Calculators/Physics/Aerodynamic drag

Aerodynamic drag

F = ½·C_d·ρ·A·v² · air resistance

Aerodynamic drag — illustration
F = ½·C_d·ρ·A·v²
60.63 N

Drag grows with the square of speed — moving twice as fast gives four times the drag. Air density ρ ≈ 1.29 kg/m³. A streamlined shape (low C_d) strongly reduces the drag force.

The aerodynamic drag force slows a body moving through a fluid (air, water):

F=12 Cd ρ A v2F=\tfrac12\,C_d\,\rho\,A\,v^2

where CdC_d is the drag coefficient (shape-dependent), ρ\rho is the density of the medium (air ≈ 1.29 kg/m³), AA is the cross-sectional area, and vv is the speed.

The key feature is the dependence on the square of the speed: driving twice as fast means four times the drag (and sharply rising fuel use). A streamlined shape (low CdC_d) drastically reduces drag — a droplet has Cd≈0.04C_d\approx0.04, whereas a flat plate reaches ≈1.3\approx1.3.

Examples

Sphere (C_d=0.47), A=0.5 m², v=20 m/s
→ F = ½·0.47·1.29·0.5·400 ≈ 60.6 N
Doubling the speed
→ drag grows 4× (v² dependence)

Frequently asked questions

Why does drag grow with the square of speed?+

Because a faster-moving body "meets" more air in the same time and imparts a greater speed to it — the energy dissipated grows in proportion to v². Hence the v² in the formula.

What does the drag coefficient C_d mean?+

A dimensionless measure of how "streamlined" a shape is. The smaller it is, the smoother the flow and the lower the drag. A droplet has about 0.04, a car ~0.3, a parachute ~1.3.

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