Capillary Rise Calculator (Jurin's Law)
How high a liquid climbs, or is pushed down, in a narrow tube from its surface tension, the contact angle, the density and the tube radius.
Results
The dashed line marks the value you entered.
What this tool does
Water climbs a clean glass tube until the weight of the column balances the pull of the surface film along the wall, giving h = 2γ cos θ ÷ ρ g r — twice as narrow a tube lifts it twice as high. A 0.5 mm radius tube raises water about 30 mm, a 0.05 mm one about 30 cm, the same effect that draws water into paper towels, soil and plant stems. Mercury does the opposite: its contact angle is above 90°, so the column is pushed down below the outside level. The capillary length is the size below which surface tension beats gravity.
Formula
h = 2 γ cos θ ÷ (ρ g r) (Jurin's law) · l_c = √(γ ÷ ρ g)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
r | Inner radius of the tube | mm |
gm | Surface tension of the liquid (water at 20 °C is about 72.8) | mN/m |
th | Contact angle (0° for water on clean glass, above 90° for mercury) | ° |
ro | Density | kg/m³ |
H | Rise in the tube (negative means it is pushed down) | mm |
PM | Pressure step across the curved surface | Pa |
LC | Capillary length | mm |
Worked example
- Inner radius of the tube0.5 mm
- Surface tension of the liquid (water at 20 °C is about 72.8)72.8 mN/m
- Contact angle (0° for water on clean glass, above 90° for mercury)0 °
- Density998 kg/m³
- Rise in the tube (negative means it is pushed down)29.75 mm
- Pressure step across the curved surface291.2 Pa
- Capillary length2.73 mm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.