Young-Laplace Equation Calculator — Capillary Pressure
The Young-Laplace equation gives the pressure jump across any curved fluid interface as a function of surface tension and the principal radii of curvature. Select the geometry (liquid droplet, soap bubble, cylinder or general surface), enter the surface tension and radius, and get the Laplace pressure in Pa, kPa, mmHg and bar.
Geometry
N/m
m
Excess pressure on the concave (inner) side of the interface — Pa
145.6 Pa
ΔP- 1
Surface tension γ
0.0728 - 2
Pressure difference ΔP = 2γ ÷ R
2 × 0.0728 ÷ 0.001 = 145.60Liquid droplet has one interface — excess pressure on the concave inner side.
How does this calculator work?
ΔP = γ(1/R₁ + 1/R₂): the pressure jump across a curved fluid interface equals surface tension times the sum of the two principal curvatures. For a liquid droplet ΔP = 2γ/R, for a soap bubble ΔP = 4γ/R, and for a cylinder ΔP = γ/R. Smaller radius → larger pressure jump.
Formula
How this is calculated
The Young-Laplace equation states that the pressure difference across a curved fluid interface equals the surface tension γ multiplied by the sum of the two principal curvatures (1/R₁ + 1/R₂). The pressure is always higher on the concave (inner) side of the interface. For a spherical liquid droplet suspended in a gas there is one interface, giving ΔP = 2γ/R. A soap bubble has an inner and outer surface, doubling the contribution: ΔP = 4γ/R. For an infinite cylinder only one principal radius is finite, so ΔP = γ/R. For a general saddle-shaped surface R₂ may be negative (the two centres of curvature lie on opposite sides), reducing ΔP.
The equation is the cornerstone of capillarity: it explains why small water droplets are nearly spherical (the surface-tension pressure resists deformation), why capillary rise occurs in narrow tubes, and how gas pockets in biological tissues are stabilised or destabilised. In biology it governs alveolar pressure in the lung (where pulmonary surfactant reduces γ to prevent collapse) and in engineering it controls bubble nucleation in boiling and droplet formation in sprays.
Limitations: the equation assumes a perfectly smooth, chemically homogeneous interface and a static (equilibrium) configuration. Dynamic effects (viscosity, inertia, contact-line motion), surface contamination, and non-spherical geometries require more advanced treatment.
Frequently asked questions
A soap bubble has two air-water interfaces (inner and outer film surfaces), each contributing a surface-tension pressure of 2γ/R, giving a total excess pressure of 4γ/R. A liquid droplet in air has only one interface, so the Laplace pressure is 2γ/R.
The Laplace pressure is inversely proportional to radius: halving the droplet radius doubles the internal excess pressure. This is why fine sprays, aerosols and nanodroplets have very high internal pressures and why very small bubbles dissolve rapidly into the surrounding liquid.
Common values at 20 °C: water–air 0.0728 N/m, mercury–air 0.480 N/m, ethanol–air 0.022 N/m, oil–water ≈ 0.05 N/m (varies with type). Surface tension decreases with temperature and is strongly affected by surfactants — use measured values for precision work.
Also known as
TG we-Calculate Editorial Team. (2026). Young-Laplace Equation Calculator — Capillary Pressure [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/young-laplace-equation-calculator
TG we-Calculate Editorial Team. "Young-Laplace Equation Calculator — Capillary Pressure." TG we-Calculate. 2026. https://we-calculate.com/calculator/young-laplace-equation-calculator.
TG we-Calculate Editorial Team, "Young-Laplace Equation Calculator — Capillary Pressure," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/young-laplace-equation-calculator
@misc{wecalculate_young_laplace_equation_calculator, title = {Young-Laplace Equation Calculator — Capillary Pressure}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/young-laplace-equation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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