Terminal Velocity Calculator
Find the steady fall speed where air drag balances gravity.
≈ 154.02 km/h — the steady speed where air drag balances gravity.
Terminal velocity is the constant speed a falling object reaches when air drag balances gravity, given by v_t = √(2mg ÷ (ρ·A·C_d)). A belly-down skydiver (80 kg, A ≈ 0.7 m², C_d ≈ 1.0, ρ = 1.225 kg/m³) reaches about 43 m/s — roughly 154 km/h.
What terminal velocity is
As an object falls, gravity pulls it down while air pushes back with a drag force that grows with the square of speed. At first the object accelerates, but the faster it goes the harder the air resists. Eventually drag exactly cancels the weight, the net force reaches zero, and the object stops speeding up — it has hit its terminal velocity and falls at a steady rate for the rest of the drop.
Because drag depends on the object’s shape and the air it moves through, terminal velocity is not a single number. It rises with heavier mass and falls with larger frontal area, a higher drag coefficient, or denser air — which is why a skydiver, a feather, and a raindrop each settle at very different speeds.
m = mass (kg), g = 9.81 m/s², ρ = air density (1.225 kg/m³ at sea level), A = cross-sectional area (m²), C_d = drag coefficient (dimensionless)
Worked example
A skydiver in the belly-down (spread-eagle) position: m = 80 kg, A = 0.7 m², C_d = 1.0, ρ = 1.225 kg/m³, g = 9.81 m/s².
- 1 Gather the inputs. m = 80 kg, A = 0.7 m², C_d = 1.0, ρ = 1.225 kg/m³, and g = 9.81 m/s².
- 2 Multiply out the numerator. 2 × m × g = 2 × 80 × 9.81 = 1569.6.
- 3 Multiply out the denominator. ρ × A × C_d = 1.225 × 0.7 × 1.0 = 0.8575.
- 4 Divide, then take the square root. v_t = √(1569.6 ÷ 0.8575) = √1830.4 ≈ 42.78 m/s.
- 5 Convert to km/h. 42.78 m/s × 3.6 ≈ 154 km/h.
Typical drag coefficients
Approximate C_d values for common shapes moving through air; real values vary with speed and surface.
| Shape | Drag coefficient (C_d) |
|---|---|
| Flat plate (face-on) | ~1.28 |
| Skydiver (belly-down) | ~1.0 |
| Smooth sphere | ~0.47 |
| Modern car | ~0.3 |
| Streamlined / teardrop body | ~0.04 |
Reading the result
Terminal velocity is reached only when drag balances gravity. Before that point the object is still accelerating, so this speed is a ceiling, not the speed at every instant of the fall. A short drop may never get close to it.
Posture and area matter enormously. A skydiver who pulls into a head-down dive shrinks A and C_d, and terminal velocity can more than double to over 90 m/s; opening a parachute multiplies A dozens of times and drops it to a survivable few m/s. Thinner air at altitude (lower ρ) also raises terminal velocity, which is why high-altitude jumps start faster.