Why does drag increase with the square of speed?
At higher speed you sweep through more fluid mass per second AND give each parcel more momentum — both scale with v, giving v².
Drag Force Calculator
F = ½ρv²C_DA
Calculate aerodynamic drag force. F = ½ρv²C_DA — resistance from moving through a fluid.
Calculate
Enter values above to calculate
How it calculates
1
F = ½ × ρ × v² × C_D × A
2
ρ = fluid density, v = speed, C_D = drag coefficient, A = frontal area
3
Result in newtons
Formula
F = ½ρv²C_DA
Variable Table
| Symbol | Quantity | SI Unit |
|---|---|---|
| F | Drag force | N |
| ρ | Fluid density | kg/m³ |
| v | Speed relative to fluid | m/s |
| C_D | Drag coefficient | dimensionless |
| A | Frontal cross-section area | m² |
How to Use This Calculator
This drag force calculator is built for quick physics checks and worked-problem review. Enter values in the units shown beside each input, then compare the result with the formula and variable table before using it in a longer solution. The calculator does the arithmetic, but the physics still depends on choosing a model that matches the situation.
Start by identifying the system, the known quantities, and the quantity you want to find. If a value is given in a non-SI unit, convert it before substitution. A correct numerical answer with mixed units can still be physically wrong, especially when squared units, inverse seconds, charges, temperatures, or distances are involved.
Assumptions and Limits
The formula F = ½ρv²C_DA is a model, not a universal description of every possible case. It assumes the quantities in the variable table are the relevant quantities for the problem and that hidden effects are either negligible or already included in the inputs. If friction, drag, relativistic speeds, changing fields, non-constant temperature, or geometry-specific effects matter, check whether a more complete model is needed.
Use the result as a magnitude and units check. Ask whether the answer has the right sign, whether it grows or shrinks when an input changes, and whether the limiting cases make sense. Setting an input to zero, doubling a quantity, or using a very large value is often enough to catch a formula choice or unit mistake before it reaches a final answer.
Worked Example
A car at 30 m/s: ρ=1.225, C_D=0.3, A=2.2 m². Find drag force.
Step 1: F = ½ρv²C_DA
Step 2: F = 0.5 × 1.225 × 900 × 0.3 × 2.2
Answer: F ≈ 364 N
Common Mistakes
- Drag ∝ v² — doubling speed quadruples drag (and roughly 8× the power at that speed)
- C_D depends on shape: ~0.3 for cars, ~0.04 for an aerofoil, ~0.47 for a sphere
- Use air density 1.225 kg/m³ at sea level
Related
Frequently Asked Questions
What is a drag coefficient?
A dimensionless number capturing shape efficiency. Lower is more streamlined: a sports car ≈ 0.3, a sphere ≈ 0.47.