Capillary Rise Calculator (Jurin’s law)

Understanding the capillary rise calculator — concept and principle

Capillary rise is the climb of a liquid up a narrow tube, against gravity, driven by surface tension. Jurin's law gives the equilibrium height from the tube radius, the liquid's surface tension, the contact angle between liquid and wall, and the liquid density. It explains water rising in soil, paper and plant tissues, rising damp in walls, wicking fabrics, and is used in lab measurements of surface tension.

The default 0.5 mm tube lifts water 29.8 mm; height doubles each time the radius halves.

How it is calculated

h = 2γ cos θ ÷ (ρ g r)

γ: surface tension in N/m (water at 20 °C ≈ 0.0728 N/m).
θ: contact angle in degrees; 0° means the liquid wets the wall completely.
ρ: liquid density in kg/m³; g = 9.80665 m/s².
r: tube radius, entered in mm and converted to m. The height is shown in mm.

The principle

Where the liquid surface meets the wall, surface tension pulls along the edge of the meniscus with a force γ per metre of contact line. Around a tube of circumference 2πr, the upward component is 2πrγ cos θ. The liquid stops rising when this pull equals the weight of the raised column, ρgπr²h. Solving gives h = 2γ cos θ ÷ (ρgr), described by James Jurin in 1718. The same result follows from the Laplace pressure under a curved meniscus. If θ is above 90°, cos θ is negative and the liquid is pushed down instead, as mercury is in glass.

Worked example

Inputs: r = 0.5 mm = 0.0005 m, γ = 0.0728 N/m, θ = 0°, ρ = 998 kg/m³.
Numerator: 2 × 0.0728 × cos 0° = 0.1456 N/m.
Denominator: 998 × 9.80665 × 0.0005 = 4.8935 N/m².
h = 0.1456 ÷ 4.8935 = 0.029754 m = 29.75 mm (shown as 29.75364341).

Each point is the calculator re-run with only “Tube radius (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Tube radius (mm)	Height (mm)
0.125	119.0145736
0.25	59.50728682
0.375	39.67152454
0.5	29.75364341
0.625	23.80291473
0.75	19.83576227
1	14.8768217

How to read the result

Height is inversely proportional to radius: a tube ten times narrower, 0.05 mm, would lift water about 298 mm. That is why fine-grained soils such as clays and silts can draw water much higher than sands. The law works best when the radius is small compared with the capillary length √(γ/ρg), about 2.7 mm for water; in wider tubes the meniscus flattens and the formula overestimates.

Common mistakes

Entering the diameter instead of the radius, which halves the result.
Assuming θ = 0° for dirty or coated glass; contamination can raise θ a lot and reduce the height.
Ignoring temperature: surface tension of water falls as it warms, so rise is lower in hot water.

Keep in mind: Jurin's law assumes a clean, uniform, vertical circular tube and a liquid at equilibrium. Real porous materials have irregular pores, so use it as an order-of-magnitude guide; building moisture problems need professional assessment.

Frequently asked questions

Why does mercury go down in a glass tube?

Mercury does not wet glass; its contact angle is well above 90°, so cos θ is negative and the meniscus is depressed.

Does capillary rise depend on tube length?

No, only on radius and fluid properties, provided the tube is taller than h. A shorter tube does not overflow; the meniscus just flattens at the top.

Does it work between two plates?

Yes, but for a gap of width w the rise is h = 2γ cos θ ÷ (ρgw), half that of a tube with diameter w.

Sources: J. Jurin, Philosophical Transactions of the Royal Society 30 (1718) 739–747 · P.-G. de Gennes, F. Brochard-Wyart and D. Quéré, Capillarity and Wetting Phenomena, Springer, 2004

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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