Formula of Surface Tension: T = F/L, SI Unit and Examples

The formula of surface tension is $T = \frac{F}{L}$ : the force a liquid surface exerts along a line drawn on it, divided by the length of that line. The surface behaves like a stretched skin, and T tells you how strongly that skin pulls. Water at room temperature has T ≈ 0.072 N/m.

Books use T, S or the Greek γ for the same quantity. Surface tension explains why water forms round drops, why a steel needle can rest on water and why water climbs up a thin glass tube. It belongs to the mechanical properties of fluids in Class 11, listed with the other results on the fluids formula sheet.

Quick facts

Formula
$T = \frac{F}{L}$
SI unit
newton per metre (N/m), equal to J/m²
Dimensional formula
[M¹ L⁰ T⁻²]
Soap film
two surfaces, so $T = \frac{F}{2L}$
Capillary rise
$h = \frac{2 T \cos\theta}{r \rho g}$
Excess pressure
drop $\frac{2T}{r}$ , soap bubble $\frac{4T}{r}$
Type
Scalar, falls as temperature rises

Symbols and the soap film case

Quantities in T = F / L
Symbol	Meaning	SI unit
$T$	Surface tension of the liquid	N/m
$F$	Force from the surface, acting along it and at right angles to the line	N
$L$	Length of the line along which the surface pulls	m

A thin film, such as soap solution on a wire frame, has two surfaces, front and back. Both pull on the wire, so the force is doubled for the same length:

$F = 2TL \qquad\Rightarrow\qquad T = \frac{F}{2L}$

When you use the calculator, enter the total contact length, which is 2L for a film on a straight slider. A ring lifted out of water also has two edges, the inner and outer circles, so its total length is about $2 \times 2\pi r$ .

Unit and dimensions

Force over length gives N/m. Since 1 N/m = 1 N m/m² = 1 J/m², surface tension also equals the energy needed to make one square metre of new surface. That link is developed on the formula of surface energy page.

$[T] = \frac{[\text{M L T}^{-2}]}{[\text{L}]} = [\text{M}^1\,\text{L}^0\,\text{T}^{-2}]$

The same dimensions belong to spring constant and to force per unit length in general. Each step of that working is laid out on the dimensional formula of surface tension page.

Worked examples

Example 1: a soap film on a slider

A soap film is held on a U shaped frame by a straight slider 6.0 cm long. A force of 3.6 × 10⁻³ N is needed to keep the slider still. Find the surface tension of the soap solution.

The film has two surfaces, so the total length is 2 × 0.060 = 0.12 m.

$T = \frac{3.6 \times 10^{-3}}{0.12} = 0.030\ \text{N/m}$

Example 2: capillary rise

Water (T = 0.072 N/m, angle of contact 0°) rises in a clean glass tube of radius 0.50 mm. How high does it go?

Convert: r = 5.0 × 10⁻⁴ m. With θ = 0°, cos θ = 1.

$h = \frac{2 T \cos\theta}{r \rho g} = \frac{2 \times 0.072}{5.0\times10^{-4} \times 1000 \times 9.8} = \frac{0.144}{4.9} = 0.029\ \text{m}$

About 2.9 cm. A tube half as wide would lift water twice as high.

Example 3: pressure inside a soap bubble

A soap bubble of radius 1.0 cm is made from solution with T = 0.030 N/m. Find the excess pressure inside it.

$\Delta P = \frac{4T}{r} = \frac{4 \times 0.030}{0.010} = 12\ \text{Pa}$

A liquid drop of the same size has only one surface, so its excess pressure would be 2T/r = 6.0 Pa.

Count surfaces before you substitute: one for a drop or a liquid in a tube, two for a film or a bubble.

Where the formula of surface tension shows up

Capillary action: $h = \frac{2T\cos\theta}{r\rho g}$ . Water wets glass (θ near 0°) and rises; mercury does not wet it (θ above 90°) and is pushed down.
Drops and bubbles: the curved surface squeezes the inside, giving excess pressure 2T/r for a drop and 4T/r for a soap bubble.
Floating needles and insects: the surface pull along the contact line supports a small weight.
Detergents: soap lowers T, which lets water spread into fabric instead of beading up.

Surface tension is not the same as pressure: pressure acts across an area, surface tension along a line.

Common mistakes

Forgetting the second surface of a film. This halves the answer.
Using the diameter for r in capillary rise. The formula takes the radius.
Writing the unit as N/m². That is pressure. Surface tension is N/m.
Ignoring temperature. T falls as a liquid warms, which is why hot water cleans better.

Frequently asked questions

What is the formula of surface tension?

T = F / L, the force acting along the surface per unit length of a line in it. For a soap film with two surfaces, T = F / 2L.

What is the SI unit of surface tension?

Newton per metre, N/m. It can also be written J/m² because surface tension equals surface energy per unit area.

Is surface tension a scalar or vector?

Surface tension is a scalar property of a liquid surface. The force it produces on a line has a direction, along the surface and perpendicular to the line.

Why are raindrops round?

Surface tension pulls the surface to the smallest area for a given volume, and a sphere has the least surface area of any shape.

How does temperature affect surface tension?

It decreases as temperature rises, because the molecules gain energy and the attraction holding the surface together weakens.