The terminal velocity calculator computes the maximum speed a falling object reaches when drag force balances gravity. Uses the full drag equation v_t = √(2mg/ρACd). Select from 14+ real drag coefficient presets for shapes and objects, or enter custom values. Supports metric and imperial units with optional altitude-based air density adjustment.
Object Parameters
Enter parameters and calculate
How to Use the Terminal Velocity Calculator
Terminal velocity occurs when the drag force on a falling object exactly equals its weight (mg). At this point, acceleration becomes zero and the object falls at a constant speed. The terminal velocity formula v_t = √(2mg / ρACd) combines gravitational force, drag coefficient, cross-sectional area, and fluid density.
Step 1: Enter Object Parameters
Enter mass and cross-sectional area. For a human skydiver in belly-down position, mass ≈ 80 kg and frontal area ≈ 0.7 m² (roughly a 70 cm × 100 cm rectangle). Select a drag coefficient preset or enter a custom value. Cd=1.0 is standard for belly-down skydiving position; Cd=0.7 for head-down/headfirst position.
Step 2: Set Fluid Density
Air density at sea level is 1.225 kg/m³. At altitude, density decreases exponentially. Enter an altitude to auto-calculate air density using the barometric formula ρ = 1.225 × e^(-h/8500). At 4,000 m, ρ ≈ 0.819 kg/m³, increasing terminal velocity by about 22% compared to sea level.
Skydiver Example
An 80 kg skydiver, Cd=1.0, A=0.7 m², air density 1.225 kg/m³: v_t = √(2 × 80 × 9.81 / (1.225 × 0.7 × 1.0)) = √(1569.6 / 0.8575) = √(1830.6) ≈ 42.8 m/s ≈ 154 km/h ≈ 95.7 mph. This matches observed skydiver terminal velocities of about 55 m/s — differences arise from actual body position and CdA product in practice.
FAQ
What is terminal velocity?
Terminal velocity is the constant maximum speed reached by a falling object when drag force equals gravitational force. At this point, net force is zero and acceleration stops. For a skydiver in belly-down position with Cd=1.0, mass=80 kg, A=0.7 m², the terminal velocity is about 54 m/s (120 mph). Headfirst reduces Cd to ~0.7, raising terminal velocity to ~63 m/s (141 mph).
What is the terminal velocity formula?
v_t = √(2mg / (ρ × A × Cd)), where m is mass (kg), g = 9.81 m/s², ρ is fluid density (1.225 kg/m³ for air at sea level), A is the cross-sectional area (m²), and Cd is the dimensionless drag coefficient. Doubling mass increases terminal velocity by √2 ≈ 1.41x. Doubling area reduces it by the same factor.
What is the drag coefficient?
The drag coefficient (Cd) is a dimensionless number representing an object's aerodynamic resistance. A streamlined body like a sports car has Cd ≈ 0.30. A flat plate perpendicular to airflow has Cd ≈ 1.28. A skydiver belly-down has Cd ≈ 1.0. Lower Cd means less drag and higher terminal velocity.
How does altitude affect terminal velocity?
Air density decreases with altitude, following approximately ρ = 1.225 × e^(-h/8500) kg/m³. At 10,000 m altitude (typical skydive), ρ ≈ 0.414 kg/m³ (about 34% of sea level). Lower density means less drag and higher terminal velocity at altitude versus near the ground.
Is this tool free?
Yes, completely free with no signup required. All calculations run locally in your browser.
How long does it take to reach terminal velocity?
The time to reach 99% of terminal velocity depends on the mass and drag. A rough estimate for a skydiver is about 12-15 seconds, covering roughly 450 m of fall. This calculator estimates the time and distance using 63.2% of terminal velocity at one time constant τ = m/(ρ×A×Cd×v_t/2).