Surface Tension Calculator
Calculate capillary rise height from surface tension, contact angle, density, and tube radius.
Or solve for surface tension from a measured rise height.
Surface tension is the tendency of liquid surfaces to minimize their area, acting like a stretched elastic membrane. It arises from cohesion between molecules at the surface having fewer neighbors than interior molecules.
Capillary rise formula
When a narrow tube is placed in a liquid, surface tension pulls the liquid up (or pushes it down for mercury). The equilibrium height is:
h = 2γ cos(θ) / (ρgr)
Where: γ = surface tension in N/m θ = contact angle between liquid and tube wall ρ = liquid density in kg/m³ g = 9.81 m/s² r = tube inner radius in meters
For water in glass: γ ≈ 0.0728 N/m, θ ≈ 0°, ρ = 998 kg/m³. In a 0.5 mm radius tube: h = 2(0.0728)(1)/(998 × 9.81 × 0.0005) ≈ 0.0298 m = 29.8 mm.
Contact angle
When θ < 90°, the liquid wets the surface and the meniscus curves up — capillary rise occurs (water in glass). When θ > 90°, the liquid does not wet the surface and the meniscus curves down — capillary depression occurs (mercury in glass, θ ≈ 140°).
For mercury in glass with γ ≈ 0.485 N/m, θ = 140°, ρ = 13,546 kg/m³: h is negative, meaning the mercury sits below the outside level.
Surface tension values (N/m at 20°C)
Water: 0.0728, Ethanol: 0.0223, Mercury: 0.485, Acetone: 0.0237, Glycerin: 0.0634
Rearranging for γ
If you measure the capillary rise height and know the other parameters, you can back-calculate γ: γ = hρgr / (2cos(θ))
Select the calculation mode below.