Inputs
Select what to solve for. Enter known values with units. For best accuracy, use measured temperature-dependent properties.
Formula used
Capillary rise in a narrow tube comes from balancing surface tension with the weight of the liquid column. The standard model is:
h = (2 γ cos(θ)) / (ρ g r)
- h is the rise height above the reservoir (m).
- γ is surface tension of the liquid (N/m).
- θ is the contact angle between liquid and tube wall.
- ρ is liquid density (kg/m³), g is gravity (m/s²), and r is tube radius (m).
This ideal form assumes a clean, circular tube and negligible viscous losses during the rise.
How to use this calculator
- Select what you want to compute using Solve for.
- Enter known properties and choose units for each value.
- If you are not solving for height, enter a Target rise height.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for reports.
Example data table
Sample scenarios for water near room temperature, using θ ≈ 0°.
| γ (N/m) | ρ (kg/m³) | θ (deg) | r (mm) | h (cm) approx |
|---|---|---|---|---|
| 0.0728 | 998 | 0 | 0.25 | 5.95 |
| 0.0728 | 998 | 0 | 0.50 | 2.97 |
| 0.0728 | 998 | 0 | 1.00 | 1.49 |
| 0.0728 | 998 | 30 | 0.50 | 2.57 |
Real results vary with temperature, contamination, and tube roughness.
Capillary rise notes and guidance
1) What the capillary rise model predicts
Capillary rise estimates the equilibrium height a wetting liquid can climb inside a small tube or pore. It balances an upward surface-tension pull around the meniscus against the hydrostatic weight of the lifted column. The result is most reliable for clean, circular capillaries and slow, near-static conditions.
2) Variables that control the height
The equation shows that height increases with surface tension (γ) and stronger wetting (larger cos(θ)). Height decreases with density (ρ), gravity (g), and tube radius (r). Because r is in the denominator, halving the radius roughly doubles the predicted rise, which is why micro-capillaries can lift fluids noticeably.
3) Practical ranges and reference values
For water near room temperature, γ is about 0.072 N/m and ρ is about 998 kg/m³. With θ near 0°, a tube radius of 0.50 mm gives a rise near 0.0297 m (≈ 2.97 cm), while 0.25 mm gives about 5.95 cm. These numbers match the example table and help verify inputs.
4) Unit conversions and consistent input checking
This calculator converts common engineering units to SI internally, then reports the output in your chosen display unit. If results look unreasonable, check that radius is not entered as diameter, and confirm gravity units. A sign change usually indicates a non-wetting case where cos(θ) becomes negative.
5) Interpreting contact angle in real materials
Contact angle captures surface chemistry and roughness effects. θ < 90° implies a wetting meniscus and a positive rise. θ > 90° implies capillary depression rather than rise. When solving for θ, the calculator enforces a real solution by requiring the implied cos(θ) to remain between −1 and +1.
6) Solving for unknowns beyond height
Advanced workflows often measure a rise height and then back-calculate an unknown. Choose “Solve for r” to estimate an equivalent pore radius from a measured rise, or “Solve for γ” to infer surface tension from a calibrated capillary. You can also solve for ρ or g as a consistency check in special setups.
7) Measurement details that change outcomes
Real systems deviate from the ideal model. Contamination can lower γ, temperature shifts change both γ and ρ, and trapped air bubbles alter the effective meniscus. Tube tilt and noncircular cross-sections also matter. For porous media, the “radius” is an effective value that reflects a distribution of pore sizes.
8) Reporting results and sharing calculations
For professional reporting, record the input set (γ, θ, ρ, r, g), the computed quantity, and the assumed temperature or material state. Use the CSV export for lab notebooks and the PDF export for attachments. When comparing experiments, keep θ consistent and vary only one parameter at a time.
FAQs
1) Why does a smaller tube produce a higher rise?
Surface tension acts along the perimeter, while weight scales with cross-sectional area. As radius decreases, perimeter-to-area ratio increases, so the upward surface-tension effect dominates more strongly.
2) What happens if the contact angle is greater than 90°?
cos(θ) becomes negative, indicating a non-wetting meniscus. The model predicts capillary depression rather than rise. If you compute a negative height, interpret it as a downward displacement.
3) Should I enter tube diameter or radius?
Enter the radius. If you only know the diameter, divide by two first. Using diameter directly will roughly halve the predicted height, causing a noticeable discrepancy.
4) Can this be used for porous materials like soil or paper?
Yes, but treat the radius as an effective pore radius. Porous media contain many pore sizes and pathways, so the model gives an approximate, averaged behavior rather than an exact height.
5) Why do my experimental results differ from the calculation?
Common causes include surface contamination, temperature variation, wall roughness, evaporation, and dynamic effects before equilibrium. Ensuring clean surfaces and stable temperature usually improves agreement.
6) Is viscosity included in this calculator?
No. The formula here is an equilibrium model. Viscosity primarily affects how fast the liquid rises, not the final static height, unless other losses or hysteresis dominate.
7) When is solving for γ or θ most useful?
Use it when you have a calibrated tube and a measured rise height. It can estimate surface tension for known wetting, or infer an apparent contact angle for a specific liquid–solid pair.