Capillary Rise Calculator

Capillary action drives liquids up narrow tubes against gravity through a combination of adhesion (liquid to glass) and cohesion (liquid to itself). It is why water rises in plant stems.

💧 Surface Physics📐 h = 2γcosθ/ρgr🧪 Chemistry
Tube Radius (m)
Surface Tension (N/m)
Contact Angle (deg)
Fluid Density (kg/m³)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Rise Heighthh = 2γcosθ/(ρgr)m
Surface TensionγWater: 0.0728 N/m at 20°CN/m
Contact Angleθ0° for water-glass; 140° for mercury-glassdeg
DensityρWater: 1000 kg/m³kg/m³
Tube RadiusrInner radiusm

Step-by-Step Examples

Example 1
Water in Glass Tube

r=0.5 mm, gamma=0.0728 N/m, theta=0, rho=1000.

  • h = 2×0.0728×cos0/(1000×9.81×0.0005)
  • h = 0.1456/4.905 = 0.0297 m
✓ 2.97 cm rise in 0.5 mm radius tube
Example 2
Mercury Depression

Mercury in glass: r=1 mm, gamma=0.485 N/m, theta=140°, rho=13,600.

  • h = 2×0.485×cos140°/(13600×9.81×0.001)
  • h = -0.743/133.4 = -5.57 mm
✓ 5.57 mm depression (mercury is repelled by glass)
Example 3
Tree Water Transport

Xylem radius ~20 μm in trees.

  • h = 2×0.073×1/(1000×9.81×0.00002)
  • h = 0.146/0.1962 = 0.74 m
✓ 74 cm capillary rise — helps water reach tree leaves

Real-World Applications

🌳
Plant Water Transport
Capillary action in xylem tubes (r~20 μm) contributes to water rising in plants.
🧹
Wick Absorption
Candle wicks, paper towels, and sponges use capillary rise to draw liquid upward.
🧪
Chromatography
Capillary action drives solvent through paper and TLC plates, separating components.
🏗️
Construction
Water rises through capillaries in concrete and brick, causing dampness and structural damage.

Common Mistakes to Avoid

⚠️
Forgetting negative rise (depression)

When contact angle > 90° (like mercury-glass), cosθ is negative and liquid is depressed below the flat surface.

⚠️
Using diameter instead of radius

Formula uses radius r, not diameter. A 2 mm diameter tube has r = 1 mm.

⚠️
Ignoring temperature dependence

Surface tension and contact angle both vary with temperature. Water gamma drops from 0.076 at 0°C to 0.059 at 100°C.

Frequently Asked Questions

Why does water rise in glass but mercury fall? ▾
Water wets glass (contact angle ~0°, adhesion > cohesion), so surface curves up. Mercury does not wet glass (contact angle ~140°, cohesion > adhesion), so surface curves down.
How high can capillary action lift water? ▾
In a 1 μm radius tube: h = 14.8 m. This helps explain water transport in tall trees, though transpiration pull is the main driver for heights >1 m.
What is contact angle? ▾
Angle between the liquid surface and the solid surface at the contact line. 0° = complete wetting; 180° = complete non-wetting. Lotus leaves have contact angle ~160° (superhydrophobic).
How does capillary action relate to inkjet printing? ▾
Inkjet nozzles use precise surface tension and wettability control to form droplets of exact size for high-resolution printing.
Can capillary action work in zero gravity? ▾
Yes and better — without gravity opposing the rise, liquid spreads freely through porous materials. This is a challenge for fluid management in spacecraft.
What is the Jurin law? ▾
The capillary rise formula h = 2*gamma*cos(theta)/(rho*g*r) is called Jurin law, published 1718. It shows h ∝ 1/r.
Why does paper absorb water? ▾
Paper is a porous network of cellulose fibers. Water wets cellulose (low contact angle), and the tiny gaps between fibers act as capillary tubes.
How is surface tension measured? ▾
By capillary rise (using Jurin law), pendant drop method, or Wilhelmy plate method measuring the force to pull a plate from a liquid surface.

Related Physics Calculators

💧 Surface Tension💧 Viscosity⚖️ Pressure💨 Bernoulli🔧 Pascal Law

Formula Explorer connections

Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.

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