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Capillary Rise Calculator

Find the capillary rise of a liquid.

How it is calculated

The tool uses Jurin's law with a fixed gravity of 9.81 m/s²:

h = 2 · γ · cos(θ) / (ρ · g · r)

Use SI units: γ is surface tension in N/m, θ is the contact angle in degrees (0 to 180), ρ is liquid density in kg/m³, and r is the inner radius of the tube in metres. The height comes out in metres and in millimetres. Density and radius must be above zero. When the angle is above 90° the cosine is negative and the result is negative, which means the liquid is pushed down below the outside level (as mercury is in glass), not raised.

Worked example

Water at about 20 °C in a clean glass tube of 0.5 mm radius: γ = 0.0728 N/m, θ = 0°, ρ = 1000 kg/m³, r = 0.0005 m. Numerator: 2 × 0.0728 × cos 0° = 0.1456. Denominator: 1000 × 9.81 × 0.0005 = 4.905. So h = 0.1456 / 4.905 = 0.02968 m, which is 29.68 mm.

Try this example →

Common mistakes

  • Entering the diameter, or a radius in millimetres, instead of the radius in metres; 0.5 mm must be typed as 0.0005.
  • Using surface tension in mN/m (72.8) instead of N/m (0.0728), which makes the result 1,000 times too large.
  • Assuming a contact angle of 0° for every liquid and surface; a waxy or dirty tube has a much larger angle and a smaller rise.
  • Being surprised by a negative height: for angles over 90°, such as mercury in glass, it indicates depression, not a mistake.
  • Applying it to wide tubes; the formula assumes a narrow tube with a spherical meniscus, so large radii give unrealistic heights.

About this calculator

This calculator applies the Jurin's law equation, h = 2γcosθ/(ρgr), to find how high a liquid climbs inside a narrow capillary tube, where γ is surface tension, θ is the contact angle between liquid and tube wall, ρ is liquid density, g is gravitational acceleration, and r is the tube's inner radius. The rise happens because adhesive forces between the liquid and the tube wall pull the liquid upward until that pull is balanced by the weight of the risen column — narrower tubes and liquids with higher surface tension (like water) produce a more dramatic rise.

Physics and chemistry students verifying surface-tension lab results, soil scientists and hydrologists studying how water moves through fine soil pores, and engineers designing wicking materials, inkjet nozzles, or microfluidic devices use this.

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Comments (1)

  • Editorial team

    The contact angle is the input most often guessed, and it moves the answer a lot. With the water example of 0.5 mm radius, a clean-glass angle of 0 gives 29.68 mm, but 60 degrees gives 14.84 mm, exactly half. Dirty or coated tubes can sit well away from zero. Also make sure you enter the inner radius, not the diameter, since halving the radius doubles the rise. What liquid and tube material are you looking at?

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