# Drag Equation Calculator

Created by Davide Borchia
Last updated: Aug 24, 2022

Drag slows you when you are moving in a fluid: learn how to calculate the equation for the drag force with CalcTool. Our calculator will solve the drag force formula, giving you the result and, maybe, some inspiration to explore the topic. Drag is the first occurrence where you will see physics put aside its approximations to leave space for what happens in real life.

Keep reading our short article to learn what drag is, how to calculate the drag force and the explanation of the role of the factors in the equation. We will teach you how to calculate the drag coefficient, the area of the moving object, and much more.

## What is drag? Physics admits defeat

Drag is the resisting force resulting from the movement of a body through a fluid. This friction force is usually neglected in the basic physics model. Why?

• Drag is challenging to model correctly;
• Drag's effect becomes relevant only in certain situations; or
• Drag is outside our problem's scope.

However, for many situations (cycling fast enough, flying, swimming), we can't ignore the presence of the fluid, and we have to include drag in our solutions.

We can model drag at various levels: in our drag equation calculator, we will introduce you to the most widely used formula for the motion of objects in fluids. You can use it, e.g., to include drag force in the maximum height formula of projectile motion.

## The drag force equation: when spherical cows fall into ideal air

The most common drag equation in physics was developed by Lord Rayleigh. The equation to calculate the drag force $F_{\text{d}}$ is:

$F_{\text{d}} = \frac{1}{2}\cdot \rho\cdot u^2\cdot A\cdot C_{\text{d}}$

Where we find:

• $\rho$ — The density of the fluid;
• $u$ — The relative velocity of the body (one of the dominant factors in the drag equation due to the exponent);
• $A$ — The reference area; and
• $C_{\text{d}}$ — The drag coefficient.

As you can see, the formula for the drag force is nothing but multiplication. The story gets more complex when we analyze the single factors.

## The reference area in the drag force formula

When calculating the drag equation, we need to choose the area of the moving object. However, unless we are dealing with bodies with flat surfaces moving "face first", we can't directly input the area of the object.

As in many other physics problems, we need to calculate the cross-sectional area. This quantity is the projection of the body in the plane perpendicular to the direction of motion. A sphere and a cone with the same radius have identical cross-sectional areas (if the cone moves apex-first). The same cube moving face-first or vertex-first has different values of the reference area.

We can't teach you how to calculate the drag force's reference area: you need to apply different calculations for each problem.

## How to calculate the drag coefficient in the drag equation

The drag coefficient in the equation for the drag force contains most of the approximations we introduce in our calculations for this phenomenon.

$C_{\text{d}}$, the drag coefficient, is a dimensionless number that models the aerodynamics (or hydrodynamics) of a body. It mostly depends on the shape of the body*, being lower for streamlined objects, thus reducing the drag force, and higher for objects with flat surfaces such as cubes and cylinders.

The shape, however, is not everything: the Reynolds number, discriminating between turbulent and laminar flow, affects the drag coefficient. In a somewhat surprising way (due to fluid dynamics), the drag coefficient decreases when the fluid becomes more turbulent.

However, the increased speed of the fluid makes up for this, causing an increase in the drag force.

We can calculate the drag coefficient using the formula for the drag force, but since both are usually unknown, we often resort to tabulated values to find the value of $C_{\text{d}}$.

We associated different values with different shapes; hence we can choose, for example:

• $C_{\text{d}}=1.15$ for a short cylinder (the worst value you can plug in the drag equation);
• $C_{\text{d}}=1.05$ for a cube;
• $C_{\text{d}}=0.80$ for an angled cube (lower since it "pierces" the fluid);
• $C_{\text{d}}=0.50$ for a cone (now you know why fighter jets have such long noses);
• $C_{\text{d}}=0.47$ for a sphere (and for spherical cows); and
• $C_{\text{d}}=0.04$ for a streamlined body.

Use these values in our drag equation calculator, or search for tabulated values online. Check our other tools to find more about various shapes. We have, for example, the cone volume calculator or the tetrahedron volume calculator, which might be useful for the drag equation in physics.

Davide Borchia
Density
kg/m³
Velocity
m/s
Drag coefficient
Area
Drag force
N
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