Surface Tension formula

What is Surface Tension?

Surface tension is the attractive force in liquids that pulls surface molecules into the rest of the liquid, minimizing the surface area. These attractive forces are due to electrostatic forces. We typically refer to this cohesion at the gas-liquid surface (not liquid-solid or liquid-liquid surfaces). We often see this occur with water, but it occurs with all other liquids to some degree.

Also Surface Tension can also be defined as the energy required to increase the surface area of a liquid by a unit of area. The surface tension of a liquid results from an imbalance of inter-molecular attractive forces, the cohesive forces between molecules.

It has the dimension of force per unit length, or of energy per unit area. The two are equivalent, but when referring to energy per unit of area, it is common to use the term surface energy, which is a more general term in the sense that it applies also to solids.

Image result for surface tension


Surface tension = (surface force)/(length force acts)

The equation is

γ = F /d

We have:

γ: Surface tension

F: Force applied on the liquid

d: length where the force acts


1) A small piece of metal of 1cm long weights 0.1 N, what is the surface tension?

Answer: The surface tension is calculated using the formula,

γ = F/d

γ = 0.1N/1 cm = 0.1 N/ 0.01 m = 10 N/m.

2) If the surface tension is measured to be 5 N/m, and a small insect of about 1.5 cm long is posed on the water. What is the approximate mass of the insect?

Answer: From the surface tension is found the force, which in this case is the weight:

F = γ d

F = 5 N/m * 1.5 cm = 5 N/m * 0.015 m = 0.075 N

Then the mass of the insect is given by,

M = F/g

Where g = 9.8 m/s2 is the acceleration of gravity.


M = 0.075 N / 9.8 m/s2 = 0.0076 Kg = 7.6 grams


Beading of rainwater on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape because a sphere has the smallest possible surface area to volume ratio.

  • Formation of drops occurs when a mass of liquid is stretched. The animation (below) shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension can no longer keep the drop linked to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water was running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.
  • Flotation of objects denser than water occurs when the object is non-wettable and its weight is small enough to be borne by the forces arising from surface tension. For example, water striders use surface tension to walk on the surface of a pond in the following way. The non-wettability of the water strider’s leg means there is no attraction between molecules of the leg and molecules of the water, so when the leg pushes down on the water, the surface tension of the water only tries to recover its flatness from its deformation due to the leg. This behavior of the water pushes the water strider upward so it can stand on the surface of the water as long as its mass is small enough that the water can support it. The surface of the water behaves like an elastic film: the insect’s feet cause indentations in the water’s surface, increasing its surface area and the tendency of minimization of surface curvature (so area) of the water pushes the insect’s feet upward.
  • Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called “interface tension”, but its chemistry is the same.
  • Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

Contact Angle

The surface of any liquid is an interface between that liquid and some other medium. Surface tension is not a property of the liquid alone, but a property of the liquid’s interface with another medium eg. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container.

Where the two surfaces meet(liquid and some other medium), they form a contact angle, θ, which is the angle the tangent to the surface makes with the solid surface. Note that the angle is measured through the liquid.


Image result for contact angle and surface tension

Practical Applications

Some common examples of Surface Tension are given below.

  •  Mosquito eggs can float on water because of its surface tension. Kerosene is sprayed on water so that the mosquito eggs sink and the breeding stops.
  • Warm water is used for washing purpose as heating increases the surface area and reduces surface tension. This action is replicated by adding detergents to cold water.
  • A needle placed on water can be made to float due to the tension of water. If the surface is ruffled, the needle will quickly sink.
  • The test for jaundice involves the use of surface tension properties. Sulfur powder is sprinkled on the urine sample. If it does not contain bile, the sulfur powder floats due to surface tension. If bile is present in the sample, the surface tension of urine reduces and the sulfur powder sinks.
  • Toothpaste contains soap, which reduces the surface tension and helps it spread freely in the mouth.
  • Disinfectants have low surface tension, which allow them to spread through cell walls of bacteria.

Commercial Applications

  • Chemical industry manufactures paints, inks, coloring ingredients, insecticides which are dependent on the Tension of the liquid.
  • Automobile manufacturing (surface preparation prior to painting, treatment of glass to prevent water from dewetting, treatment of tires to promote adhesion even on wet or icy roadways)
  • Glass (anti-stain or anti-frost treatment)
  • Food (dissolving powders such as milk or cocoa)
  • Soil science (penetration of liquids into porous rocks)
  • Construction (waterproofing of concrete, protection of monuments, treatment of greenhouse plastic)
  • Domestics (spreading of creams, application of mascara to eyelashes, self-drying shampoos)

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