Drag Force Formula
Calculate aerodynamic or hydrodynamic drag on an object moving through fluid.
Key to vehicle and aircraft design.
The Formula
F_D = ½ × ρ × v² × C_D × A
Drag force opposes the motion of any object moving through a fluid (air, water, etc.). It increases with the square of velocity — doubling speed quadruples drag.
Variables
| Symbol | Meaning |
|---|---|
| F_D | Drag force (Newtons) |
| ρ | Fluid density (kg/m³) — air ≈ 1.225, water ≈ 1000 |
| v | Velocity of the object relative to the fluid (m/s) |
| C_D | Drag coefficient (unitless, depends on shape) |
| A | Reference area — typically frontal cross-section (m²) |
Example 1
Find the drag on a car (C_D = 0.3, A = 2.2 m²) at 100 km/h in air
v = 100 km/h = 27.78 m/s, ρ = 1.225 kg/m³
F_D = 0.5 × 1.225 × (27.78)² × 0.3 × 2.2
F_D = 0.5 × 1.225 × 771.7 × 0.3 × 2.2
F_D ≈ 312 N
Example 2
Find the drag on a sphere (C_D = 0.47, diameter 0.1 m) at 5 m/s in water
A = π × (0.05)² = 0.00785 m², ρ = 1000 kg/m³
F_D = 0.5 × 1000 × 25 × 0.47 × 0.00785
F_D ≈ 46.1 N
When to Use It
Use the drag force formula when:
- Designing vehicles, aircraft, or boats for efficiency
- Calculating fuel consumption at different speeds
- Estimating terminal velocity of falling objects
- Optimizing the aerodynamic shape of structures