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 = √(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 from roughly 55 m/s to a safe few m/s.

Does altitude matter?

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

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This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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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·Cᶆ = mg, and solving for v gives vᵗ = √(2mg ÷ (ρ · A · Cᶆ)), 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 Cᶆ 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 vᵗ 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: Cᶆ ≈ 1.0, frontal area A ≈ 0.7 m², air density ρ = 1.225 kg/m³ at sea level. Then vᵗ = √(2 × 75 × 9.80665 ÷ (1.225 × 0.7 × 1.0)) = √(1471 ÷ 0.8575) ≈ √1715 ≈ 41.4 m/s, or 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, Cᶆ 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 5–7 m/s.

Drag Coefficient & Air Density Notes

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

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

Streamlined teardrop: Cᶆ ≈ 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 reach 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, large relative area → very low vᵗ), and why dust stays suspended in air almost indefinitely.

Common Mistakes & Limitations

This calculator gives the drag-limited steady speed - it is distinct from free-fall or projectile-motion calculators, 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 Cᶆ (it actually varies with Reynolds number and shape 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.

Terminal Velocity Calculator

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