Capillary Rise Calculator
Capillary action lifts a wetting liquid up a narrow tube until the upward pull of surface tension balances the weight of the raised column. Jurin's law sets the equilibrium height from four properties: the liquid surface tension, the contact angle with the tube wall, the liquid density and the tube radius. This calculator returns the rise height for any combination, including the negative result that signals a capillary depression for non-wetting liquids such as mercury. It is widely used in soil science, plant physiology, microfluidics and laboratory work.
Jurin's law formula
h = 2 * gamma * cos(theta) / (rho * g * r)
gamma = surface tension (N/m)
theta = contact angle (converted to radians)
rho = liquid density (kg/m3), g = gravity (m/s2), r = tube radius (m)
The contact angle is entered in degrees and converted to radians inside the calculation. A contact angle below 90 degrees gives a positive rise; above 90 degrees the cosine is negative, giving a capillary depression.
Capillary action context
- Rise height is inversely proportional to tube radius: halving the radius doubles the height.
- Water on clean glass has a contact angle near 0 degrees, so cos(theta) is about 1.
- Mercury on glass has a contact angle near 140 degrees, producing a depression rather than a rise.
- Surface tension of water at 20 degrees Celsius is approximately 0.0728 newtons per metre.
- Capillary action helps move water through soil and up the xylem of plants.
Capillary rise: frequently asked questions
What is capillary rise?
Capillary rise is the spontaneous movement of a liquid up a narrow tube against gravity, driven by surface tension and the liquid wetting the tube wall. The narrower the tube, the higher the liquid climbs. Water rising in a thin glass tube or sap moving up a plant stem are everyday examples.
What is Jurin's law?
Jurin's law gives the equilibrium height of capillary rise: h = 2 * gamma * cos(theta) / (rho * g * r), where gamma is surface tension, theta is the contact angle, rho is liquid density, g is gravitational acceleration and r is the tube radius. Height is inversely proportional to tube radius.
What contact angle should I use?
The contact angle depends on the liquid and the tube material. Water on clean glass is close to 0 degrees (full wetting), giving maximum rise. Mercury on glass is about 140 degrees, which makes cos negative and produces a depression rather than a rise. Enter the angle for your specific pairing.
What surface tension value should I enter?
Surface tension is a property of the liquid and temperature. For water at 20 degrees Celsius it is about 0.0728 newtons per metre. Because it is empirical and temperature dependent, it ships here as a user-editable input so you can set the correct value for your liquid and conditions.
Why does a negative result appear for mercury?
When the contact angle exceeds 90 degrees its cosine is negative, so Jurin's law returns a negative height. This represents capillary depression: the liquid level inside the tube sits below the outside level, as happens with mercury in glass. The magnitude still tells you how far it drops.
Official sources
- U.S. National Institute of Standards and Technology: Physical Measurement Laboratory.
- USGS Water Science School: Capillary action and water.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.