Drag Force Calculator

Drag is the force that impedes an object's motion through a fluid (whether air or water). This calculator computes drag from the fluid density, velocity, projected area and drag coefficient which describes shape using the standard drag equation.

If any one of the five input fields are left blank then the program will switch to mode for computing that value. So you can use this same tool to compute drag, derive the drag coefficient from a measured drag or determine the velocity at which a given drag occurs.

What is resistance?

When an object and a fluid move relative to each other, the fluid impedes the motion of the object. This impedance is drag, and its direction is always opposite to that of motion. The magnitude of drag is affected by four factors: the density of the fluid, the speed of the object, the projected area of the object, and the shape, particularly how streamlined it is. Speed has the greatest effect because it appears as a square in the expression, which means that a small increase in speed leads to a large increase in drag.

The drag coefficient $C_d$ describes the shape. For a flat plate perpendicular to the flow it is about 1.28. For a teardrop shaped object with smooth surface it goes down to about 0.04. A teardrop shaped object, for the same projected area, will experience drag that is about 97% less.

How to use this calculator:

Enter the fluid density, velocity, reference area and drag coefficient and the calculator will return the drag. To calculate a value, leave blank the field for which you would like to solve and enter values for the remaining four fields. No mode selection is required; the program directly solves for the empty input field. This allows common tasks such as calculating the drag on an automobile or ship hull, determining the drag coefficient from a measured drag, or finding the velocity at which a particular drag occurs. If you enable the "object motion" option and enter a mass, then you can also calculate the terminal velocity and acceleration due to drag.

Formula for resistance:

The drag force $F_d$ can be calculated from the standard formula for drag, which is based on the conservation of momentum in fluid mechanics.

where $\rho$ is the density of the fluid, $v$ is the velocity, $A$ is the reference area and $C_d$ is the drag coefficient. So let's say a plate with an area of 1 m$^2$ is placed in air above sea level and exposed to a wind of 10 m/s coming directly at it, where the drag coefficient is 1.28.

To hold this plate in place requires about 78 newtons of force, which is roughly the weight of an 8 kg bag. The following table shows the individual symbols and values used in this example.

Now consider a car. If the air density remains 1.225 kg/m$^3$ and the car is traveling at 30 m/s with a frontal area of about 2.2 m$^2$ and a drag coefficient typical for modern cars (0.28), then the drag will be about 340 N. If the speed doubles to 60 m/s, the drag does not double but increases by about four times to 1,358 N. This is because the velocity factor is squared. This is one reason why driving at high speeds on a highway uses more fuel than most drivers expect.

Formula for calculating any values:

The formula for resistance is a simple multiplication and can therefore be easily modified. The calculator uses the following format and selects the appropriate formula based on what fields are filled in.

The first format converts the measured force into a drag coefficient to convert wind tunnel measurements into published values. The second format indicates how fast an object must move to experience a particular amount of drag.

The other two dimensions that are shown by the calculation tool:

In addition to drag, the calculator also displays dynamic pressure and power. Dynamic pressure $q = \tfrac{1}{2}\rho v^{2}$ is the pressure exerted by a moving fluid, and is the actual cause of drag. Power $P = F_d\,v$ is the rate at which energy is expended in overcoming drag at that speed. Since drag increases with the square of velocity, and power is the product of drag and the velocity factor, power increases proportionally to the cube of velocity.

Resistance coefficient:

The drag coefficient is a dimensionless number that represents the influence of an object's shape on its drag. Smooth, streamlined objects have lower values because they can move through a fluid more easily. Blunt or flat shapes have higher values. The drag coefficient changes slightly depending on flow conditions determined by the Reynolds number, but for everyday speeds single values are usually sufficient to get reasonable results. Typical values are given below as reference.

Fluid density used:

The formula for drag can be applied to any fluid, so the difference between air and water is due to density. Air at sea level is usually used as a baseline, while the density of water is about 800 times that. So running in waist deep water at full speed feels completely different than running on land. As the density decreases with altitude, drag will be less at high altitudes than it would be at sea level even if the same speed were reached.

Final speed and deceleration:

If you enable the option for object motion and add mass two additional results are available. A falling object accelerates until drag is large enough to balance gravity. At that point the resultant force is zero and the speed stabilizes. If you set the drag force equal to gravity and calculate the speed, you get terminal velocity.

A skydiver with a mass of 80 kg in the belly position has an end speed of about 43 m/s, which is approximately 155 km/h, at a drag coefficient of about 1.0 and an area of about 0.7 m$^2$. The calculator also shows the deceleration caused by the drag $a = F_d / m$, which indicates how much the object slows down with given input speed and is directly derived from Newton's second law.

Forms of resistance.

The drag coefficient is just a number but it combines several different physical effects. The shape drag, also called pressure drag, comes from the flow remaining behind an object. Blunt shapes create more turbulent flow and thus higher drag while teardrop shaped objects allow the fluid to smoothly rejoin behind the object.

Surface friction drag is caused by the fluid rubbing against the surface so a rougher surface causes more drag. The dimples on a golf ball are for this reason. Although it seems counterintuitive at first they create a thin turbulent layer that clings to the ball longer, reducing the separation and overall drag. Induced drag is the price paid to generate lift. This is because high pressure fluid flowing around the wingtips creates vortices which carry away energy.

Important applications of resistance

Drag affects the design of cars, airplanes, rockets and trains. In these areas, less drag means lower fuel consumption and higher speeds. Drag has also contributed to the development of equipment for cycling, swimming and motor sports, where even small differences in shape can lead to noticeable performance improvements. Drag also has positive applications. Parachutes are pure drag devices, brake flaps slow jet aircraft down, and wind turbines generate energy from the movement of air. When you want to slow an object down or extract energy from a flowing fluid, drag is your friend.

Tips for a good estimate

Make sure the reference area matches that used for the drag coefficient you choose. All published coefficients are based on a particular area, usually the frontal area. Use a fluid density appropriate to your environment and conditions, not always air at sea level. The result can be considered a reasonable estimate. Actual drag also depends on surface roughness, flow separation, and compressibility at high speeds, but a single coefficient cannot fully capture these factors.