Terminal Velocity Calculator
Terminal velocity is the maximum speed reached by a falling object when the aerodynamic drag force equals gravity, resulting in zero net acceleration. The formula is v = sqrt(2mg / (ρ A Cd)), where m is mass (kg), g is gravitational acceleration (m/s²), ρ (rho) is the fluid density (1.225 kg/m³ at sea level for air), A is the reference cross-sectional area (m²), and Cd is the dimensionless drag coefficient. Enter these values to find the terminal velocity. The result also shows the drag force at terminal speed, which equals the weight of the object.
Terminal velocity formula
v = √(2mg / (ρ × A × Cd))
Where m is mass (kg), g is gravitational acceleration (m/s²), ρ is fluid density (kg/m³), A is reference cross-sectional area (m²), and Cd is the drag coefficient (dimensionless). At terminal velocity drag equals weight: F_drag = (1/2) ρ A Cd v² = mg.
Common drag coefficient values
- Sphere: Cd = 0.47
- Long cylinder (perpendicular to flow): Cd = 0.82
- Flat plate (perpendicular): Cd = 1.28
- Skydiver (spread-eagle): Cd = 1.0
- Streamlined bullet: Cd = 0.295
- Typical car: Cd = 0.25 to 0.35
Terminal velocity: frequently asked questions
What is terminal velocity?
Terminal velocity is the constant speed reached when the drag force from air resistance exactly balances the gravitational force on a falling object. At terminal velocity there is no net force, so acceleration is zero and speed remains constant. It is given by v = sqrt(2mg / (rho A Cd)).
What factors affect terminal velocity?
Terminal velocity increases with mass (heavier objects fall faster) and decreases with drag coefficient Cd (streamlined shapes are faster), cross-sectional area A (larger area means more drag), and air density rho (thinner air at altitude means faster fall).
What is a typical drag coefficient?
Cd depends on shape: a sphere has Cd = 0.47; a streamlined car about 0.25-0.35; a flat plate perpendicular to flow about 1.28; a skydiver in stable spread position about 1.0; a skydiver in head-down position about 0.7.
What is the terminal velocity of a skydiver?
A typical skydiver (mass 80 kg) in a stable spread position (A = 0.7 m², Cd = 1.0) in standard air (rho = 1.225 kg/m³) reaches terminal velocity of about 56 m/s (200 km/h). In head-down orientation (A = 0.3 m², Cd = 0.7) speed approaches 90 m/s (320 km/h).
How does altitude affect terminal velocity?
At higher altitudes air is less dense (lower rho), which reduces drag. Since v = sqrt(2mg / rho A Cd), lower rho increases terminal velocity. At 30,000 m altitude where air density is about 1% of sea level, terminal velocity would be about 10 times higher than at sea level.
Official sources
- NASA Glenn Research Center: Terminal Velocity.
- NIST Reference on Constants: Standard acceleration of gravity.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.