Drag Equation Calculator

The drag equation calculator helps you compute a force exerted on a moving object immersed in a fluid. Reading the text below, you will discover what the equation for drag force is, how the shape of the object influences the force and what the drag coefficient is.

If an object moves through a fluid, it experiences a resisting force, the drag force. The value of this force depends on the size and shape of an object, the density of the fluid, and the relative velocity of the object and the fluid. The equation is

Fd = 1/2 × ρ × u² × A × Cd,

where:

• Fd – Drag force;
• ρ – Liquid's density;
• u – Relative velocity;
• A – Reference area; and
• Cd – Drag coefficient.

The reference area A for an object of a simple shape is the cross-sectional area orthogonal to the direction of the motion. For example, for a sphere of radius r, we would simply take A = π × r². For an object of a more complicated shape, like a car, the reference area is more difficult to specify, but usually, it's larger than the cross-sectional area.

For an application of the drag force, you can check the free fall with air resistance calculator and the Stokes' law calculator.

The drag force equation depends on the drag coefficient Cd. What is this? The drag coefficient is a dimensionless number that depends on the shape of the object. If an object has a smooth shape, then Cd is a small number, and the resulting drag force is small as well. For example, it's equal to 0.04 for a streamlined body, whereas it equals 1.05 for a cube.

The drag coefficient itself depends on the Reynolds number Re. The dependence is mild for a small enough Reynolds number (of a few thousand or smaller), and the drag coefficient is approximately constant. Check the Reynolds number calculator to learn more about different flows and their classification with Reynolds number.

How to use our drag equation calculator? Simply choose a liquid, immersed object, and the relative velocity between them. For example, for olive oil, the density ρ = 920 kg/m³, with an immersed long cylinder (Cd = 0.82) with cross-section A = 1 cm² and the relative velocity u = 3 m/s the resulting drag force is Fd = 0.3395 N.