity of familiar things
| Object | Terminal speed | Approx. mph |
|---|---|---|
| Raindrop (2 mm) | ≈ 6.5 m/s | ≈ 15 mph |
| Ping-pong ball | ≈ 9 m/s | ≈ 20 mph |
| Baseball | ≈ 33 m/s | ≈ 74 mph |
| Skydiver, belly-to-earth | ≈ 54 m/s | ≈ 120 mph |
| Skydiver, head-down | ≈ 76 m/s | ≈ 170 mph |
Typical published values; terminal speed depends on mass, frontal area, shape, and air density.
Common mistakes
- Forgetting that area and drag coefficient go together — a small Cd with a large area can still fall slowly.
- Using weight in pounds-force as mass without converting to kilograms first.
- Assuming heavier always means much faster — terminal speed grows only with the square root of mass.
- Expecting a single number at all altitudes; thinner air high up raises terminal velocity.
Frequently asked questions
What is the terminal velocity formula?
v = √(2mg / (ρ·A·Cd)): mass times g times two, divided by air density times frontal area times the drag coefficient, all under a square root. In SI the answer comes out in meters per second.
Why do heavy and light objects fall at different speeds in air?
In a vacuum they fall together, but air drag depends on area and shape, not mass. A heavier object of the same size must reach a higher speed before drag balances its greater weight, so it falls faster.
What drag coefficient should I use?
Use about 1.0 for a skydiver belly-to-earth, 0.7 for a head-down dive, and 0.47 for a smooth sphere. These are the presets here; a real value depends on exact shape and surface.
How fast does a human reach terminal velocity?
A skydiver reaches roughly 95 percent of terminal speed in about 12 seconds and around 450 meters of fall. Belly-to-earth that top speed is near 120 mph at low altitude.
Does air density really change the result?
Yes. Terminal velocity scales as one over the square root of density, so the thinner air at high altitude lets an object fall noticeably faster than it would near sea level.