Determine the constant speed an object reaches when the force of gravity is balanced by the upward drag force. Use our Terminal Velocity Calculator to solve for velocity, mass, or drag coefficients with precision.
Terminal Velocity Calculator
Terminal Velocity Formula
Formula Source: NASA Glenn Research Center
Variables Explained:
- vₜ (Terminal Velocity): The constant speed attained by an object in free fall.
- m (Mass): The mass of the falling object (measured in kilograms).
- g (Gravity): Acceleration due to gravity (Earth standard is ~9.81 m/s²).
- ρ (Density): The density of the fluid the object is falling through (Air is ~1.225 kg/m³ at sea level).
- A (Area): The projected cross-sectional area of the object.
- Cd (Drag Coefficient): A dimensionless number that represents the aerodynamic resistance.
What is Terminal Velocity?
Terminal velocity is the maximum speed an object can reach while falling through a fluid (like air or water). As an object falls, it accelerates due to gravity. However, it also experiences air resistance (drag), which increases with speed. Eventually, the upward force of drag equals the downward force of gravity.
At this specific point, net acceleration becomes zero, and the object continues to fall at a constant velocity. This state is critical in aerodynamics, parachute design, and understanding planetary atmospheres.
How to Calculate Terminal Velocity (Example)
Follow these steps to calculate the speed of a typical skydiver:
- Identify Mass: Assume a skydiver with gear weighs 90 kg ($m=90$).
- Fluid Density: Use standard air density ($ρ=1.225$).
- Projected Area: A human belly-to-earth has an area of roughly 0.7 m² ($A=0.7$).
- Drag Coefficient: A typical value for a human is 1.0 ($C_d=1.0$).
- Apply Formula: Plug values into $v_t = \sqrt{(2 \cdot 90 \cdot 9.81) / (1.225 \cdot 0.7 \cdot 1.0)}$.
- Result: $v_t \approx 45.3$ m/s (approx 163 km/h).
Frequently Asked Questions (FAQ)
Does a heavier object have a higher terminal velocity? Yes. According to the formula, terminal velocity is proportional to the square root of the mass. A heavier object requires more drag force (and thus more speed) to reach equilibrium.
What factors affect the drag coefficient? The shape of the object and the roughness of its surface are the primary factors. Streamlined shapes like teardrops have lower $C_d$ values compared to flat plates.
How does altitude affect terminal velocity? Higher altitude means lower air density ($\rho$). Since density is in the denominator, terminal velocity increases at higher altitudes where the air is “thinner.”
Is terminal velocity the same in water? No. Water is much denser than air, so the drag force becomes equal to gravity at much lower speeds compared to falling through air.