Terminal Velocity Calculator — When Drag Equals Gravity
Calculate terminal velocity for falling objects using mass, drag coefficient, and cross-sectional area. Includes skydiving, raindrops, and projectile examples.
Terminal velocity is the maximum speed a falling object reaches when air resistance perfectly balances gravity. At that point, net force is zero and acceleration stops — the object falls at constant speed from there. It sounds like an endpoint, but it's actually a state of dynamic equilibrium that's constantly being negotiated as density and speed interact.
The CalcHub terminal velocity calculator computes terminal velocity from mass, drag coefficient, and falling object dimensions.
The Formula
v_t = √( 2mg / (ρ_air × C_d × A) )- v_t = terminal velocity (m/s)
- m = mass of object (kg)
- g = gravitational acceleration (9.81 m/s²)
- ρ_air = air density (~1.225 kg/m³ at sea level)
- C_d = drag coefficient (dimensionless)
- A = cross-sectional area (m²)
Drag Coefficients
| Object | C_d |
|---|---|
| Sphere | 0.47 |
| Human (belly-down) | 1.0–1.3 |
| Human (head-first) | 0.7 |
| Car (sedan) | 0.30–0.40 |
| Parachute | 1.75 |
| Streamlined teardrop | 0.04 |
Real-World Terminal Velocities
| Object | Terminal Velocity |
|---|---|
| Raindrop | 5–9 m/s |
| Ping pong ball | ~9 m/s |
| Baseball | ~43 m/s |
| Skydiver (belly-down) | ~55 m/s |
| Skydiver (head-first) | ~90 m/s |
| Felix Baumgartner's jump | ~372 m/s (stratosphere, low air density) |
Worked Example
Estimate terminal velocity for a skydiver: mass 80 kg, belly-down position, A ≈ 0.7 m², C_d ≈ 1.1
v_t = √( 2 × 80 × 9.81 / (1.225 × 1.1 × 0.7) )
= √( 1569.6 / 0.9428 )
= √(1664.9)
≈ 40.8 m/s (~147 km/h)
Professional skydivers often cite ~55 m/s for standard position, but that accounts for specific body position, weight, and altitude. The formula gives a reasonable ballpark.
Why does terminal velocity increase with altitude?
Air density decreases with altitude. Lower ρ_air means less drag, so the falling object must go faster before drag equals gravity. At very high altitudes (like the stratosphere), air is so thin that terminal velocity can exceed the speed of sound before the denser lower atmosphere slows things down.
How long does it take to reach terminal velocity?
It's asymptotic — you technically never fully reach it, but objects get to ~95% of terminal velocity within a few seconds for small dense objects, or 10–15 seconds for a skydiver. The calculator can model the speed-vs-time curve if you need it.
Does a parachute work by reducing terminal velocity?
Exactly. Opening a parachute dramatically increases both C_d (up to 1.75) and A (canopy area of 40–70 m²), which increases the drag force for any given speed. This brings terminal velocity down to ~5–7 m/s — survivable landing speed.