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Terminal Velocity Calculator

Find the terminal velocity.

How it is calculated

At terminal velocity the drag force equals the weight, so v = √(2 × m × g ÷ (ρ × A × Cd)). Here m is mass in kilograms, g is fixed at 9.81 m/s², ρ is air density in kg/m³, A is the cross-sectional area facing the airflow in m², and Cd is the dimensionless drag coefficient. The result is in metres per second with two decimals.

If density is left empty, zero or negative, the tool uses 1.225 kg/m³, the usual sea-level value. Mass, area and drag coefficient must all be above zero, otherwise there is no result. The model assumes constant density and a constant drag coefficient, so it ignores speed-dependent changes in drag and the thinner air at altitude unless you enter a lower density yourself.

Worked example

An 80 kg skydiver falls belly-down with a frontal area of 0.7 m² and a drag coefficient of 1.0, at the default density of 1.225 kg/m³. Weight term: 2 × 80 × 9.81 = 1,569.6. Denominator: 1.225 × 0.7 × 1.0 = 0.8575. Ratio = 1,569.6 ÷ 0.8575 = 1,830.4, and the square root is 42.78 m/s, about 154 km/h. In thinner air at 0.9 kg/m³ the same body settles at 49.91 m/s, which is why high-altitude falls reach higher speeds.

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Common mistakes

  • Entering the mass in grams or pounds. The tool expects kilograms; a wrong unit changes the speed by the square root of the factor.
  • Using the total surface area instead of the cross-sectional area facing the flow. A person falling flat presents far less area than their whole body surface.
  • Mixing up area units, for example square centimetres instead of square metres.
  • Using a Cd that does not match the shape. A sphere, a flat plate and a parachute have very different drag coefficients.
  • Keeping the default sea-level air density for a high-altitude fall. Thinner air raises terminal velocity.

About this calculator

This calculator finds terminal velocity — the constant speed a falling object reaches when air resistance (drag) exactly balances gravity — using v = √(2mg / (ρACd)), where m is mass, ρ is air density, A is cross-sectional area and Cd is the drag coefficient.

Skydivers and physics students use it to understand why a falling body stops accelerating, and engineers use the same drag relationship when designing parachutes, projectiles and anything that falls or moves through air. A larger surface area or higher drag coefficient lowers terminal velocity; more mass raises it.

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Comments (1)

  • Editorial team

    Body position matters more than most people expect. An 80 kg skydiver with 0.7 m² and a drag coefficient of 1.0 settles at 42.78 m/s, while a head-down dive with 0.18 m² and a coefficient of 0.7 gives 100.84 m/s, using the same mass and the sea-level density. Frontal area and drag coefficient are estimates, so treat the answer as an order of magnitude. What are you dropping, and from what height?

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