Contact Angle Calculator

Reviewed By: Patrick Myers (BSME)

Enter the contact angle and the surface tensions of the interfaces into the calculator to determine the missing variable.

Young’s Equation

Work of Adhesion

Surface Energy (OWRK)

Roughness (Wenzel)

Cassie–Baxter

Enter any 3 values to calculate the missing variable

Contact Angle

Surface Tension of Solid-Liquid Interface

Surface Tension of Solid-Gas Interface

Surface Tension of Liquid-Gas Interface

Liquid preset (γLG):

Related Calculators

Contact Angle Formula

The following formula is used to calculate the contact angle for a given set of surface tensions.

cos(θ) = (γ_{SG} - γ_{SL}) / γ_{LG}

Variables:

θ is the contact angle in degrees
γ_SG is the surface tension of the solid-gas interface (N/m)
γ_SL is the surface tension of the solid-liquid interface (N/m)
γ_LG is the surface tension of the liquid-gas interface (N/m)

To calculate the contact angle, subtract the surface tension of the solid-liquid interface from the surface tension of the solid-gas interface. Divide the result by the surface tension of the liquid-gas interface and take the arccosine of the result to get the contact angle in degrees.

What is a Contact Angle?

A contact angle is the angle at which a liquid interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid. The contact angle is determined by the balance of adhesive and cohesive forces at the interface. A high contact angle indicates poor wettability, while a low contact angle indicates good wettability. Contact angles are used in various applications, including material science, surface chemistry, and fluid mechanics, to understand and control the interactions between liquids and solid surfaces.

How to Calculate Contact Angle?

The following steps outline how to calculate the Contact Angle.

First, determine the surface tension of the solid-liquid interface (γ_SL).
Next, determine the surface tension of the solid-gas interface (γ_SG).
Next, determine the surface tension of the liquid-gas interface (γ_LG).
Finally, calculate the contact angle using the formula cos(θ) = (γ_SG – γ_SL) / γ_LG.
After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Surface tension of the solid-liquid interface (γ_SL) = 0.03 N/m

Surface tension of the solid-gas interface (γ_SG) = 0.07 N/m

Surface tension of the liquid-gas interface (γ_LG) = 0.05 N/m