formula.expert

Drag Force (F = ½CdρAv²)

Also known as air resistance force · wind load on a body

FD=12CdρAv2F_D = \tfrac{1}{2} C_d \rho A v^{2}

Worked example: Cd 0.3, 2.2 m² at 30 m/s → 363.83 N — press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Try different units for next level excitement!

Here the solver did the work — could you?

Drag and terminal speed →

UniversityEngineering Mechanics

Test your skills in the Exam Room: new numbers every attempt — free lessons for students, no sign-up, just pure learning.

See your Report Card
Compete with your friends
share your results
Learning zone

Drag Force (F = ½CdρAv²) explained

vFDACdρ

Above walking pace, resistance through a fluid follows the quadratic law F=12CdρAv2F = \tfrac{1}{2} C_d \rho A v^2, where CdC_d is a shape factor measured in a wind tunnel: about 1.1 for a flat plate, 0.47 for a sphere, 0.25–0.35 for a modern car, and roughly 0.04 for a sailplane fuselage. A car with CdC_d = 0.3 and 2.2 m² of frontal area meets 0.5 × 0.3 × 1.225 × 2.2 × 30² ≈ 364 N of drag at 30 m/s. Gustave Eiffel, having finished his tower, spent his later years dropping instrumented shapes down its side and then building France's first serious wind tunnel, producing the earliest reliable drag coefficients.

The v² is the entire story of highway fuel economy: drag force quadruples when you double speed, and since power is force times velocity, the power needed to overcome it grows with the cube — 8× the power from 50 to 100 km/h. That is why the last few km/h of top speed cost so much engine, why cyclists draft, and why the formula multiplies CdC_d by A rather than treating them separately; a slippery shape on a huge frontal area still pushes a lot of air.

Drag Force (F = ½CdρAv²) formula

FD=12CdρAv2F_D = \tfrac{1}{2} C_d \rho A v^{2}
Where
  • FDF_D= Drag force (N)
  • CdC_d= Drag coefficient
  • ρ\rho= Fluid density (kg/m³)
  • AA= Frontal area (m²)
  • vv= Speed (m/s)

Missing one of these? Work it out first, then come back