Terminal Velocity Calculator
Pick an object preset or choose custom and enter your own mass, drag coefficient and frontal area. Choose air or water as the fluid.
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Formula
v_t = √(2 m g / (ρ × C_d × A))
- m is mass (kg), g = 9.80665 m/s², ρ is the fluid density (air 1.225 kg/m³ at sea level, 0.9093 kg/m³ at 3000 m, water 1000 kg/m³).
- C_d is the drag coefficient and A is the frontal area in m².
- Approach to terminal speed:
v(t) = v_t × tanh(g t / v_t), so 95% is reached att = v_t × atanh(0.95) / g.
Worked example
An 80 kg skydiver, belly to earth, with C_d = 1.0 and A = 0.7 m² in sea-level air:
v_t = √(2 × 80 × 9.80665 / (1.225 × 1.0 × 0.7)) = √1829.8 = 42.78 m/s
That is 153.99 km/h or 95.69 mph. They reach 95% of it after about 7.99 s and roughly 217 m of fall.
Presets use typical estimates, not measurements. Real values change with posture, clothing, shape and temperature.
Frequently asked questions
What is the terminal velocity formula?
v = √(2mg / (ρ × Cd × A)). For an 80 kg skydiver with Cd 1.0 and 0.7 m² in air of 1.225 kg/m³: √(2 × 80 × 9.80665 / (1.225 × 1.0 × 0.7)) = 42.8 m/s, about 154 km/h.
What drag coefficient should I use?
It depends on shape. A sphere is about 0.47, a flat-faced object about 1.0 to 1.3, a streamlined body 0.04 to 0.1 and a parachute about 1.5. The presets use typical textbook values, so treat results as estimates.
Why is a head-down skydiver faster?
Less frontal area and a lower drag coefficient. With Cd 0.7 and 0.18 m² the same 80 kg person reaches 100.8 m/s, about 363 km/h, instead of 42.8 m/s.
How long does it take to reach terminal velocity?
You approach it gradually. With quadratic drag the speed is v = vt × tanh(g t / vt), reaching 95% of vt after t = vt × atanh(0.95) / g. For vt = 42.8 m/s that is about 8.0 s and 217 m of falling.