Physics

Terminal Velocity Calculator

Calculate terminal velocity using v_t = √(2mg / (ρACd)).

CALCULATOR

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Instant results
40.0204 m/s

v_t = √(2mg / (ρACd))

= √(2 × 70 × 9.81 / (1.225 × 0.7 × 1))

= √(1373.4000 / 0.8575)

= 40.0204 m/s

THE NUMORIX GUIDE

How to use the Terminal Velocity Calculator

Last reviewed September 14, 2026

What this calculator does

The engine uses the quadratic-drag terminal-speed formula vt = sqrt(2*m*g/(rho*A*Cd)).

Formula and method

The engine uses the quadratic-drag terminal-speed formula vt = sqrt(2*m*g/(rho*A*Cd)). It treats mass m, gravity g, air density rho, projected cross-sectional area A, and drag coefficient Cd as inputs and returns terminal speed in m/s.

Variables and inputs

Enter mass in kg, gravity in m/s^2, air density in kg/m^3, cross-sectional area in m^2, and a dimensionless drag coefficient. The default scenario is 70 kg, 9.81 m/s^2, 1.225 kg/m^3, 0.7 m^2, and Cd = 1.0; the live UI does not validate positive denominators.

Worked example

For the defaults, vt = sqrt((2*70*9.81)/(1.225*0.7*1.0)) = sqrt(1601.6327) = 40.0204 m/s. This is the speed at which the modeled drag balances the object's weight.

How to interpret the result

Terminal velocity is an equilibrium speed for the selected conditions, not the speed immediately after release. Increasing mass or gravity raises the result, while greater area, air density, or drag coefficient lowers it.

Common mistakes to avoid

Use projected area facing the flow, not total surface area, and use mass in kilograms rather than weight in newtons. Choose a drag coefficient for the object's shape and orientation, and do not confuse still-air terminal speed with ground speed in wind.

Assumptions and limitations

The formula assumes steady quadratic drag, constant air density, fixed area and Cd, no buoyancy, and enough distance for terminal speed to be approached. Cd can vary with Reynolds number and attitude, while altitude, wind, rotation, parachute deployment, and near-ground effects are omitted.

Practical use and checks

The Terminal Velocity Calculator uses the quadratic-drag estimate vt = square root of (2*m*g divided by rho*A*Cd). Enter mass 70 kg, gravity 9.81 m/s^2, air density 1.225 kg/m^3, area 0.7 m^2, and drag coefficient 1.0 as a check; the result should be about 40.02 m/s. Increasing projected area while keeping every other input fixed should lower terminal speed, while increasing mass should raise it by a square-root relationship. Use projected frontal area and a drag coefficient that match the object's shape and orientation. The result is a limiting speed at which modeled drag balances weight, not the speed immediately after release and not the ground speed in wind. The formula assumes steady quadratic drag, constant density, fixed area and Cd, no buoyancy, and enough distance for the limit to be approached. In reality Cd can change with Reynolds number, attitude, deployment, and speed; air density changes with altitude and weather. Zero area, zero drag coefficient, or a nonpositive density makes the denominator invalid. The calculator does not provide fall time, impact speed before terminal behavior, or a parachute trajectory. Use it as a baseline and check real equipment, altitude, stability, and exposure conditions before making a descent or safety decision.

Sources and references

COMMON QUESTIONS

Frequently asked questions

Does an object instantly travel at terminal velocity?

No. Terminal velocity is the limiting speed after acceleration and drag balance. The engine calculates that limit but does not simulate the time or distance needed to approach it.

Why does a heavier object have a higher terminal velocity?

With the same shape and conditions, a heavier object has greater weight to balance. The square-root formula therefore raises vt with the square root of mass, not in direct proportion.