Surface Tension Converter (N/m, mN/m, dyn/cm)

Understanding the surface tension converter — concept and principle

This converter changes surface tension between newtons per metre (N/m), millinewtons per metre (mN/m), dynes per centimetre (dyn/cm) and pound-force per inch (lbf/in). Surface tension describes how strongly a liquid surface pulls together, and it is quoted in coatings, printing inks, detergents, adhesives, inkjet and lab data, often in the older dyn/cm unit.

How it is calculated

The value is converted to mN/m and then divided by the size of the target unit. The factors are:

• 1 dyn/cm = 1 mN/m exactly, since 1 dyn = 10⁻⁵ N and 1 cm = 10⁻² m.
• 1 N/m = 1,000 mN/m.
• 1 lbf/in = 4.4482216152605 N ÷ 0.0254 m = 175.1268 N/m = 175,126.8 mN/m.

The principle

Molecules inside a liquid are pulled equally in every direction by their neighbours, but molecules at the surface have neighbours only on one side, so the surface behaves like a stretched skin. Surface tension γ is the force along the surface per unit length of an edge (N/m), which is the same as the energy needed to create one square metre of new surface (J/m², because 1 J = 1 N·m). It explains why droplets are round and how capillary rise works: the pressure jump across a curved surface is ΔP = 2γ ÷ r for a sphere of radius r. Surfactants such as soap lower γ, letting water spread and wet surfaces.

Worked example

Default inputs: 72.8 mN/m converted to dyn/cm.

1. Convert to the base unit: 72.8 mN/m is already in mN/m.
2. Divide by the size of 1 dyn/cm, which is 1 mN/m: 72.8 ÷ 1 = 72.8.
3. Result: 72.8 mN/m = 72.8 dyn/cm.
4. The same value is 0.0728 N/m, or 0.0004157 lbf/in.

How to read the result

72.8 mN/m is the value for pure water at about 20 °C, among the highest of common liquids. Ethanol is about 22 mN/m, and water with detergent can drop to around 30 mN/m. Surface tension falls as temperature rises. In coating and printing, a liquid wets a solid well when its surface tension is lower than the surface energy of the solid; that is why low-energy plastics are often treated before printing.

Common mistakes

• Thinking dyn/cm and mN/m need a conversion factor; they are numerically identical.
• Mixing up N/m and mN/m, a factor of 1,000.
• Comparing values measured at different temperatures without correction.
• Using surface tension values for interfacial tension between two liquids, which is a different measurement.

FAQ

Frequently asked questions

Is dyn/cm the same as mN/m?

Yes. 1 dyn/cm = 1 mN/m exactly, so the number does not change.

What is the surface tension of water?

About 72.8 mN/m at 20 °C, decreasing as the water gets warmer.

Why is surface tension also given in J/m²?

Because N/m and J/m² are the same SI unit; one is force per length, the other energy per area.

Sources: IAPWS, Revised Release on Surface Tension of Ordinary Water Substance (2014) · NIST Special Publication 811 (2008), Appendix B, conversion factors