Compute capillary rise and depression, determine surface tension from capillary-tube measurements, solve Young-Laplace pressures for droplets and soap bubbles, convert between N/m, mN/m, dyn/cm and lbf/ft, and look up reference surface tensions of common liquids. Everything runs in your browser; no data leaves your device.
Capillary rise / depression
h = 2γ cosθ / (ρ g r)
Tip: pick a liquid in the Material Table tab to fill γ, ρ and θ automatically. Contact angles above 90° (e.g. mercury on glass) give a negative h: capillary depression.
Surface tension (γ) is the force per unit length acting along a liquid surface, measured in newtons per meter (N/m). It is caused by unbalanced attractive forces on molecules at the surface, and it is numerically equal to the surface energy per unit area (J/m²). Water at 20 °C has a surface tension of 0.0728 N/m.
2. What is the capillary rise formula?
h = 2γcosθ / (ρgr), where γ is surface tension, θ the contact angle, ρ the liquid density, g gravity (9.80665 m/s²) and r the tube radius. Example: water (γ = 0.0728 N/m, θ = 0°) in a tube of radius 0.5 mm rises 29.75 mm.
3. Why does mercury go down in a capillary tube instead of rising?
Mercury does not wet glass: its contact angle is about 130°, so cosθ is negative and the formula gives a negative h, a capillary depression. In a 0.5 mm radius tube mercury (γ = 0.465 N/m) is depressed by about 9.01 mm.
4. What is the Young-Laplace equation for a droplet and a soap bubble?
For a spherical droplet Δp = 2γ/R; for a soap bubble Δp = 4γ/R because the bubble has two liquid films. Example: a water droplet of radius 1 mm has an internal excess pressure of 145.6 Pa, while a 5 cm soap bubble has only 5.824 Pa.
5. How do surface tension units convert?
1 dyn/cm = 1 mN/m = 0.001 N/m exactly. So 72.8 mN/m = 0.0728 N/m = 72.8 dyn/cm. One N/m equals about 0.06852 lbf/ft; for example 0.0728 N/m = 0.004988 lbf/ft.
6. What is the contact angle?
The contact angle θ is the angle a liquid surface makes with a solid. Near 0° the liquid wets the solid (water on clean glass) and rises; above 90° it does not wet (mercury on glass, about 130°) and is depressed. At exactly 90° there is no capillary rise.
7. Does surface tension change with temperature?
Yes, surface tension falls as temperature rises because molecular attraction weakens. Water drops from 0.0728 N/m at 20 °C to about 0.0720 N/m at 25 °C. Reference values are therefore always quoted with their temperature.
8. How is surface tension measured in the lab?
Common methods: capillary-rise (measure h in a tube of known radius and invert the formula), the Du Noüy ring (force to pull a ring from the surface), the Wilhelmy plate, and the pendant-drop method (fit a droplet silhouette). This calculator's second tab inverts capillary-rise data.
9. What is the capillary length?
The capillary length λc = √(γ/ρg) is the length scale where surface tension and gravity balance. For water it is about 2.73 mm: drops and puddles much smaller than this are shaped by surface tension, much larger ones by gravity.
10. Where do the reference values in the table come from?
The anchor values water 0.0728 N/m, ethanol 0.0223 N/m, glycerol 0.0634 N/m and mercury 0.465 N/m at 20 °C were spot-checked against CRC Handbook / Haynes compilations and IAPWS data for water (72.86 mN/m). Note mercury literature values span 465–486 mN/m depending on source and purity; the table is for quick estimates, not metrology.
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