What is the Young equation?

The Young equation relates the contact angle (θ) to the three interfacial energies at the solid–liquid–vapor triple line: γSV = γSL + γLV cos(θ). Here γSV is the solid–vapor surface energy, γSL is the solid–liquid interfacial energy, and γLV is the liquid–vapor surface tension. It describes the mechanical equilibrium of a sessile droplet on an ideal flat solid.

What is surface energy and what are its units?

Surface energy (or surface free energy) is the excess energy at the surface of a material compared to its bulk. It represents the energy required to create a unit area of new surface. It is measured in millinewtons per meter (mN/m) or equivalently millijoules per square meter (mJ/m²), which are numerically equal.

What contact angle indicates good wettability?

Contact angles below 90° indicate hydrophilic wetting (the liquid spreads). Angles below 10° are considered superhydrophilic. Angles above 90° indicate hydrophobic behavior, and angles above 150° indicate superhydrophobicity. A contact angle of 0° means complete spreading.

What is the work of adhesion?

The work of adhesion (W_A) is the energy needed to separate the liquid–solid interface and create two new free surfaces. It is given by the Dupre formula: W_A = γLV (1 + cosθ). It quantifies how strongly the liquid adheres to the solid.

Can I use this for non-water liquids?

Yes. Enter the surface tension of any probe liquid. Common values include water (72.8 mN/m at 20°C), ethanol (22.4 mN/m), diiodomethane (50.8 mN/m), and glycerol (63.4 mN/m). Using multiple liquids (Owens–Wendt method) gives more accurate surface energy component analysis.

What are the limitations of the Young equation?

The Young equation assumes an ideal, flat, chemically homogeneous, and rigid surface. Real surfaces show contact angle hysteresis due to roughness and heterogeneity. On rough surfaces, the Wenzel or Cassie–Baxter equations may be more appropriate. The equation also assumes thermodynamic equilibrium.

Surface Energy Calculator

Enter a liquid contact angle and its known surface tension to calculate the solid surface energy using the Young equation.

Surface Energy Inputs

γ_SV = γ_SL + γ_LV cosθ

Preset probe liquids (click to load γ_LV)

Contact Angle (θ) degrees (0–180)

Liquid Surface Tension (γ_LV) mN/m

Solid–Liquid Interfacial Energy (γ_SL) mN/m — optional

Example scenarios (click to load)

Enter contact angle and liquid surface tension, then click Calculate

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Summary

The Surface Energy Calculator applies the Young equation (γSV = γSL + γLV cosθ) to determine the solid–vapor surface energy from a measured contact angle and the known surface tension of the probe liquid. It also computes the work of adhesion (Dupre work) and wettability classification. All calculations run entirely in the browser with no server communication.

How it works

Enter the contact angle (θ) of the liquid droplet on the solid surface in degrees (0–180).
Enter the surface tension of the probe liquid (γLV) in mN/m (millinewtons per meter).
Optionally enter the solid–liquid interfacial energy (γSL) if known; without it, only the adhesion tension (γSV − γSL) can be determined.
Click Calculate to get the solid surface energy when γSL is known, or adhesion tension when it is omitted.
Review the wettability classification (superhydrophilic, hydrophilic, hydrophobic, superhydrophobic).
Use the preset liquids to auto-fill common surface tension values.

Use cases

Determine whether a coating or polymer surface is hydrophilic or hydrophobic.
Calculate solid surface energy from goniometer contact angle measurements.
Assess wettability of biomaterial surfaces for biomedical device design.
Estimate adhesive bonding potential between two materials.
Quality-control surface treatment processes such as plasma activation or chemical etching.
Screen surfaces for ink or paint adhesion in printing and coating applications.
Verify cleanliness of glass or metal surfaces before bonding.
Teach surface chemistry and wetting concepts in materials science courses.

Frequently Asked Questions

Last updated: 2026-09-30 · Reviewed by Nham Vu