Drag Coefficient Calculator

Drag force

Fluid density

Velocity

Reference area

Drag coefficient

Find the Reynolds number

Add a size dimension and the fluid viscosity to find the Reynolds number for this flow.

Add induced and total drag

For a wing, split drag into a base part and a lift-induced part and add them up.

Drag coefficient

Drag force: N
Dynamic pressure: Pa
Drag area (Cd x A): m²

Power to overcome drag: kW

The drag coefficient stays about the same as speed changes, but the drag force does not. Force grows with the square of speed, so doubling the speed roughly quadruples the drag.

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Show drag force vs speed

Plot how the drag force grows as speed rises for this drag coefficient.

Show power vs speed

Plot the power needed to push through the fluid at each speed.

Show the speed impact table

Compare drag and power at several speeds around your input.

Drag force and power at speeds around your input
Velocity (m/s)	Drag force (N)	Power (W)	Change vs current
15	90.96	1,364.34	-75.0%
22.5	204.65	4,604.66	-43.7%
30	363.83	10,914.75	+0.0%
37.5	568.48	21,317.87	+56.3%
45	818.61	36,837.28	+125.0%
60	1,455.3	87,318	+300.0%

The drag coefficient is a single number that indicates how much resistance an object experiences when moving through a fluid. It combines the effects of shape, surface and flow into one dimensionless value, making it possible to compare objects like spheres, cars or wings on the same scale.

This calculator can calculate the drag coefficient from measured values and vice versa. If one of the five fields is left blank, the corresponding value will be calculated.

What is a drag coefficient?

When an object moves through air or water the fluid creates a force that resists it. This force is drag. The drag coefficient, denoted by $C_d$ , gives the proportion of drag that depends on shape while providing no information about size, speed, or the fluid itself. A teardrop shaped object has a low drag coefficient and can move easily through a fluid. A flat plate facing into a flow has a higher drag coefficient.

Because the drag coefficient is dimensionless it has wide applicability. As long as flow conditions match, values measured in a wind tunnel can be used to predict drag at different speeds or altitudes.

How to use this calculator:

If you input the drag, fluid density, velocity and reference area, this tool will calculate the drag coefficient. This is how a wind tunnel test works. First, flow conditions are set up and drag is measured, then the drag coefficient is found by dividing.

If you want to calculate values, leave the desired field blank and enter the remaining four values. This tool will then show you the object's drag, the speed required to produce a known drag or the area corresponding to a given coefficient. Two additional options allow for further calculations: one calculates the flow's Reynolds number while the other decomposes an airfoil's drag into its parasite and induced lift components.

Formula for calculating the resistance coefficient

The resistance coefficient $C_d$ can be directly derived from the resistance equation.

C_d = \frac{2 F_d}{\rho\,v^{2}\,A}

Here, $F_d$ is the drag force, $\rho$ is the fluid density, $v$ is the velocity and $A$ is the reference area. The same relationship in the full drag equation is:

F_d = \tfrac{1}{2}\,\rho\,v^{2}\,A\,C_d

Consider a car traveling at 30 m/s. The car is moving through the air above sea level and has a speed of about 108 km/h. The frontal area is 2.2 m $^2$ , and the measured drag in a wind tunnel is 363.8 N.

The drag coefficient is calculated as follows:

C_d = \frac{2 (363.8)}{(1.225)(30)^{2}(2.2)} \approx 0.30

This value of 0.30 is typical for modern cars. The following table shows the individual symbols and their numerical values for this example.

Symbol	Meaning	Example
$C_d$	Drag coefficient	0.30
$F_d$	Drag force	363.8 N
$\rho$	Fluid density	1.225 $kg/m^3$
$v$	Velocity	30 m/s
$A$	Reference area	2.2 $m^2$

Typical resistance coefficient values

The drag coefficient depends mainly on the shape and can change slightly for blunt bodies due to flow separation. The following are general reference values that may be used as a starting point for estimates or to check the validity of results.

Shape	Approximate Cd
Streamlined body or airfoil	0.04
Modern car	0.25 to 0.30
Sphere	0.47
Solid hemisphere, flat side back	0.42
Hollow hemisphere, open side forward	1.42
Long cylinder, side on	0.82
Cube, flat face forward	1.05
Flat plate, face on	1.28
Open parachute	1.3 to 1.5

The reference area is important.

