Quadratic Drag Calculator

Calculator Inputs

Mass (kg)

Object mass used in weight and acceleration calculations.

Initial Velocity (m/s)

Use positive values for downward motion.

Drag Coefficient, Cd

Sphere values often begin near 0.47.

Fluid Density (kg/m³)

Typical sea-level air density is 1.225.

Gravity (m/s²)

Earth standard gravity is 9.81.

Area Input Mode

Choose how the projected frontal area is defined.

Diameter (m)

Used when the calculator derives area from a circle.

Projected Area (m²)

Used when you already know frontal area.

Dynamic Viscosity (Pa·s)

Needed for Reynolds number estimation.

Characteristic Length (m)

Leave positive for custom Reynolds scaling.

Simulation Duration (s)

Controls the plotted velocity and position histories.

Time Step (s)

Smaller values produce smoother simulation lines.

Plotly Graphs

The first chart shows simulated velocity versus time. The second chart shows how quadratic drag force increases with speed.

Example Data Table

This sample table shows how different inputs affect drag force and terminal velocity.

Object	Mass (kg)	Cd	Area (m²)	Density (kg/m³)	Speed (m/s)	Drag Force (N)	Terminal Velocity (m/s)
Small sphere	2.00	0.47	0.0254	1.225	18.00	4.8836	35.7886
Flat plate	1.20	1.17	0.0400	1.225	12.00	4.1294	20.6668
Compact drone body	3.40	0.90	0.0600	1.225	22.00	16.0083	31.7072
Skydiver posture	80.00	1.00	0.7000	1.225	45.00	868.2188	42.7667

Formula Used

The calculator uses the quadratic drag model, where drag grows with the square of speed. This is common for fast-moving bodies in air and other fluids.

Drag Force: F_d = 0.5 × ρ × C_d × A × v²

Net Downward Force: F_net = m × g − F_d

Downward Acceleration: a = F_net / m

Terminal Velocity: v_t = √((2 × m × g) / (ρ × C_d × A))

Reynolds Number: Re = (ρ × v × L) / μ

Variable meanings: ρ is fluid density, C_d is drag coefficient, A is projected area, v is speed, m is mass, g is gravity, L is characteristic length, and μ is dynamic viscosity.

How to Use This Calculator

Enter the object mass and current velocity.
Provide drag coefficient and fluid density.
Choose whether area comes from diameter or direct area.
Enter viscosity and characteristic length for Reynolds number.
Set the simulation duration and time step.
Press the calculate button to show results above the form.
Review the graphs and example table for interpretation.
Use the CSV or PDF buttons to export the output.

Frequently Asked Questions

1) What is quadratic drag?

Quadratic drag is a resistance model where force increases with the square of speed. It is widely used for objects moving quickly through air or water.

2) When should I use this calculator?

Use it when drag changes strongly with speed. It fits falling bodies, sports projectiles, drone bodies, parachute cases, and other medium-to-high Reynolds number motion.

3) Why is drag coefficient important?

Drag coefficient captures shape effects. Smooth, streamlined objects usually have smaller values, while blunt or spread-out objects often produce higher drag forces.

4) What does projected area mean?

Projected area is the frontal area facing the flow. It is the effective surface used in the drag equation, not always the total object surface area.

5) What is terminal velocity?

Terminal velocity is the speed where drag equals weight for downward motion. At that point, net force becomes zero and acceleration approaches zero.

6) Why does the calculator estimate Reynolds number?

Reynolds number helps you judge the flow regime. It compares inertial and viscous effects and supports better interpretation of drag behavior.

7) Is the simulation exact?

The simulation is numerical. It is very useful for practical estimates, but real systems can differ due to lift, rotation, turbulence, changing density, or changing orientation.

8) Can I export the results?

Yes. The page includes CSV and PDF export buttons. They use the generated simulation table and summary values from your latest calculation.