Terminal Velocity Calculator
This terminal velocity calculator finds the speed at which air drag and weight are equal. Example: 80 kg, a drag coefficient of 1.0 and 0.7 m² give about 42.78 m/s (154 km/h).
Example: Mass m 80 kg · Drag coefficient C_d 1 · Cross-sectional area A 0.7 m² · Air density ρ 1.225 kg/m³ · Gravitational acceleration g 9.8067 m/s² → Result: Terminal velocity v_t = 42.776 m/s (153.99 km/h). Source: Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Drag force and terminal speed“ (siehe Wikipedia – Terminal velocity). Updated: .
How it is calculated
Terminal velocity is the speed at which the drag force equals the weight, so the body stops accelerating. A falling body first speeds up, but air drag grows with the square of speed until the two forces cancel.
Formula
From m·g = ½·ρ·C_d·A·v² we get v_t = √(2·m·g / (ρ·C_d·A)). Heavier, smaller and more streamlined means faster; denser air slows more. Buoyancy of the displaced air is neglected. The time to 95% of terminal velocity follows from v(t) = v_t · tanh(g·t / v_t). The air density is the standard value of 1.225 kg/m³ from the International Standard Atmosphere.
Worked example
Mass 80 kg, C_d = 1.0, A = 0.7 m². Then v_t = √(2 · 80 · 9.80665 / (1.225 · 1.0 · 0.7)) ≈ 42.78 m/s, about 154 km/h or 95.7 mph. 95% of that is reached after about 7.99 s, during which the body falls roughly 217 m.
- A smaller area, for example in a head-down posture, raises the terminal velocity considerably.
- At high altitude the air is thinner, so terminal velocity is higher than near the ground.
- The result is a model value and not a basis for safety decisions.
Frequently asked questions
How do you calculate terminal velocity?
With v_t = √(2·m·g / (ρ·C_d·A)). Example: 80 kg, C_d 1.0, 0.7 m² and an air density of 1.225 kg/m³ give about 42.78 m/s.
Why does a heavier body fall faster than a light one?
With the same shape and area, the heavier body needs more drag to balance its larger weight, and that only happens at a higher speed.
How quickly is terminal velocity reached?
Strictly only asymptotically. In practice, 95% is reached after about 8 seconds in the example.
Sources and legal basis
- Halliday/Resnick/Walker, Fundamentals of Physics, Kap. „Drag force and terminal speed“ (siehe Wikipedia – Terminal velocity)
- Luftdichte 1,225 kg/m³: Internationale Standardatmosphäre (ISA), Meereshöhe, 15 °C
- NIST – Standard acceleration of gravity g_n = 9,80665 m/s² (exakt, CGPM 1901)
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