Does body position change Cd?

Yes. For a human, tucking into a streamlined position can significantly reduce drag coefficient and area, increasing terminal velocity; spreading out in a belly-to-earth or “spread eagle” position increases drag and lowers terminal speed.

Can I use this calculator for parachutes?

You can approximate a parachute descent by using a large drag coefficient and cross-sectional area for the canopy plus jumper, but actual parachute behavior is more complex and changes with inflation, oscillation, and airflow. Treat any results for parachutes as rough estimates only.

How do I convert the result to mph or km/h?

Multiply m/s by 2.237 to approximate mph, or by 3.6 to get km/h. For example, 50 m/s is about 112 mph or 180 km/h.

Why doesn’t my real-world measurement match this exactly?

Real falls are affected by changing body position, wind, turbulence, varying air density, and measurement errors. This model assumes constant parameters and ideal conditions, so treat it as a first-order estimate rather than an exact prediction.

science calculator

Terminal Velocity Calculator

Estimate the terminal velocity of a falling object using drag coefficient, mass, and cross-sectional area.

Results

Terminal velocity (m/s): 42.78

How to use this calculator

Enter the object’s mass in kilograms. For a person or skydiver, use body mass plus gear.
Enter the drag coefficient C_d, which depends on shape and orientation (for example, ~1.0 for a human in a belly-to-earth position, lower for a streamlined shape).
Enter the cross-sectional area A in square meters, representing the frontal area facing the flow.
Enter the fluid density ρ in kg/m³. For air at sea level, use about 1.225 kg/m³; for water, use about 1000 kg/m³.
We apply v_t = √(2 m g ÷ (ρ C_d A)) using g ≈ 9.81 m/s² and return terminal velocity in m/s.
Interpret the result by comparing speeds for different body positions, shapes, or fluids, or convert to km/h or mph as needed for real-world context.

Inputs explained

Mass: Object mass in kilograms (kg). For a skydiver, include body, clothing, and gear. For equipment or test objects, use the actual mass you measured or specified.
Drag coefficient (Cd): A dimensionless number that describes how streamlined or bluff the object is. Typical values: ~1.0 for a human in belly-to-earth freefall, ~0.7 or lower for a streamlined head-down position, ~0.47 for a smooth sphere, and larger values for very bluff shapes.
Cross-sectional area: The frontal area facing the flow, in square meters (m²). For a person, this is roughly the projected area of the body in the current position; for objects, it is the area of the face that meets the flow.
Fluid density: The density ρ of the fluid the object falls through, in kilograms per cubic meter (kg/m³). Air at sea level is about 1.225 kg/m³; higher altitudes have lower density, and water is about 1000 kg/m³.

How it works

We model drag using the standard quadratic drag law: F_drag = ½ × ρ × C_d × A × v², where ρ is fluid density, C_d is drag coefficient, A is cross-sectional area, and v is speed.

Weight is given by F_gravity = m × g, where m is mass and g is acceleration due to gravity (≈ 9.81 m/s² near Earth’s surface).

At terminal velocity, forces balance so that drag equals weight: m × g = ½ × ρ × C_d × A × v_t².

Solving this equation for v_t gives v_t = √(2 m g ÷ (ρ C_d A)). This is the formula we implement in the calculator.

You provide m, C_d, A, and ρ; we plug them into this equation and output terminal velocity in meters per second (m/s). You can convert to km/h or mph separately if desired.

The model assumes steady vertical fall, constant C_d, constant cross-sectional area, and a uniform fluid—assumptions that are good enough for many teaching and back-of-the-envelope engineering estimates.

Formula

At terminal velocity, drag balances weight:\n\nWeight: F_g = m × g\nQuadratic drag: F_d = ½ × ρ × C_d × A × v²\n\nSet F_g = F_d at terminal:\n m × g = ½ × ρ × C_d × A × v_t²\nSolve for v_t:\n v_t = √(2 m g ÷ (ρ C_d A))

When to use it

Estimating terminal velocity for skydivers in different body positions (belly-to-earth vs head-down) to understand freefall speeds.
Modeling falling object speeds for safety evaluations, such as dropped tools, small payloads, or test articles in air or water.
Teaching drag, force balance, and the concept of terminal velocity in high school or introductory university physics courses.
Providing rough inputs for more advanced simulations or safety calculations where a quick terminal-velocity estimate is useful before detailed modeling.
Exploring how changes in altitude (air density), clothing, or equipment affect fall speed in outdoor sports and engineering contexts.

