Terminal Velocity Calculator
Calculate terminal velocity using v_t = √(2mg / ρACd). Enter mass, drag coefficient, cross-sectional area, and air density.
TERMINAL VELOCITY
41.418 m/s
IN km/h
149.1047 km/h
IN mph
92.6495 mph
FORMULA
vt = √(2mg/ρACd)
Terminal Velocity — Examples
| Object | vt (m/s) | vt (mph) |
|---|---|---|
| Skydiver (belly) | 55 | 123.0317 |
| Skydiver (head-down) | 90 | 201.3246 |
| Tennis ball | 31 | 69.3451 |
| Baseball | 42 | 93.9515 |
| Golf ball | 70 | 156.5858 |
| Raindrop | 9 | 20.1325 |
💡 How to Calculate Terminal Velocity
What Is Terminal Velocity?
Terminal velocity is the maximum speed a falling object can reach when the drag force (air resistance) equals the object's weight. At terminal velocity, the net force on the object is zero, so there is no further acceleration — the object falls at a constant speed.
Terminal velocity depends on the object's mass, its shape (drag coefficient), its cross-sectional area, and the density of the air it is falling through.
How to Calculate Terminal Velocity
Terminal Velocity Formula
Where:
- vt = terminal velocity (m/s)
- m = mass (kg)
- g = 9.81 m/s²
- ρ = air density (≈ 1.225 kg/m³ at sea level)
- A = cross-sectional area (m²)
- Cd = drag coefficient
Worked Example: Skydiver
A 75 kg skydiver in belly-down position (Cd = 1.0, A = 0.7 m²) at sea level:
vt = √(2 × 75 × 9.81 / (1.225 × 0.7 × 1.0))
vt = √(1,471.5 / 0.8575)
vt ≈ 41.4 m/s ≈ 93 mph
In a head-down position (Cd ≈ 0.4, A ≈ 0.3 m²), the same skydiver reaches about 90 m/s (200 mph) because both drag coefficient and area are reduced.
Drag Coefficients for Common Shapes
| Shape | Cd |
|---|---|
| Sphere | 0.47 |
| Cube | 1.05 |
| Flat plate | 1.28 |
| Skydiver (belly) | 1.0 |
| Streamlined body | 0.04 |