Free Fall with Air Resistance Calculator

In physics, free fall is the motion of an object under the influence of gravity alone, with no other forces acting on it. Strictly speaking, 'free fall' implies no air resistance — but in reality, any object falling through the atmosphere experiences drag. This calculator accounts for that aerodynamic drag force using the quadratic drag model F = k × v².

Terminal velocity is the constant maximum speed an object reaches when the upward drag force exactly equals the downward gravitational force, resulting in zero net acceleration. At terminal velocity, the object stops accelerating and falls at a steady speed. It is calculated as v_t = √(m·g / k), where k = ρ·A·C_d / 2.

Terminal velocity is the theoretical maximum speed the object asymptotically approaches as drag balances gravity — it would only be truly reached after an infinite fall distance. Maximum (impact) velocity is the actual speed at the moment the object hits the ground, which is limited by both the terminal velocity and the available fall height. If the drop height is short, the object may never approach terminal velocity.

The calculator uses the quadratic drag model: F_drag = k × v², where k = (ρ × A × C_d) / 2. Here ρ is the air density, A is the object's cross-sectional area, and C_d is the drag coefficient. This gives terminal velocity v_t = √(m·g / k). The velocity and position over time are computed by numerically integrating the equation of motion m·(dv/dt) = m·g − k·v².

The drag coefficient (C_d) is a dimensionless number that characterizes how aerodynamically streamlined an object is. Typical values: a skydiver in spread-eagle position ≈ 1.0, a sphere ≈ 0.47, a streamlined teardrop ≈ 0.04, and a flat plate ≈ 1.28. Lower values mean less drag. The drag coefficient depends on object shape and, at high speeds, also on the Reynolds number.

Higher air density increases the drag force, reducing terminal velocity and slowing the fall. At high altitudes, air is thinner (lower density), so objects fall faster and terminal velocity is higher. At sea level with standard air (1.225 kg/m³) drag is strongest. Changing the air density preset or entering a custom value lets you model falls at different altitudes or in different atmospheric conditions.

Unlike the simple vacuum case (t = √(2h/g)), fall time with drag has no simple closed-form solution for the quadratic model. This calculator uses numerical integration (Euler method with small time steps) to integrate the velocity over time until the cumulative distance equals the drop height. The result gives a realistic fall time that accounts for the slowing effect of aerodynamic drag throughout the descent.

Yes! A typical skydiver in freefall has a mass of around 75–90 kg, a drag coefficient of about 1.0, and a cross-sectional area of roughly 0.5–0.9 m². At standard air density, this gives a terminal velocity of approximately 53–60 m/s (190–216 km/h). After parachute deployment, both C_d and A increase dramatically, reducing terminal velocity to a safe landing speed of about 5–6 m/s.