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Chemistry

Young-Laplace pressure (capillary) calculator

Pressure difference across a curved liquid interface, from surface tension and curvature.

What this calculator does

Young-Laplace pressure (capillary) works out pressure difference across a curved liquid interface, from surface tension and curvature. Enter your own figures above and the answer updates as you type: nothing is fixed in the code, so the result reflects exactly the numbers you supply.

The formula this calculator evaluates is printed under the tool and explained below, so you can check the working by hand or reuse it in a spreadsheet.

The formula

FormulaΔP = γ(1/R₁ + 1/R₂); a sphere (R₁=R₂=R) reduces to ΔP = 2γ/R

The inputs explained

FieldWhat to enter
Surface tension γ (N/m)A number, measured in N/m. Starts at 0.0728.
First principal radius R₁ (m)A number, measured in m. Starts at 0.001.
Second principal radius R₂ (= R₁ for a sphere) (m)A number, measured in m. Starts at 0.001.

Worked examples

Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.

How the answer changes with surface tension γ

Every other input is held at the calculator’s starting values while surface tension γ varies. Select any row to load that scenario into the calculator.

How the answer changes with surface tension γ
Surface tension γ (N/m)Pressure difference ΔPPressure difference ΔPSurface tension used
0.0480.00 Pa0.0800 kPa0.0400 N/m
0.05100.00 Pa0.1000 kPa0.0500 N/m
0.07140.00 Pa0.1400 kPa0.0700 N/m
0.11220.00 Pa0.2200 kPa0.1100 N/m
0.15300.00 Pa0.3000 kPa0.1500 N/m
0.22440.00 Pa0.4400 kPa0.2200 N/m