Solve Young’s equation for contact angle or any interfacial energy, calculate adhesion and spreading, or average measured left and right drop angles.

Young’s model assumes an ideal smooth, rigid, chemically uniform surface at equilibrium. Contact angle is measured through the liquid.

Optional settings

Optional; blank means 1. Actual wetted area / projected area; assumes fully wetted roughness.

Related Calculators

Contact Angle Formula

Young’s equation gives the equilibrium contact angle through the liquid for an ideal smooth, rigid, chemically uniform surface. Use compatible interfacial-energy units and a positive liquid–gas tension; the ratio must be within −1 to 1 for a real angle. Roughness, chemical variation and contact-angle hysteresis can limit this model.

cos(θ) = (γSG - γSL) / γLG

Variables:

  • θ is the contact angle in degrees
  • γSG is the surface tension of the solid-gas interface (N/m)
  • γSL is the surface tension of the solid-liquid interface (N/m)
  • γLG 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.

  1. First, determine the surface tension of the solid-liquid interface (γSL).
  2. Next, determine the surface tension of the solid-gas interface (γSG).
  3. Next, determine the surface tension of the liquid-gas interface (γLG).
  4. Finally, calculate the contact angle using the formula cos(θ) = (γSG – γSL) / γLG.
  5. 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 (γSL) = 0.03 N/m

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

Surface tension of the liquid-gas interface (γLG) = 0.05 N/m. The ratio is (0.07 − 0.03) / 0.05 = 0.8, giving θ ≈ 36.87°.