Lift Coefficient Calculator

Created by Gabriela Diaz
Last updated: Nov 16, 2022

This lift coefficient calculator can assist you in designing or evaluating an aerodynamic surface. With this tool, you can obtain the lift coefficient by simply indicating the lift force and the aerodynamic conditions of your problem.

With applications that range from aircraft in aeronautics, pipes undersea, and even studying the trajectory of a tennis ball, the lift coefficient is a vital factor in the aerodynamics of objects. So, what exactly is the lift coefficient? What factors influence the lift coefficient? What is the lift coefficient formula? Keep reading to find out! 🛩

The drag coefficient and the drag force are other essential factors when studying a problem's aerodynamic aspects. Learn more about these with our drag equation calculator!

What is the lift coefficient?

The lift coefficient is a dimensionless parameter used primarily in the aerospace and aircraft industries to define the relationship between the angle of attack and wing shape and the lift it could experience while moving through air.

This coefficient allows us to compare the lifting ability of a wing at a given angle of attack. We'll typically find these two plotted in a lift coefficient vs. angle of attack (AoA or $\alpha$) graph, showing a linear relationship until stall. It's worth mentioning that the lift coefficient is also influenced by Mach number and Reynold's number.

💡 In fluid mechanics, these numbers are of great importance. You can read more about them at our Reynolds number calculator and Mach number calculator.

How to calculate lift coefficient – Lift coefficient equation

Now that we've seen what the lift coefficient is, let's go on to how to calculate it. We can obtain the value of this coefficient with a simple formula that relates the lift force, the surface area, and dynamic pressure. This is the coefficient of lift equation:

$\small C_\text L = \cfrac{F}{A \, q}$

where:

• $C_\text L$ – Lift coefficient, this a dimensionless value;
• $F$ – Vertical lift force, it can be expressed in N or lbf;
• $A$ – Surface area of the wing; and
• $q$ – Dynamic pressure.

Recall that the dynamic pressure $q$ is affected by flow speed $V$ and the density of the fluid $\rho$. We calculate $q$ with this expression:

$\small q = \cfrac{1}{2}\rho V^2$

Then we can simply substitute this in the initial $C_\text L$ formula, resulting in the following lift coefficient formula:

$\small C_\text L = \cfrac{2\, F}{A \, \rho \, V^2}$

Different factors, such as temperature and pressure, can affect the air's density. Our air density calculator can provide you with a more accurate density value that adjusts to your particular problem's conditions 🌬

🙋 This lift coefficient equation results from rearranging the equation for lift force: $F = \cfrac{1}{2} \rho V^2 A C_\text L$. Lift coefficients are usually measured in a wind tunnel test.

How to use this lift coefficient calculator

By simply entering four values, this lift coefficient calculator will determine the lift coefficient of your problem. Let's go over to see how to use this tool:

1. Begin by entering the Lift force (F).
2. Next, indicate the Flow speed (V).
3. Input the Surface are (A) of the wing.
4. The calculator is already pre-filled with a value for air density. If the medium under consideration is not air, enter its density in the calculator's Density (ρ) field.
5. Once these values are defined, the calculator will display the value for the Lift coefficient (CL).
6. That's all! 😉
Gabriela Diaz
Lift force (F)
lbf
Flow speed (V)
ft/s
Surface area (A)
in²
Density (ρ)
lb/cu ft
Lift coefficient (Cₗ)
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