Surface tension is the force a liquid surface pulls with along every centimetre of its edge — γ = F / (n·L), in newtons per metre. This free calculator solves for the surface tension itself, for the force a film exerts, for the excess pressure inside a droplet or a bubble, and for how far a liquid climbs a narrow tube, showing every step of the working.
What Is the Surface Tension Calculator?
The surface tension calculator is a free online tool built on the formula γ = F / (n · L). Enter the values you already know, in whichever units suit you, and it solves for surface tension, force, excess pressure or capillary rise and shows every step of the substitution. Surface Tension is force per unit length, plus bubble pressure and capillary rise.
| Symbol | Quantity | Default unit | Also accepts | Example value |
|---|---|---|---|---|
| F | Force on the wire | N | mN, µN | 0.003 |
| L | Wetted length | m | cm, mm | 0.06 |
| n | Liquid surfaces (1 or 2) | surfaces | — | 2 |
| γ | Surface tension | N/m | mN/m, dyn/cm | — |
| R | Drop / bubble radius | m | cm, mm, µm | — |
| r | Capillary tube radius | m | cm, mm, µm | — |
| θ | Contact angle | ° | — | 0 |
| ρ | Liquid density | kg/m³ | g/cm³ | 1000 |
How to calculate surface tension
A liquid surface behaves like a stretched skin, and surface tension measures how hard that skin pulls: divide the force by the length of the line it acts along, γ = F / (n·L). The n is a count of liquid surfaces, and it is the step most often skipped. A soap film on a wire frame has a front face and a back face, so a slider wire feels two pulls and the measured force must be halved before dividing by the length. A bare water surface has one. Water at 20 °C comes out at 0.0728 N/m, mercury at roughly 0.485 N/m, and soap solution near 0.025 N/m. Where that skin comes from, and the everyday effects it explains, are covered in the guide to surface tension.
The same γ then answers two further questions. Curve the surface and it squeezes what is inside: the excess pressure across a single interface is ΔP = 2γ/R, so a small droplet is under far more pressure than a large one. A soap bubble has two interfaces rather than one, which is why its answer is 4γ/R — set the surfaces field to 2 and the calculator applies it. Because this is a pressure like any other, it adds to whatever the surroundings supply; the pressure calculator handles the ambient part, including the P = ρgh term that grows with depth.
Put the liquid in a narrow tube and the same tension lifts it: h = 2γ·cosθ / (ρ·g·r), with g fixed here at 9.81 m/s². Three things follow immediately. Narrower tubes lift further, because r is in the denominator — halve the bore and the liquid climbs twice as high. Denser liquids climb less, which is where the density calculator earns its place. And the contact angle decides the direction: below 90 degrees the cosine is positive and the liquid rises, above 90 degrees it is negative and the liquid is pushed down instead. Mercury in glass sits at about 140 degrees and does exactly that. The calculator returns the negative number rather than hiding it, because the sign is the physics.
To watch all three behaviours at once rather than reading them off, the surface tension simulator redraws a bead and a capillary column live as you drag the tension, angle and radius. For the neighbouring liquid property that governs how fast a liquid flows rather than how hard its surface pulls, see the viscosity converter.
Worked example
A rectangular wire frame carries a soap film, and the movable slider wire is 6.0 cm long. A force of 3.0 × 10-3 N holds it in place. The film has two faces, so γ = F / (n·L) = 0.0030 / (2 × 0.060) = 0.025 N/m, or 25 mN/m — a typical soap solution. Blow that same solution into a bubble of radius 2.0 cm and the excess pressure is ΔP = 4γ/R = 4 × 0.025 / 0.020 = 5.0 Pa. For comparison, a 1.0 mm water droplet, which has only one surface, holds 2γ/R = 2 × 0.0728 / 0.0010 = 145.6 Pa. Drop a clean glass capillary of 0.20 mm bore into water and it climbs h = 2 × 0.0728 × cos(0°) / (1000 × 9.81 × 0.00020) = 0.0742 m, about 7.4 cm.
Why it matters
Surface tension sets the size of raindrops and the shape of a mercury bead, lets pond skaters stand on water, and drives the capillary action that carries sap up plants, ink through paper and water through soil and concrete. It governs how detergents and lung surfactant work, how inkjet and 3D-printing nozzles break a stream into drops, how solder wets a joint, and how bubbles in foams and boiling liquids grow or collapse. Wherever a liquid meets a surface it does not simply spread across, surface tension is the reason.
Frequently asked questions
What unit is surface tension measured in?
The SI unit is the newton per metre (N/m), because surface tension is a force per unit length of the line the surface pulls along. Laboratory values are usually quoted in millinewtons per metre: water at 20 degrees C is 72.8 mN/m, or 0.0728 N/m. The older CGS unit, the dyne per centimetre, is numerically identical to the millinewton per metre. An equivalent reading of the same number is energy per unit area, in joules per square metre, since 1 N/m equals 1 J/m2.
Why do I set 2 surfaces for a soap film?
A soap film stretched across a wire frame has two faces, a front and a back, and each one pulls on the slider wire. The measured force is therefore twice what a single surface would give, so the surface tension is F divided by 2L rather than by L. A bubble is the same idea wrapped into a sphere: it has an inner wall and an outer wall. A plain liquid surface, such as a water droplet or a liquid in a tube, has only one and counts as 1.
Why is bubble pressure double droplet pressure?
The Young-Laplace excess pressure across a single curved liquid surface is 2 gamma / R. A liquid droplet has exactly one such surface, so that is its answer. A soap bubble is a thin shell with two surfaces, an inner and an outer, and each contributes its own 2 gamma / R, giving 4 gamma / R in total. At the same radius and the same surface tension, a bubble therefore holds twice the excess pressure of a droplet. This calculator applies whichever the surfaces field says.
What contact angle should I use for water on glass?
Clean water on clean glass is close to 0 degrees, which is why 0 is the default and why water climbs a glass capillary so strongly. Slightly contaminated or ordinary laboratory glass is nearer 20 to 30 degrees. Water on paraffin wax is about 105 degrees, water on PTFE roughly 108, and mercury on glass around 140. Anything above 90 degrees gives a negative cosine and so a negative rise.
Why is my capillary rise negative?
Because you entered a contact angle above 90 degrees. Capillary rise is h = 2 gamma cos(theta) / (rho g r), and cos(theta) is negative for any angle past 90 degrees, so h comes out negative. That is not an error: it is a capillary depression, where the liquid in the tube sits BELOW the level of the surrounding reservoir. Mercury in a glass tube does exactly this. The calculator reports the negative value rather than clamping it to zero, because the sign is the physics.
References & formula source
- Young, T. — "An Essay on the Cohesion of Fluids", Philosophical Transactions of the Royal Society of London (the original contact-angle relation).
- Laplace, P.-S. — Traité de Mécanique Céleste, supplement on capillary action (the excess-pressure result).
- Bush, J. W. M. — MIT 1.63J/2.21J, Surface Tension Module, Lecture 1: definition, units and scaling.
- Further reading: Surface tension — Wikipedia