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Quadratic-Drag Terminal Velocity Calculator — result sheet
Estimate terminal speed when gravitational force balances quadratic drag in a fluid.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: At terminal speed mg = ½CρAv², so vₜ = √[2mg/(CρA)].
Terminal speed is reached in this model when downward weight and upward quadratic drag balance. Changing orientation or shape changes the supplied area and drag coefficient.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Object mass — kg; minimum 1.0E-6; maximum 1000000000
- Gravitational acceleration — m/s²; minimum 1.0E-6; maximum 1000000
- Fluid density — kg/m³; minimum 1.0E-6; maximum 1000000
- Drag coefficient — minimum 1.0E-6; maximum 1000
- Reference area — m²; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Object mass | 0.2 |
| Gravitational acceleration | 9.80665 |
| Fluid density | 1.225 |
| Drag coefficient | 0.47 |
| Reference area | 0.01 |
Quadratic-drag terminal speed ≈ 26.39 m/s (95.0 km/h).
Assumptions and limits
- The object falls steadily in a uniform fluid and quadratic drag is appropriate.
- Mass, gravity, density, area, and coefficient are positive and use SI units.
- Acceleration toward terminal speed, buoyancy, wind, compressibility, turbulence, and shape changes are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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