Surface Tension Calculator

Enter the capillary rise height, tube radius, liquid density, and contact angle to calculate surface tension using the capillary rise method (gamma = rho x g x h x r / (2 x cos theta)).

Quick Facts

Formula
γ = ρgh r / (2 cosθ)
Capillary rise method (Jurin's Law), rearranged to solve for surface tension γ.
Water at 20°C
≈ 72.8 mN/m
Surface tension drops roughly 0.15 mN/m per °C as temperature rises.
SI unit
N/m = J/m²
Surface tension is equivalently force per unit length or energy per unit area.
Unit conversion
1 dyn/cm = 1 mN/m
The older cgs unit (dyn/cm) is numerically identical to the SI mN/m.

Your Results

Calculated
Surface Tension
-
γ in N/m
Surface Tension
-
γ in mN/m (= dyn/cm)
Laplace Pressure
-
ΔP = ρgh, in Pa
Comparison
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How this compares to known liquids

Ready

Enter your capillary rise measurements, then press Calculate.

Formula and Method for Surface Tension

Surface tension (γ) is the force per unit length acting along the surface of a liquid, caused by cohesive forces between molecules pulling the surface inward like a stretched elastic sheet. It is equivalently the energy required to increase the surface area by one unit, so its SI unit N/m is identical to J/m². This calculator uses the capillary rise method, one of the oldest and most direct ways to measure it: when a thin tube is dipped into a liquid that wets it, the liquid climbs the tube until surface tension balances the weight of the raised column. Rearranging that balance (Jurin's Law) for γ gives γ = ρ g h r / (2 cosθ), where ρ is the liquid's density, g is standard gravity (9.80665 m/s²), h is the height of the rise, r is the tube's inner radius, and θ is the contact angle between the liquid and the tube wall.

How the calculation works

Enter the height the liquid rose (h) and the tube's inner radius (r) in the same length unit, the liquid's density (ρ), and the contact angle (θ) — use 0° for a liquid that fully wets clean glass, such as water or most organic solvents. The calculator converts everything to SI units (meters and kg/m³), then computes γ = ρgh r / (2 cosθ). It also reports the Laplace (capillary) pressure ΔP = ρgh, the pressure difference across the curved meniscus that exactly balances the upward pull of surface tension, and compares your result against known reference liquids so you can sanity-check the order of magnitude.

Common mistakes

  • Radius vs. diameter: because r appears directly (not squared) in the formula, using a tube's diameter instead of its radius doubles the computed surface tension.
  • Ignoring the contact angle: assuming θ = 0° for a liquid or tube that does not fully wet (a dirty or greasy tube, for example) will overstate γ, since cosθ shrinks as the contact angle grows.
  • Mixing length units: the rise height and tube radius must use the same unit before you compare them — this calculator's shared unit selector handles that conversion automatically.

Real-world applications

  • Formulating detergents, inks, and coatings, where lowering surface tension improves wetting and spreading on a target surface.
  • Inkjet printing and microfluidics, where droplet formation and capillary flow through narrow channels depend directly on γ.
  • Quality control for oils, cosmetics, and pharmaceuticals, where surface tension shifts can signal contamination or formulation drift.
  • Soil science and hydrology, where capillary rise through pore spaces governs how water moves through unsaturated soil.

Frequently Asked Questions

What formula does this surface tension calculator use?
This calculator uses the capillary rise method, an application of Jurin's Law solved for surface tension: γ = ρ g h r / (2 cosθ), where ρ is liquid density, g is gravitational acceleration (9.80665 m/s²), h is the height the liquid rises in the capillary tube, r is the tube's inner radius, and θ is the contact angle between the liquid and the tube wall.
Why does the contact angle matter?
The contact angle θ measures how well the liquid wets the tube surface. For a liquid that fully wets clean glass, like water, θ ≈ 0° and cosθ = 1, so it drops out of the formula. As θ increases toward 90°, the liquid wets the surface less strongly and rises less for the same surface tension, so cosθ in the denominator corrects for that weaker vertical pull. At 90° or more, the liquid no longer rises (or is depressed, as with mercury in glass), and this rise-based formula no longer applies.
What is a typical surface tension value, and how do units compare?
Pure water has a surface tension of about 72.8 mN/m (0.0728 N/m) at 20°C, dropping by roughly 0.15 mN/m per degree as temperature increases. Ethanol is much lower at about 22 mN/m, while liquid mercury is far higher at about 487 mN/m. Note that 1 dyn/cm, the older cgs unit, equals exactly 1 mN/m, so values from older references convert directly.
Why does the tube radius matter so much?
Surface tension is directly proportional to the tube radius in this formula, so measuring a diameter instead of a radius (or misreading a bore size) throws the result off by a factor of two. Always confirm you are using the internal radius of the capillary bore, not its outer diameter or wall thickness.

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