Capillary Rise Height Calculator

Formula used

For a circular tube, the calculator uses \(h = 2γ\cosθ/(ρgr)\). The diameter form is \(h = 4γ\cosθ/(ρgd)\). Positive results indicate rise, while negative results indicate depression.

How to use this calculator

1. Select a liquid preset or enter custom fluid properties.
2. Choose the capillary geometry and enter its relevant dimensions.
3. Select units for size, surface tension, density, angle, and result.
4. Choose a gravity preset or provide custom acceleration.
5. Set decimal formatting, then select Calculate height.
6. Review pressure, wetting behavior, warnings, charts, and calculation steps.
7. Copy, print, or download the result as CSV or PDF.

Example data

Understanding capillary rise height

Capillary action occurs when surface forces compete with gravity. A liquid climbs when adhesion to the wall dominates cohesion. It falls when the wall is poorly wetted.

Surface tension acts along the contact line. Its vertical component supports or lowers the liquid column. The contact angle controls that useful vertical component.

A contact angle below ninety degrees produces positive cosine. This usually creates a concave meniscus and capillary rise. Angles above ninety degrees create capillary depression instead.

Narrower openings generate larger pressure differences across curved interfaces. Therefore, smaller tubes usually produce greater rise magnitudes. Doubling a circular diameter approximately halves the predicted height.

Density appears in the equation denominator. Denser liquids need more pressure to support equal heights. Lower gravity also permits taller equilibrium liquid columns.

Surface tension depends on fluid composition and temperature. Contamination can alter both surface tension and contact angle. Accurate work should use measured values for actual surfaces.

The circular-tube equation assumes a static axisymmetric meniscus. It also assumes a uniform tube and constant fluid properties. Dynamic filling can differ because viscosity controls the rate.

Parallel plates use their gap as the characteristic opening. Rectangular channels require two principal curvature contributions. The calculator treats these geometries with idealized equilibrium expressions.

Hydraulic radius is useful for approximate non-circular comparisons. However, it cannot capture every corner or wetting effect. Detailed microfluidic systems may require numerical surface-shape modeling.

Capillary pressure is the pressure jump across the interface. Dividing that pressure by density and gravity gives height. Its sign follows the cosine of contact angle.

The Bond number compares gravity with surface-tension effects. Values below one indicate strong capillary influence at that scale. Larger values suggest gravity significantly shapes the interface.

Capillary length provides another useful characteristic scale. Features smaller than this length often show strong curvature effects. Larger systems increasingly display gravity-dominated free surfaces.

The sensitivity charts show how dimensions and angles change results. They help compare design choices without repeated manual calculations. Near ninety degrees, small angle errors matter greatly.

Preset fluid data should be treated as representative only. Published values vary with purity, pressure, temperature, and substrate. Replace presets whenever reliable experimental measurements are available.

Very tall theoretical values may exceed available tube length. Evaporation, trapped gas, roughness, and contamination can then dominate. Use warnings before applying results to equipment decisions.

Capillary rise supports wick design and porous-media analysis. It also matters in soil, coatings, diagnostics, and microchannels. Careful inputs make the ideal model more informative.

The result is an equilibrium prediction, not filling time. Viscous models are required for transient penetration calculations. Always document assumptions when reporting engineering estimates.

Use consistent units when checking results independently. The calculator converts every supported input into SI units. This reduces hidden conversion mistakes during technical comparisons.

Negative height does not mean an invalid calculation. It identifies a downward shift relative to the outside level. Mercury in clean glass commonly illustrates this behavior.

Measurement uncertainty should accompany high-precision laboratory conclusions. Contact angle often contributes substantial uncertainty near neutral wetting. Repeat measurements improve confidence in final capillary estimates.

Frequently asked questions