Surface Tension Calculator
Enter force and contact length to compute surface tension, plus capillary rise. Water at 20°C γ≈0.0728 N/m.
Input Data
Results
At a glance:Surface tension is the contractile force at a liquid surface produced by cohesive molecular forces, with unit N/m (= J/m²). It is measured as γ=F/L (force per contact length). Capillary action makes a liquid rise (wetting) or fall (non-wetting) in a narrow tube: h = 2γcosθ/(ρgr). It decreases with temperature (stronger molecular motion), drops sharply with surfactants (the basis of washing), and depends on solutes. Typical values: water 20°C γ=0.0728 N/m, alcohol 0.0223, mercury 0.487. Applications: (1) capillary transport (plant xylem, paper wicking); (2) droplet shape (minimum-surface sphere); (3) soap bubbles (two-sided film); (4) detergency (surfactants lower γ); (5) medicine (lung surfactant, neonatal respiratory distress).
Formula
Surface tension: γ = F / L
Capillary rise: h = 2γ·cosθ / (ρ·g·r)
Pulling method (film): F = γ·2L (two-sided film)
Pressure difference: ΔP = 2γ/R (spherical droplet)
$$\gamma = \frac{F}{L}, \quad h = \frac{2\gamma\cos\theta}{\rho g r}$$How to Use
- Enter the force F (N) and contact length L (m).
- Enter the liquid density ρ (kg/m³), tube radius r (m) and contact angle θ (°).
- Enter gravity g (m/s²).
- The tool returns surface tension γ and capillary rise h.
Case Studies
Capillary action and plant water transport
Plant xylem radius 0.0001 m, water γ=0.0728 N/m.
h = 2×0.0728/(1000×9.8×0.0001) ≈ 0.148 m.
Capillary force helps roots draw water, but tall trees rely mainly on transpiration pull.
Soap bubbles and surfactants
A soap film has two surfaces, so the pulling force is F=γ·2L.
Surfactants lower γ, letting bubbles form at lower pressure.
This is the physical basis of detergents and foams.
FAQ
What is surface tension?
The contractile force at a liquid surface from cohesive molecular attraction, measured as γ=F/L (force per contact length), unit N/m. It makes the surface behave like an elastic skin.
How is it measured?
Common methods: the ring (Du Noüy) and plate (Wilhelmy) tensiometers measure the force F needed to pull a ring/plate through the surface, then γ=F/L (a film gives F=2γL for two surfaces).
Why do surfactants lower surface tension?
Surfactant molecules migrate to the surface and weaken intermolecular cohesion, lowering γ. This lets water wet greasy surfaces and is the basis of soaps and detergents.
Why does a droplet form a sphere?
A sphere minimizes surface area for a given volume, thus minimizing the surface-energy cost γ·A. Surface tension therefore pulls droplets into spheres in the absence of gravity.
What is capillary rise?
In a narrow tube, surface tension pulls a wetting liquid upward against gravity until h=2γcosθ/(ρgr); a non-wetting liquid (θ>90°, e.g. mercury) is depressed instead.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.