Compute the maximum falling speed of an object
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There’s a fascinating moment in every free-fall experience when the acceleration stops and the falling object reaches its maximum speed this is terminal velocity. It’s the point where the downward force of gravity is perfectly balanced by the upward force of air resistance, and it’s a concept that applies to everything from skydivers to rain drops to parachutes. Understanding terminal velocity helps explain why a feather falls slowly while a rock drops quickly, and it’s essential knowledge for aerospace engineers, skydivers, and physics students alike.
This calculator determines the terminal velocity of any object falling through a fluid (usually air) using the standard drag equation. It accounts for mass, cross-sectional area, drag coefficient, air density, and gravitational acceleration. Whether you’re analyzing a skydiver’s fall, designing a parachute system, or simply exploring the physics of motion, this tool provides instant answers. All calculations run locally in your browser for complete privacy.
Enter the mass of the falling object using the first input field, then select kilograms, grams, or pounds.
Specify the cross-sectional area, the frontal area perpendicular to the direction of motion and choose from m², cm², or ft².
Input the drag coefficient for the object’s shape, or click one of the shape presets (sphere, cube, flat plate, streamlined) to auto-fill a typical value.
Set the air density — the default value of 1.225 kg/m³ represents sea-level air at 20°C, but you can adjust it for different altitudes or fluids.
Choose the gravitational acceleration from presets for Earth, Moon, Mars, or Jupiter, or enter a custom value.
Click Calculate or simply wait for automatic updates — the terminal velocity appears instantly with conversions to km/h, mph, and ft/s.
The calculator applies the fundamental drag equation that describes the balance between gravitational force and drag force at terminal velocity. When an object falls through a fluid, gravity pulls it downward while drag resists the motion upward. Terminal velocity is reached when these forces equalize.
Formula: vₜ = √(2mg / (ρ·A·C_d))
Where vₜ is terminal velocity in meters per second, m is mass in kilograms, g is gravitational acceleration in m/s², ρ is fluid density in kg/m³, A is cross-sectional area in m², and C_d is the drag coefficient (dimensionless). The derivation starts from the drag equation F_d = ½ρv²AC_d and the gravitational force F_g = mg. At terminal velocity, F_d = F_g, so ½ρv²AC_d = mg. Solving for v gives the terminal velocity formula.
The calculator automatically converts all inputs to SI units before computation, then displays results in multiple unit systems for your convenience.
A skydiver with a mass of 80 kg (including equipment) falls in the spread-eagle position with a cross-sectional area of 0.7 m² and a drag coefficient of 1.0. Air density is 1.225 kg/m³ at sea level. What is the terminal velocity?
Step 1: Gather the known values
m = 80 kg
g = 9.81 m/s²
ρ = 1.225 kg/m³
A = 0.7 m²
C_d = 1.0
Step 2: Apply the terminal velocity formula
vₜ = √(2 × 80 × 9.81 / (1.225 × 0.7 × 1.0))
vₜ = √(1569.6 / 0.8575)
vₜ = √(1830.4)
vₜ = 42.78 m/s
Step 3: Convert to other units
42.78 m/s × 3.6 = 154.0 km/h
42.78 m/s × 2.23694 = 95.7 mph
42.78 m/s × 3.28084 = 140.4 ft/s
Interpretation: The skydiver reaches a terminal velocity of about 43 m/s (154 km/h or 96 mph) in the spread-eagle position. This is the typical speed experienced by skydivers during free-fall before deploying a parachute.
A human skydiver in the spread-eagle (belly-to-Earth) position has a terminal velocity of approximately 55 m/s (200 km/h or 120 mph). In a head-down or streamlined position, terminal velocity can reach 90 m/s (320 km/h or 200 mph). These values depend on the jumper’s weight, equipment, and body position.
Higher altitudes have lower air density, which reduces drag and increases terminal velocity. At 10,000 meters (about 33,000 feet), air density is roughly one-third of sea-level value, so terminal velocity can be significantly higher. This is why skydivers can reach higher speeds during high-altitude jumps.
Typical drag coefficients (for flow perpendicular to the object) include: sphere 0.47, cube 1.05, flat plate 1.28, streamlined body 0.04, cylinder (axis perpendicular) 1.2, and human (spread-eagle) 1.0. These values vary with Reynolds number and orientation.
A feather has a much larger cross-sectional area relative to its mass compared to a rock. The feather’s high drag-to-weight ratio means it reaches terminal velocity very quickly at a low speed. The rock’s low drag-to-weight ratio means it continues accelerating to a much higher terminal velocity.
No — terminal velocity is the maximum speed an object can reach while falling through a fluid under the influence of gravity. Once terminal velocity is reached, the object falls at constant speed. However, external factors like gusts of wind or changes in orientation can temporarily alter the speed.
Water is about 800 times denser than air, so terminal velocity in water is much lower than in air for the same object. A small stone dropped in water reaches terminal velocity almost immediately at a speed of a few m/s, while the same stone in air would accelerate for much longer and reach a much higher terminal velocity.
Raindrops range in size from about 0.5 mm to 5 mm diameter. Terminal velocity ranges from approximately 2 m/s for a drizzle drop to 9 m/s for a large raindrop. Larger drops fall faster but may break up due to aerodynamic forces before reaching their theoretical maximum speed.
The formula provides accurate estimates for most practical purposes. However, it assumes steady, incompressible flow and a constant drag coefficient, which are reasonable approximations for subsonic speeds in air. At very high speeds (approaching Mach 1), compressibility effects become significant and the formula requires modification.
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