What is the Young equation?

Young's equation relates the three interfacial surface tensions at a three-phase contact line: cos θ = (γSV − γSL) / γLV, where γSV is solid-vapor, γSL is solid-liquid, and γLV is liquid-vapor surface tension.

What does a contact angle below 90° mean?

A contact angle below 90° means the surface is hydrophilic — the liquid tends to spread. Angles below 10° indicate near-complete wetting. Common examples are clean glass with water.

What does a contact angle above 90° mean?

A contact angle above 90° indicates a hydrophobic surface where the liquid beads up rather than spreading. Angles above 150° are superhydrophobic, like the lotus leaf effect.

What units should I use for surface tension?

Surface tension is typically expressed in millinewtons per meter (mN/m) or dynes per centimeter (dyn/cm), which are numerically equivalent. Common values: water-air ≈ 72.8 mN/m at 20°C.

When does the calculation fail?

If (γSV − γSL) / γLV falls outside the range [−1, 1], arccos is undefined. This typically means the input surface tensions are physically inconsistent or the Young equation assumptions do not apply.

What is the spreading coefficient?

The spreading coefficient S = γSV − γSL − γLV. When S ≥ 0 the liquid spreads completely (θ = 0°). This calculator also displays the spreading coefficient for reference.

Contact Angle Calculator

Enter solid-vapor, solid-liquid, and liquid-vapor surface tensions to calculate the contact angle and determine surface wettability.

Surface Tension Inputs

All values in mN/m (= dyn/cm)

Solid-Vapor Surface Tension (γ_SV)

mN/m

Solid-Liquid Interfacial Tension (γ_SL)

mN/m

Liquid-Vapor Surface Tension (γ_LV)

mN/m

Quick Presets

Contact Angle (θ)

—

degrees

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Summary

The Contact Angle Calculator uses the Young equation (cos θ = (γSV − γSL) / γLV) to compute the equilibrium contact angle formed between a liquid droplet and a solid surface. A contact angle below 90° indicates a hydrophilic (wettable) surface, while angles above 90° indicate hydrophobic behavior. Angles above 150° are classified as superhydrophobic.

How it works

Enter the solid-vapor surface tension (γSV) in mN/m.
Enter the solid-liquid interfacial tension (γSL) in mN/m.
Enter the liquid-vapor surface tension (γLV) in mN/m.
The calculator applies Young's equation: cos θ = (γSV − γSL) / γLV.
The contact angle θ is computed via arccos and displayed in degrees.
A wettability classification (hydrophilic, hydrophobic, or superhydrophobic) is shown.

Use cases

Evaluate the wettability of coating materials in materials science.
Assess adhesive bonding quality on different substrate surfaces.
Design waterproof or anti-fouling coatings in engineering applications.
Study ink-substrate interactions in printing and packaging industries.
Analyze biological surface compatibility for medical implants.
Optimize surface treatments for semiconductor wafer cleaning.
Research lotus-effect superhydrophobic surfaces.
Teach thermodynamic surface energy concepts in academic settings.

Frequently Asked Questions

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

Contact Angle Calculator

Use the Contact Angle Calculator

Surface Tension Inputs

Summary

How it works

Use cases

Frequently Asked Questions