Tips & cautions

Drag coefficients can vary widely with orientation and Reynolds number—look up C_d values from reliable tables or literature for your object when possible.
Make sure cross-sectional area matches the profile facing the flow; if the object changes orientation or deploys a parachute, compute terminal velocity separately for each configuration.
Use appropriate fluid densities: use air density adjusted for altitude and temperature if you need higher accuracy, or water/oil densities for submerged objects.
Terminal velocity is only reached after some falling distance; very short falls may not reach the steady-state speed predicted here.
For a quick mph estimate, multiply m/s by about 2.237; for km/h, multiply m/s by 3.6.
Assumes constant drag coefficient and cross-sectional area; real objects may change shape, orientation, or C_d with speed and conditions.
Ignores compressibility, Mach effects, and turbulence transitions at very high speeds, which can significantly modify drag.
Assumes vertical, steady-state fall in a uniform fluid with no horizontal wind, lift forces, or other aerodynamic complexities.
Uses a fixed gravitational acceleration g ≈ 9.81 m/s²; actual g varies slightly with altitude and planetary body.
Not suitable by itself for safety-critical engineering or parachute design; treat it as a first-pass estimate.

Worked examples

80 kg skydiver (Cd ≈ 1.0, area 0.7 m²) in air

Mass m = 80 kg, C_d ≈ 1.0, A ≈ 0.7 m², ρ ≈ 1.225 kg/m³.
Plug into v_t = √(2 m g ÷ (ρ C_d A)).
v_t ≈ √(2 × 80 × 9.81 ÷ (1.225 × 1.0 × 0.7)) ≈ √(1,569 ÷ 0.8575) ≈ √(1,830) ≈ 42.8 m/s.
Interpretation: about 43 m/s (~96 mph) as a ballpark freefall speed in a belly-to-earth position at sea level (exact numbers depend on Cd and area assumptions).

Same skydiver in a more streamlined position

Reduce C_d to 0.7 and area to 0.5 m² to approximate a head-down position.
v_t = √(2 × 80 × 9.81 ÷ (1.225 × 0.7 × 0.5))—lower drag terms increase v_t.
The calculator shows a higher terminal velocity, illustrating how body position affects freefall speed.

Small object falling in water

Use mass m appropriate for the object, choose a C_d based on shape (for example, ~0.47 for a smooth sphere), estimate a frontal area, and set ρ ≈ 1000 kg/m³ for water.
The calculator returns a much lower terminal velocity compared with air, reflecting the higher density and drag in water.

Deep dive

Estimate terminal velocity from mass, drag coefficient, cross-sectional area, and fluid density for skydiving or physics projects.

Uses the standard vₜ = √(2mg ÷ (ρ C_d A)) drag-balance formula so you can see how orientation, area, and fluid density change fall speed.

Ideal for students, instructors, and enthusiasts who want a quick, physics-based terminal velocity estimate without doing the algebra by hand.

FAQs

Does body position change Cd?: Yes. For a human, tucking into a streamlined position can significantly reduce drag coefficient and area, increasing terminal velocity; spreading out in a belly-to-earth or “spread eagle” position increases drag and lowers terminal speed.
Can I use this calculator for parachutes?: You can approximate a parachute descent by using a large drag coefficient and cross-sectional area for the canopy plus jumper, but actual parachute behavior is more complex and changes with inflation, oscillation, and airflow. Treat any results for parachutes as rough estimates only.
How do I convert the result to mph or km/h?: Multiply m/s by 2.237 to approximate mph, or by 3.6 to get km/h. For example, 50 m/s is about 112 mph or 180 km/h.
Why doesn’t my real-world measurement match this exactly?: Real falls are affected by changing body position, wind, turbulence, varying air density, and measurement errors. This model assumes constant parameters and ideal conditions, so treat it as a first-order estimate rather than an exact prediction.

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This terminal velocity calculator uses a simplified drag-balance model with constant drag coefficient, area, and fluid density and is intended for educational and preliminary estimation purposes only. It does not account for complex aerodynamics, turbulence, compressibility, changing orientation, parachute deployment dynamics, or safety margins. Do not rely on it alone for engineering design, skydiving safety planning, or critical decision-making—always consult detailed analyses, experimental data, and qualified experts for real-world applications.