Drag Coefficient Calculator Formula

Understand the math behind the drag coefficient calculator. Each variable explained with a worked example.

Formulas Used

Drag Force

drag_force = 0.5 * cd * density * area * pow(velocity, 2)

Dynamic Pressure

dynamic_pressure = 0.5 * density * pow(velocity, 2)

Variables

VariableDescriptionDefault
cdDrag Coefficient (Cd)0.47
densityFluid Density(kg/m3)1.225
areaReference Area(m2)0.01
velocityVelocity(m/s)20

How It Works

Aerodynamic Drag Force

Drag opposes the motion of an object through a fluid.

Formula

F_d = 0.5 Cd rho A v^2

  • *Cd* = drag coefficient (shape-dependent, dimensionless)
  • *rho* = fluid density
  • *A* = reference frontal area
  • *v* = velocity relative to fluid
  • Common Cd values: sphere 0.47, streamlined body 0.04, flat plate 1.28, car 0.25-0.45.

    Worked Example

    Sphere (Cd = 0.47) of cross-section 0.01 m2 in air at 20 m/s.

    cd = 0.47density = 1.225area = 0.01velocity = 20
    1. 01F_d = 0.5 * 0.47 * 1.225 * 0.01 * 400
    2. 02F_d = 0.235 * 1.225 * 4
    3. 03F_d = 1.152 N

    Frequently Asked Questions

    Why does drag scale with velocity squared?

    At moderate to high speeds, drag is dominated by inertial effects (pressure drag). The kinetic energy of deflected air grows as v^2, so the force does too.

    What determines the drag coefficient?

    Primarily the shape and surface roughness. Streamlined shapes direct flow smoothly with less separation, giving lower Cd.

    Does Cd depend on Reynolds number?

    Yes, especially for smooth objects. The drag crisis for a sphere occurs around Re = 500 000, where Cd drops sharply.

    Ready to run the numbers?

    Open Drag Coefficient Calculator