Terminal Velocity Calculator
Calculate terminal velocity using the drag equation: v_t = √(2mg / ρC_dA). Enter mass, gravity, drag coefficient, fluid density and cross-section area.
How to use this tool
- Enter mass, gravitational acceleration, drag coefficient cd, fluid density ρ and cross-sectional area a in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your terminal velocity and the full breakdown beneath it.
An object reaches terminal velocity when drag force equals gravity. The formula is v_t = √(2mg / ρC_dA), where m is mass, g gravity, ρ fluid density, C_d the drag coefficient, and A the cross-sectional area.
Formula
vt = √(2mg ÷ ρ Cd A)
Where: m = mass (kg), g = gravitational acceleration (m/s²), ρ = fluid density (kg/m³), Cd = drag coefficient, A = cross-sectional area (m²).
How it works
Terminal velocity is reached when the upward drag force on a falling object exactly equals its downward weight. Setting the drag equation Fdrag = ½ρCdAv2 equal to gravitational force mg and solving for v gives the formula above.
The calculator converts the result to km/h (multiply by 3.6) and mph (multiply by 2.23694). It assumes a rigid body in steady laminar or turbulent flow; in practice, shape changes, spin, or altitude variation can alter the true terminal speed.
Worked example
- Given: mass m = 80 kg, g = 9.81 m/s², drag coefficient Cₙ = 1.0, fluid density ρ = 1.225 kg/m³, cross-section A = 0.7 m².
- Compute numerator: 2 × 80 × 9.81 = 1569.6.
- Compute denominator: 1.225 × 1.0 × 0.7 = 0.8575.
- vₜ = √(1569.6 ÷ 0.8575) = √(1830.38...) ≈ 42.79 m/s.
Terminal velocity = 42.79 m/s.
Common mistakes to avoid
- Using a drag coefficient for a sphere (C_d approx 0.47) for a non-spherical object like a skydiver or a falling leaf, which can be off by a factor of 2 or more.
- Entering body mass in grams instead of kilograms, or cross-sectional area in cm2 instead of m2, producing a result that is orders of magnitude wrong.
- Assuming terminal velocity is reached instantly; it is an asymptotic limit that an object approaches exponentially, so a falling object is still accelerating (slowly) even at 90% of terminal velocity.
Key terms
- Terminal velocity
- The constant maximum speed reached by a falling object when drag force equals gravitational force.
- Drag coefficient (Cₙ)
- A dimensionless number representing how aerodynamically streamlined a body is. A sphere is ~0.47; a skydiver in freefall position is ~1.0.
- Fluid density (ρ)
- Mass per unit volume of the medium the object moves through. Air at sea level is approximately 1.225 kg/m³.
- Cross-sectional area (A)
- The projected area of the object perpendicular to the direction of motion, which determines how much fluid the object must push aside.
- Drag force
- The resistive force exerted by a fluid on a moving body, proportional to the square of velocity at high Reynolds numbers.
Frequently asked questions
- What is a typical skydiver terminal velocity?
- In a spread-eagle position (Cd≈1.0, A≈0.7 m²) around 55–60 m/s (200 km/h). Head-down (Cd≈0.7, A≈0.3 m²) can reach ~80 m/s (290 km/h).
- What drag coefficient should I use?
- Sphere: 0.47, cube: 1.05, flat disk: 1.17, skydiver prone: ~1.0, streamlined body: 0.04–0.1.