Understand the model
Free Fall With Quadratic Air Resistance
This calculator models a vertical drop from rest with downward taken as positive. Instead of reducing gravity by an arbitrary amount, it balances weight against aerodynamic drag proportional to velocity squared. The closed-form solution determines time and speed; sampled points are used only to draw the chart.
Real drag equation
Enter air density, drag coefficient and frontal area to calculate the drag constant.
Exact trajectory
Fall time and impact speed use the analytical constant-property solution.
Clear comparison
See the corresponding vacuum result and how close the object is to terminal velocity.
Terminal Velocity
Terminal velocity is reached asymptotically as drag approaches the object's weight. For quadratic drag, vt = √(2mg / ρCdA). A short fall may end well below this speed, while a sufficiently long fall approaches it.
Drag Coefficient
Cd describes how strongly a shape resists the flow in a particular condition. It is not universal: orientation, surface roughness and flow regime matter. The included sphere and plate values are approximate starting references, not certified data.
Why Mass Affects Terminal Velocity
With the same Cd, area and air density, a heavier object has more weight but the same drag at a given speed. It must move faster before drag balances its weight, so terminal velocity increases with the square root of mass.
Air Resistance vs Vacuum
In a vacuum there is no aerodynamic drag, so acceleration remains g throughout the fall. In the quadratic-drag model acceleration decreases as speed rises. Setting Cd, frontal area or air density to zero automatically switches the calculation to the vacuum equations.
Model assumptions and limitations
The calculation assumes a point-mass object released from rest, vertical motion, constant gravitational acceleration, constant air density, and fixed Cd and frontal area. It does not model wind, lift, tumbling, buoyancy, changing atmosphere, compressibility, parachute deployment or impact dynamics. Use appropriate measured or authoritative aerodynamic inputs for important work.
Free Fall Calculator FAQ
How does this calculator include air resistance?
It uses quadratic aerodynamic drag, Fd = 0.5 × ρ × Cd × A × v², and the analytical solution for an object released from rest under constant gravity and atmospheric properties.
What is terminal velocity?
Terminal velocity is the steady speed at which aerodynamic drag equals the object's weight. At that point the net acceleration approaches zero.
Is the drag coefficient exact?
No. Drag coefficient depends on shape, orientation, surface, Reynolds number and flow conditions. Presets are approximate references and should be replaced with suitable test or reference data when accuracy matters.
Why does a heavier object have a higher terminal velocity?
For the same shape, frontal area and air conditions, more mass means more weight must be balanced by drag. Because quadratic drag grows with velocity squared, the heavier object reaches that balance at a higher speed.
What happens when Cd or frontal area is zero?
The drag constant becomes zero, so the calculator automatically uses the exact vacuum equations. It does not show an infinite numeric terminal velocity.
Does the model account for changing air density?
No. The calculation assumes constant air density, gravity, frontal area and drag coefficient throughout the drop. Long high-altitude falls need a more detailed atmospheric model.