Estimate drag force, acceleration, terminal velocity, and motion changes using customizable object, atmosphere, unit, and simulation settings for practical physics analysis and learning today.
Quadratic drag uses Fd = ½ρCdAv².
Downward acceleration uses a = g − Fd/m.
Linear drag uses Fd = bv and a = g − bv/m.
Terminal velocity uses vt = √(2mg ÷ ρCdA).
Simulation uses fourth-order Runge-Kutta integration for changing velocity.
| Time | Velocity | Acceleration | Distance | Height |
|---|
Air resistance opposes motion through the surrounding atmosphere. Its size depends strongly on speed and shape. Quadratic drag usually fits everyday high-speed motion. The drag force grows with velocity squared. Faster objects therefore experience much stronger resistance. Mass also changes the resulting acceleration noticeably. Heavy objects need more drag for equal deceleration.
Cross-sectional area controls how much air is displaced. A larger frontal area usually creates stronger drag. Drag coefficient summarizes shape and airflow effects. Streamlined bodies usually have lower coefficients than plates. Air density also matters in every quadratic calculation. Dense air produces more resistance at equal speed. Higher altitude often reduces density and drag somewhat.
Terminal velocity occurs when drag balances an object's weight. Net force then becomes approximately zero. Acceleration also approaches zero during steady falling motion. The object can still move very quickly. Terminal velocity changes with mass, area, and shape. It also changes when atmospheric density changes.
Acceleration with drag is not normally constant. It changes as the object's velocity changes. Simple constant-acceleration formulas can therefore become inaccurate. Numerical simulation handles this changing acceleration directly. This calculator uses an RK4 integration method. Smaller time steps generally improve numerical accuracy. Very small steps can increase computing work unnecessarily.
Use the instantaneous mode for one specific velocity. Use simulation mode for motion across several seconds. Height input can estimate ground impact during descent. Results remain idealized and ignore changing winds. They also assume chosen coefficients remain reasonably constant. Real objects may tumble or change orientation. Those changes can alter drag significantly during motion.
A positive downward acceleration means downward speed increases. Negative downward acceleration means the object is slowing. Upward motion always receives downward gravity and drag. That combination usually produces strong downward acceleration initially. Compare drag with weight for quick interpretation. A ratio near one indicates near-terminal conditions. Always confirm units before comparing different examples. Use realistic inputs for safer, clearer classroom physics comparisons.
| Object | Approximate Cd | Typical note |
|---|---|---|
| Sphere | 0.47 | Common reference value |
| Cube | 1.05 | Bluff body |
| Flat plate | 1.17–1.28 | Facing airflow |
| Streamlined body | 0.04–0.15 | Low drag shape |
| Automobile | 0.25–0.40 | Varies by design |
| Skydiver | 1.0–1.3 | Spread position |
| Mass | Velocity | Cd | Area | Air density | Purpose |
|---|---|---|---|---|---|
| 80 kg | 50 m/s | 1.10 | 0.70 m² | 1.225 kg/m³ | Skydiver-style estimate |
| 1 kg | 20 m/s | 0.47 | 0.01 m² | 1.225 kg/m³ | Small sphere |
| 1200 kg | 30 m/s | 0.30 | 2.2 m² | 1.204 kg/m³ | Vehicle drag illustration |
Air resistance is a force opposing motion through air.
Quadratic drag grows with velocity squared under common conditions.
Terminal velocity occurs when drag balances weight during falling.
Quadratic drag suits many everyday objects and moderate speeds.
No. Drag always acts opposite the object's current motion.
RK4 improves accuracy when acceleration changes continuously with velocity.
Yes. Add a starting height in downward simulation mode.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.