The friction coefficient only acquires its meaning in combination with the area to which the measurement refers. Even for the same object, the resulting value depends on the surface used, whether it is the frontal surface, the base surface or the wetting surface.

For cars and most blunt bodies the frontal area is used. For wings the projected area is usually used. If you read a published drag coefficient, check which area was used and use that same area for your own calculations or else the results will differ by the ratio of the areas.

Reynolds number

The drag coefficient is not constant; it depends on the Reynold's number which compares inertial forces to viscous forces of the flow field.

Re = \frac{\rho\,v\,D}{\mu}

Here, $D$ represents a characteristic length such as diameter or chord depth and $\mu$ is the viscosity of the fluid. You can check this value by opening the Reynolds number option and entering the dimensions and the viscosity. A coefficient measured at one particular Reynolds number may be very different from another completely different Reynolds number. For that reason, wind tunnel tests are designed to match the actual flight or driving conditions as closely as possible in terms of Reynolds numbers.

Induced resistance and total resistance

The total drag on the wing is made up of two components. On one hand, there's the basic drag caused by shape and surface friction, usually denoted with $C_{d0}$ . On the other hand, there's induced drag, or the "cost" a wing pays to generate lift. Induced drag depends on the lift coefficient $C_l$ , aspect ratio $AR$ and span efficiency factor $e$ .

C_{di} = \frac{C_l^{2}}{\pi\,AR\,e}

The total drag coefficient is the sum of these two components.

C_d = C_{d0} + C_{di}

Thin wings with a high aspect ratio have lower induced drag. This is one of the reasons that glider wings are so thin. The efficiency factor in spanwise direction for an idealized elliptical lift distribution is 1.0, but real wings will be slightly less efficient and typically have a value close to 0.7. If you open up the induced drag option and add these inputs then you can check out the breakdown of the drag.

Areas of application for resistance values:

Automobile manufacturers seek to improve fuel economy and increase range by lowering drag coefficients. Aircraft and rocket designers track the drag coefficient over all speed ranges in order to determine engine size and predict performance.

The drag coefficient is also used in sports applications. From the optimized body position when cycling to the design of ski clothing - in civil engineering you must also control wind resistance that towers and bridges are exposed to.

Frequently asked questions

What is a drag coefficient?

The drag coefficient Cd is a dimensionless number that indicates how strongly a shape impedes movement in a fluid. It allows for the comparison of different objects under equal conditions by making the influence of shape independent from size, speed and fluid. Streamlined shapes have a low value while blunt ones have a high one.

How do you calculate the drag coefficient?

Use this formula: Cd = 2Fd/(ρ*v squared*A). Enter the measured drag force, fluid density, velocity and reference area. If you enter a drag coefficient into the corresponding field, then this tool will calculate it for you. This is equivalent to the division used to convert wind tunnel drag measurements into a coefficient.

How good is a good drag coefficient?

It depends on the shape. Modern cars have values between 0.25 and 0.30, a sphere has about 0.47, a cube that is hit from the front has about 1.05, and an aerodynamic wing can get close to 0.04. The lower the value, the easier it moves through the liquid.

Does the drag coefficient change with speed?

In the normal speed range it is generally relatively constant within a certain range but actually changes depending on the Reynolds number which increases with increasing speed and dimension. As you approach the speed of sound compressibility effects start to come into play resulting in larger changes. Open the option for the Reynolds number and check what value is appropriate for the state of the flow field being considered.

What is induced resistance?

Induced drag is the extra drag that occurs when lift is produced by a wing. It is equal to Cl^2 / (pi x AR x e), where Cl is the coefficient of lift, AR is the aspect ratio and e is the span efficiency factor. The total drag is made up of the base drag plus this induced drag.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

NASA Glenn Research Center: The Drag Coefficient
NASA explainer on the drag coefficient, reference area, and induced drag.
LMNO Engineering: Drag Force and Drag Coefficient
Drag force calculation with shape coefficients and the Reynolds number.
Wikipedia: Drag coefficient
Reference drag coefficients for common shapes and the underlying theory.