Terminal Velocity Calculator

Frequently Asked Questions

What is terminal velocity?

The constant speed a falling object reaches when air drag exactly balances gravity, so net force and acceleration become zero.

What determines it?

v_t = √(2mg / (ρ·A·Cd)): heavier or smaller objects fall faster; larger area, higher drag coefficient, or denser air slow them down.

Why does a skydiver slow down after opening a parachute?

The parachute massively increases area A and drag coefficient Cd, dropping terminal velocity to a safe few m/s. The free-fall speed itself depends on posture and frontal area: about 41 m/s spread flat belly-down (as in the worked example above) and closer to the classic ~55 m/s (about 120 mph) in a tighter or head-down orientation.

Does altitude matter?

Yes: air density ρ falls with altitude, so terminal velocity is higher in thin air and decreases as the object descends into denser air.

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How This Calculator Works

Terminal velocity is the constant speed a falling object reaches when aerodynamic drag exactly balances gravity, so net force is zero and acceleration stops. Setting drag equal to weight, ½ρv²A·C_d = mg, and solving for v gives v_t = √(2mg ÷ (ρ · A · C_d)), where m is mass (kg), g = 9.80665 m/s², ρ is air density (kg/m³), A is the cross-sectional area facing the airflow (m²), and C_d is the dimensionless drag coefficient. This calculator evaluates that closed-form expression and reports the result in m/s, km/h, mph, and ft/s. Note that v_t scales with the square root of mass and inversely with the square root of area and drag: doubling the mass only raises terminal velocity by about 41%.

Worked Example: A Belly-Down Skydiver

Take a 75 kg skydiver in the spread-eagle belly position: C_d ≈ 1.0, frontal area A ≈ 0.7 m², air density ρ = 1.225 kg/m³ at sea level. Then v_t = √(2 × 75 × 9.80665 ÷ (1.225 × 0.7 × 1.0)) = √(1471 ÷ 0.8575) ≈ √1715 ≈ 41.4 m/s, about 149 km/h (93 mph). The familiar ~120 mph figure quoted for skydivers reflects a smaller area or head-down orientation. Pull into a head-down dive (A drops, C_d falls toward 0.7) and terminal velocity climbs past 90 m/s; deploy a parachute (A jumps to tens of m²) and it collapses to a survivable 5 to 7 m/s.

Drag Coefficient & Air Density Notes

Human skydiver, belly-to-earth: C_d ≈ 1.0; head-down ≈ 0.7.

Smooth sphere: C_d ≈ 0.47 (a falling raindrop or hailstone).

Streamlined teardrop: C_d ≈ 0.04, the most slippery practical shape.

Air density falls with altitude: ρ ≈ 1.225 at sea level but only ≈ 0.41 kg/m³ at 10 km, so terminal velocity is roughly 70% higher up there. This is why high-altitude jumpers can reach near-supersonic speeds.

Real-World Uses

Engineers and scientists use terminal velocity to size parachutes and drogue chutes, predict hailstone and raindrop impact speeds, design safe drop zones, model sediment settling in fluids, and estimate spacecraft re-entry deceleration. It also explains everyday observations: why a feather and a hammer fall together only in vacuum, why small insects survive any fall (tiny mass and a large relative area give a very low v_t), and why dust stays suspended in air almost indefinitely.

Common Mistakes & Limitations

This calculator gives the drag-limited steady speed: it is distinct from the free-fall calculator and projectile-motion calculator, which assume no air resistance and predict an ever-increasing velocity (v = gt). Terminal velocity does not depend on the height fallen, only on the object's properties and the air. The model assumes a constant C_d (it actually varies with Reynolds number and orientation), constant air density (it changes with altitude and temperature), incompressible subsonic flow (it breaks down near and above the speed of sound), and a rigid, non-spinning body. For tumbling or deforming objects, treat the result as an order-of-magnitude estimate, not an exact figure. See also the drag force calculator for the underlying drag equation.

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