Membrane Tension and Laplace Pressure Calculator
Convert membrane tension into the pressure difference it can sustain across a curved surface, and check the resulting areal strain against the bilayer lysis limit.
🫧 What is Membrane Tension and Laplace Pressure?
Membrane tension is the in-plane force per unit length carried by a membrane, and Laplace pressure is the pressure difference that tension can sustain across a curved surface. The two are linked by the Young-Laplace equation, which for a sphere reads ΔP = 2σ/R. This calculator applies that relation for the three geometries that matter in cell biology and soft matter, a sphere with one interface, a soap bubble with two, and a cylinder such as a membrane tether, and it also converts the tension into the areal strain the membrane must be carrying.
The relation shows up constantly in practice. Respiratory physiology uses it to explain why pulmonary surfactant is essential, since without it the tension of the alveolar air-liquid interface would generate hundreds of pascals of collapse pressure in the smallest alveoli. Vesicle and liposome researchers use it to predict how much internal pressure a giant unilamellar vesicle can hold before lysing during micropipette aspiration. Cell mechanics groups use it to interpret tether-pulling experiments, and microfluidics engineers use the same equation to compute the capillary pressure needed to push a droplet through a narrow channel.
The most common error is applying the soap-bubble factor of 4 to a cell or a lipid vesicle. A soap film has two air-liquid interfaces, so both contribute, while a bilayer has a single mechanical surface and takes the factor 2. A second frequent mistake is treating membrane tension as a fixed material constant like the surface tension of water. It is not. Membrane tension is an elastic response, roughly KA times the fractional area change, so it rises steeply from near zero as the membrane is stretched and collapses back when area is added.
This calculator is useful because the unit chain from millinewtons per meter and micrometres to pascals is easy to get wrong by three or six orders of magnitude, and because it immediately reports the areal strain implied by the tension you entered. That strain check is the fastest way to see whether the scenario you are modelling is physically survivable for a lipid bilayer, which typically ruptures somewhere around 3% to 5% areal strain.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Giant Unilamellar Vesicle under Micropipette Aspiration
σ=0.5 mN/m, R=10 µm, sphere geometry, KA=240 mN/m
Example 2 — Alveolus with No Pulmonary Surfactant
σ=25 mN/m (bare air-liquid interface), R=100 µm, sphere geometry, KA=240 mN/m
Example 3 — Soap Bubble with Two Interfaces
σ=25 mN/m, R=5000 µm (a 5 mm bubble), soap bubble geometry, KA=240 mN/m
Example 4 — Membrane Tether Pulled from a Cell
σ=1 mN/m, R=0.05 µm (a 50 nm radius tube), cylinder geometry, KA=240 mN/m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Young-Laplace equation for a membrane?
For a spherical membrane the Young-Laplace equation is dP = 2 sigma / R, where dP is the pressure difference across the membrane, sigma is the membrane tension, and R is the radius of curvature. A soap bubble with two interfaces uses dP = 4 sigma / R, and a cylinder uses dP = sigma / R.
Why is the factor 4 used for a soap bubble but 2 for a cell?
A soap bubble has two air-liquid interfaces, an outer and an inner surface, and each contributes its own 2 sigma / R, giving 4 sigma / R in total. A lipid vesicle or a cell has a single mechanical membrane, so the correct factor is 2. Using 4 for a cell doubles the computed pressure.
What is a typical membrane tension in a living cell?
Resting plasma-membrane tension in animal cells is usually measured between about 0.003 and 0.04 mN/m by tether pulling, rising several-fold during spreading, migration, or osmotic swelling. Giant unilamellar vesicles under micropipette aspiration are commonly studied between 0.01 and 5 mN/m.
At what tension does a lipid bilayer rupture?
Fluid phospholipid bilayers lyse at roughly 3 to 10 mN/m, corresponding to an areal strain of about 3% to 5% because the area compressibility modulus is around 240 mN/m. This calculator reports the areal strain and flags values in that danger band.
How do I convert Laplace pressure from pascals to mmHg?
Divide the pressure in pascals by 133.322 to get millimetres of mercury. For example, a 500 Pa pressure difference is 3.75 mmHg. The calculator reports both units, plus kilopascals in the reference table.
How does radius affect Laplace pressure?
Pressure scales inversely with radius, so halving the radius doubles the pressure difference at constant tension. That is why small vesicles and capillaries sustain far higher pressure differences than large ones, and why the pressure curve on this page is a hyperbola rather than a straight line.
What is areal strain and how is it related to tension?
Areal strain is the fractional increase in membrane area, alpha = sigma / K_A, where K_A is the area compressibility modulus (about 240 mN/m for a fluid bilayer). A tension of 5 mN/m therefore stretches the membrane area by about 2%, which is already close to the rupture limit.
Why does the alveolus need surfactant according to Laplace's law?
Without surfactant the air-liquid interface of an alveolus would have a tension near 25 mN/m, producing about 500 Pa of collapse pressure at a 100 micrometre radius. Pulmonary surfactant drops the tension several-fold at small radii, which lowers the pressure and stops small alveoli from emptying into large ones.
Does Laplace pressure apply to membrane tethers and tubes?
Yes, but with the cylindrical form dP = sigma / R, because a cylinder is curved in one direction only. A 50 nm radius tether at 1 mN/m therefore sustains about 20 kPa, which is very large compared with the pressure a giant vesicle sustains at the same tension.
What is the difference between membrane tension and surface tension?
Both have units of force per length, but surface tension arises from cohesive forces at a liquid interface and is a fixed material property, while membrane tension is an elastic response to stretching, given by K_A times the areal strain. A bilayer therefore has no single fixed tension, its tension depends on how much its area has been stretched.
How is membrane tension measured in the laboratory?
The main techniques are micropipette aspiration of giant unilamellar vesicles, optical-tweezers tether pulling, atomic force microscopy indentation, and fluorescent membrane-tension probes such as Flipper-TR. Micropipette aspiration is the reference method because it sets tension directly through the suction pressure.
Can Laplace pressure explain why cells resist osmotic swelling?
Partly. As a cell swells, membrane area strain rises and tension climbs steeply because K_A is large, and the resulting Laplace pressure opposes further inflow. However the membrane can only stretch a few percent before lysing, so cells mainly rely on regulatory volume decrease and mechanosensitive channels rather than membrane elasticity alone.