Young-Laplace Equation Calculator
Determine capillary pressure differences for droplets, bubbles, and membranes with specified curvature radii.
Water at 25 C has gamma about 0.072 N/m.
Leave blank for spherical surfaces (R1 = R2).
Pressure difference (inside - outside)
144 Pa
How to Use This Calculator
Measure surface tension
Use N/m values from literature or tensiometer measurements for the interface.
Specify primary radius
Enter the principal curvature radius R1 in meters.
Optionally provide second radius
For asymmetric curvature surfaces, supply R2. Leave blank for spheres or cylinders.
Review capillary pressure
The result gives the pressure jump across the interface as predicted by Young-Laplace.
Formula
DeltaP = gamma (1/R1 + 1/R2)
For spherical droplets with equal radii, DeltaP = 2 gamma / R. Units: gamma in N/m, radii in meters, pressure in pascals.
Example
For gamma = 0.072 N/m and R = 1 mm: DeltaP = 2 * 0.072 / 0.001 = 144 Pa.
Full Description
The Young-Laplace equation connects surface curvature and tension to pressure differences in capillaries, vesicles, and bubbles.
It is fundamental in microfluidics, porous media flow, and membrane mechanics, guiding predictions of meniscus pressure and capillary rise.
Frequently Asked Questions
What if R2 is negative?
Use sign conventions carefully. This tool expects positive radii and assumes convex curvature with positive pressure inside.
Can I use diameter instead?
Convert diameter to radius by dividing by two before entering values.
Does temperature affect gamma?
Yes. Surface tension decreases with temperature. Use data measured near your operating condition.
How do I handle cylindrical menisci?
Set R2 to a large number to approximate zero curvature in one direction, or use the actual principal radii.
Is gravity included?
No. This calculation gives local pressure difference due to curvature only. Hydrostatic effects require additional terms.