Chemistry

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Young–Laplace Equation Calculator.

Calculate spherical-interface pressure difference from surface tension and radius.

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Pressure difference: 144 Pa

Pressure difference

144.000000Pa

Educational formula calculator. Keep units consistent and verify assumptions against your laboratory or course specification.

Use Cases

Bubble and droplet analysis

Determine the pressure inside a gas bubble or liquid droplet relative to the surrounding fluid, which is essential in studies of foams, emulsions, and cavitation.

Example: For a water droplet with surface tension 0.072 N/m and radius 1e-6 m, ΔP = 144,000 Pa.

Capillary and wetting phenomena

Estimate the pressure jump across curved menisci in capillary tubes or porous media, aiding in the design of microfluidic devices and inkjet printing.

Example: Calculate the pressure needed to force a liquid through a narrow capillary.

Frequently Asked Questions

What does the Young–Laplace equation calculate?
It calculates the pressure difference (ΔP) across a curved interface, such as a bubble or droplet, using the formula ΔP = 2γ/r, where γ is surface tension and r is the radius of curvature.
What units should I use for surface tension and radius?
Use SI units: surface tension in newtons per meter (N/m) and radius in meters (m). The calculator will output the pressure difference in pascals (Pa).
Can this calculator be used for non-spherical interfaces?
No, this calculator is specifically for spherical interfaces. For non-spherical shapes, the general Young–Laplace equation involves two principal radii of curvature.

Tips & Common Mistakes

Tips

  • Ensure surface tension is in N/m and radius in meters to get pressure in pascals.
  • For very small radii (e.g., nanometers), the pressure difference can be extremely large—check your inputs for scientific notation.
  • Remember that the pressure is higher on the concave side of the interface (inside a bubble or droplet).
  • Use consistent units: if you have surface tension in mN/m, convert to N/m by dividing by 1000.

Common Mistakes to Avoid

  • Using radius in millimeters or micrometers without converting to meters, leading to incorrect pressure values.
  • Confusing surface tension with surface energy—they have the same units but represent different concepts.
  • Applying the formula to flat interfaces, where the pressure difference is zero.

Last updated: August 13, 2026