Compute capillary rise height from surface tension, density, tube radius, and angle. Switch units, view metric conversions, and download reports for experiments fast today.
| Liquid | γ (N/m) | ρ (kg/m³) | θ (deg) | r (mm) | h (cm) |
|---|---|---|---|---|---|
| Water (20°C) | 0.0728 | 1000 | 0 | 0.50 | 2.97 |
| Ethanol (20°C) | 0.0223 | 789 | 0 | 0.50 | 1.15 |
| Mercury (approx.) | 0.485 | 13534 | 140 | 0.50 | -0.46 |
For a circular capillary tube, the equilibrium rise or depression height is:
Capillary rise height is the equilibrium level difference between the liquid in a narrow tube and the surrounding reservoir. The calculator uses the cylindrical-tube relation where surface tension pulls the meniscus upward while gravity and fluid weight resist. When cos(θ) is positive, the liquid rises; when it is negative, the liquid depresses.
The most influential inputs are surface tension γ, contact angle θ, density ρ, gravity g, and tube radius r. Units matter: the calculator converts mN/m to N/m, g/cm³ to kg/m³, and diameter to radius by dividing by two.
At room temperature, water has γ ≈ 0.072 N/m and ρ ≈ 1000 kg/m³. Ethanol is lower tension and density (γ ≈ 0.022 N/m, ρ ≈ 789 kg/m³), so it generally rises less for the same tube. Mercury has high density and often a large contact angle on glass, producing depression.
Contact angle summarizes wetting. Clean glass with water can approach θ ≈ 0°, making cos(θ) ≈ 1. A hydrophobic coating may raise θ toward 90°, shrinking the rise toward zero. Angles above 90° flip the sign, giving a negative height.
The height scales as 1/r. Halving radius doubles the predicted rise, so micrometer-scale capillaries can produce large height changes. For example, with water and θ = 0°, a radius of 0.50 mm yields about 3.0 cm, while 0.25 mm approaches 6.0 cm under the same conditions.
Surface tension decreases with temperature for most liquids, so warmer samples typically reduce rise. Small amounts of surfactant, oil, or dust can alter both γ and θ, sometimes by more than instrument uncertainty. If your measured height disagrees, check cleaning, temperature control, and whether the tube is truly uniform.
Read height at the meniscus consistently: use the same reference (top or bottom of the curve) across trials. Record tube inner radius from a calibrated specification or microscope measurement. For repeatability, log γ source, temperature, and the surface preparation method along with the calculated value. For quick checks, compare predicted centimeters with your scale resolution; if the rise is under 2 mm, consider a smaller tube.
Capillary rise is critical in porous media, microfluidics, wick design, ink delivery, and soil-water transport. In laboratories, quick predictions help choose tube size, estimate rise time targets, and assess whether meniscus motion will exceed measurement range. Exporting results as CSV or PDF supports reporting and peer review.
A negative value appears when the contact angle is above 90°, making cos(θ) negative. The surface tension then pulls the meniscus downward, producing capillary depression instead of rise.
Use whichever you know most reliably. The calculator converts diameter to radius internally by dividing by two, so both options yield the same physics when units are consistent.
Use the inner hydraulic radius approximated from the tube’s inner diameter. If the cross-section is not circular, the simple formula becomes approximate and measurement uncertainty increases.
Height is proportional to cos(θ). Near small angles, changes are modest; near 90°, small angle errors can drastically change cos(θ) and make the predicted rise approach zero.
Viscosity affects the rise rate, not the final static height in this model. If you care about time-to-equilibrium, you need a dynamic capillary flow model beyond this calculator.
Common causes include temperature differences, contaminated surfaces, inaccurate inner radius, and contact angle variability. Also check that the tube is vertical and the reference level is read consistently.
You can estimate behavior by using an effective pore radius, but real porous media have distributions and tortuosity. Treat results as an order-of-magnitude guide unless pore geometry is well characterized.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.