Capillary Rise Calculator
Enter surface tension, density, tube radius and contact angle to compute capillary rise from h=2γcosθ/(ρgr) and the Laplace pressure ΔP=2γ/r.
Input Data
Results
At a glance:Capillary action is the rise or fall of a liquid in a narrow tube due to surface tension and wetting. For a circular tube the equilibrium height is h = 2γcosθ/(ρgr), where γ is the surface tension (N/m), θ the contact angle, ρ the liquid density, g the gravity and r the tube radius. With θ<90° (wetting, e.g. water-glass θ≈0°) the liquid rises; with θ>90° (non-wetting, e.g. mercury-glass θ≈140°) it falls. The curved meniscus sustains a pressure jump (the Laplace pressure) ΔP = 2γ/r that balances the hydrostatic column ρgh. Capillarity explains how plants draw water up xylem, how paper and sponges wick liquid, and is central to microfluidics and porous-media flow.
Formula
Capillary rise: h = 2γcosθ / (ρgr)
Laplace pressure: ΔP = 2γ/r
Water-glass θ≈0° → rises; mercury-glass θ≈140° → falls.
$$h = \frac{2\gamma\cos\theta}{\rho g r}, \quad \Delta P = \frac{2\gamma}{r}$$How to Use
- Enter surface tension γ (N/m), liquid density ρ (kg/m³) and tube radius r (m).
- Enter the contact angle θ (°).
- The tool returns the capillary rise h and the Laplace pressure ΔP.
Case Studies
Water in a glass tube
Water-glass θ≈0°, γ=0.0728 N/m, r=1 mm, ρ=1000 kg/m³.
h = 2×0.0728×1/(1000×9.81×0.001) ≈ 0.0148 m = 14.8 mm.
The narrower the tube, the higher the rise (h ∝ 1/r).
Mercury in a glass tube
Mercury-glass θ≈140°, cosθ≈−0.766 → the liquid falls instead of rising.
This is why mercury forms a convex meniscus and depresses in a capillary tube.
Used in manometers and medical sphygmomanometers.
FAQ
Why does liquid rise in a thin tube?
Surface tension pulls the wetting liquid up the wall; the curved meniscus creates a Laplace pressure ΔP=2γ/r that supports a hydrostatic column ρgh until equilibrium h=2γcosθ/(ρgr).
Why does mercury fall instead of rising?
Mercury does not wet glass (θ≈140°), so cosθ is negative and h becomes negative — the liquid is depressed (falls) below the surrounding level, forming a convex meniscus.
How does tube radius affect the rise?
h is inversely proportional to r, so halving the radius doubles the rise. This is why capillary action is dramatic only in very narrow tubes (e.g. xylem, paper fibers).
What is the Laplace pressure?
The pressure difference across a curved liquid interface, ΔP=2γ/r for a cylindrical tube (or 2γ/R for a spherical drop). It is the driving force behind capillarity and bubble stability.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.