What Is the Drag Equation?
When an object moves through a fluid — whether air, water, or any other liquid — it experiences a resistive force known as the drag force. The drag equation lets you calculate this force precisely:
Where:
- Fd — Drag force (N or lbf)
- ρ (rho) — Fluid density (kg/m³ or lb/ft³)
- u — Relative velocity between object and fluid (m/s or ft/s)
- A — Reference area — the cross-sectional area orthogonal to the direction of motion (m² or ft²)
- Cd — Drag coefficient (dimensionless)
What Is the Drag Coefficient?
The drag coefficient Cd is a dimensionless number that captures how streamlined or blunt an object is. A lower Cd means less drag for the same size and speed:
| Object | Cd |
|---|---|
| Streamlined body (teardrop) | 0.04 |
| Half sphere (open end back) | 0.42 |
| Sphere | 0.47 |
| Cone (60° apex angle) | 0.50 |
| Long cylinder (⊥ to flow) | 0.82 |
| Human (upright) | 1.00 |
| Cube | 1.05 |
| Flat plate (⊥ to flow) | 1.28 |
| Bicycle + rider | 0.90 |
| Car (typical) | 0.30 |
Example Calculation
For a sphere (Cd = 0.47) with a cross-section of 1 cm² = 0.0001 m² moving at 3 m/s through olive oil (ρ = 920 kg/m³):
Fd = ½ × 920 × 9 × 0.0001 × 0.47
Fd ≈ 0.1945 N
How to Find the Drag Coefficient from Measured Force
Rearranging the drag equation for Cd:
- Measure the drag force on your object.
- Know the fluid density, velocity, and reference area.
- Multiply density × velocity² × area.
- Multiply your drag force by 2, then divide by the result above.
Terminal Velocity
An object reaches terminal velocity when drag force equals gravitational force (net force = 0). At that point:
Beyond terminal velocity, drag exceeds gravity and the object decelerates to that speed. This is why skydivers reach a maximum speed before deploying their parachute.
Unit Systems
This calculator supports both unit systems:
- Metric (SI): density in kg/m³, velocity in m/s, area in m² → force in Newtons (N)
- US Customary: density in lb/ft³, velocity in ft/s, area in ft² → force in pound-force (lbf). The calculator internally converts lb/ft³ to slug/ft³ (dividing by gc = 32.174 ft/s²) so the formula gives the correct result in lbf.
Frequently Asked Questions
Why does drag increase with the square of velocity?
Doubling the speed means four times the kinetic energy per unit volume of fluid that the object must push aside — hence the u² term in the equation.
What is dynamic pressure (q)?
Dynamic pressure is q = ½ × ρ × u². It represents the kinetic energy of the fluid per unit volume and acts as the "building block" of the drag force: Fd = q × A × Cd.
Does the drag coefficient change with speed?
Cd depends on the Reynolds number (Re = ρ × u × L / μ). For Re up to a few thousand it is approximately constant. At very high Reynolds numbers (turbulent transition) Cd can drop sharply — a phenomenon called the drag crisis, famously exploited by the dimples on a golf ball.