Pick your interface type (sphere, cylinder, or general surface), enter the surface tension (γ) and the relevant principal radii R₁ and R₂ (or just R for symmetric geometries), and this Young-Laplace Equation Calculator returns the pressure difference (ΔP) across the interface, along with the mean curvature and surface tension in SI units.
Pressure Difference (ΔP)
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Mean Curvature
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Surface Tension (SI)
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The Young-Laplace equation describes the pressure difference across a curved interface between two fluids due to surface tension. It calculates the capillary pressure jump: ΔP = γ(1/R₁ + 1/R₂) for general curvature, where γ is surface tension and R₁, R₂ are principal radii of curvature.
Capillary pressure is the pressure difference across a curved interface caused by surface tension forces. It's crucial in petroleum engineering for oil recovery, in biology for lung function, and in materials science for understanding wetting phenomena and droplet formation.
For spherical interfaces, use the simplified form: ΔP = 2γ/R, where R is the sphere radius. This applies to soap bubbles, water droplets, and gas bubbles in liquids. The pressure inside is always higher than outside due to surface tension.
Spherical interfaces have curvature in all directions (ΔP = 2γ/R), while cylindrical interfaces curve in only one direction (ΔP = γ/R). Cylindrical calculations apply to long tubes, fibers, or elongated bubbles where one dimension is much larger than the others.
Common surface tension units are mN/m (millinewtons per meter) or N/m. For radius, use mm, cm, or m depending on your system size. The calculator automatically converts units to ensure dimensional consistency in the final pressure result.
Capillary pressure controls fluid flow in porous rocks, affecting oil and gas extraction efficiency. It determines how fluids distribute in reservoir rocks, influences enhanced oil recovery techniques, and helps predict fluid behavior during drilling and production operations.
General curvature mode uses two principal radii (R₁ and R₂) to describe any curved surface. For saddle shapes, one radius can be negative. This mode is most accurate for irregular interfaces that aren't perfectly spherical or cylindrical.
The pressure jump results from molecular forces at the interface. Surface tension creates an inward force that must be balanced by higher pressure on the concave side. Smaller radii of curvature create larger pressure differences, which is why tiny droplets have very high internal pressure.