Calculator
Example data table
| Case | γ (N/m) | Geometry | R1 | R2 | ΔP (Pa) |
|---|---|---|---|---|---|
| Water droplet, 1 mm sphere | 0.072 | Sphere | 1 mm | 1 mm | 144 |
| Soap bubble, 50 µm sphere | 0.030 | Sphere | 50 µm | 50 µm | 1200 |
| Liquid column, 2 mm cylinder | 0.050 | Cylinder | 2 mm | ∞ | 25 |
Formula used
The Laplace pressure (pressure jump across a curved interface) is: ΔP = γ(1/R1 + 1/R2)
- γ is surface tension in N/m.
- R1, R2 are principal radii of curvature in meters.
- For a sphere: R1 = R2 = R so ΔP = 2γ/R.
- For a cylinder: R2 → ∞ so ΔP = γ/R.
If you also enter outside pressure, the inside pressure is computed using your selected sign convention.
How to use this calculator
- Select the geometry that best matches your interface.
- Enter surface tension γ in N/m.
- Provide radius R for sphere/cylinder, or both R1 and R2 for general surfaces.
- Choose a sign convention that matches your textbook or notes.
- Optionally add outside pressure to compute absolute inside pressure.
- Click Calculate to display results above this form.
- Use the download buttons to export the computed outputs.
Professional article
1) What Laplace pressure represents
Laplace pressure is the pressure difference created by surface tension at a curved interface. A smaller radius means higher curvature, so the inside–outside pressure jump increases. This is why tiny bubbles and droplets behave “stiffer” than large ones,
2) Core equation and curvature data
The governing relation is ΔP = γ(1/R1 + 1/R2). The calculator reports the combined curvature term in 1/m, so you can see how geometry drives the result. For a sphere, R1 = R2 = R and ΔP becomes 2γ/R. For a cylinder, one radius is infinite, giving ΔP = γ/R.
3) Typical surface tension values used in practice
Surface tension varies with temperature and contamination. As a reference, clean water near room temperature is about 0.072 N/m, while many soap solutions fall near 0.025–0.035 N/m. Oils can range roughly 0.020–0.035 N/m, and some liquid metals exceed 0.400 N/m.
4) Scale effects: droplets, bubbles, and aerosols
Scale strongly matters. With γ = 0.072 N/m and a spherical radius of 1 mm, ΔP ≈ 144 Pa. At 100 µm, ΔP rises to about 1.44 kPa. At 10 µm, ΔP reaches ~14.4 kPa, comparable to large fractions of atmospheric pressure, affecting stability and evaporation.
5) Engineering relevance in microfluidics
In microchannels, pressure budgets are limited, so interfacial curvature can dominate flow control. Droplet generators, emulsification, and inkjet nozzles all rely on predictable ΔP to pinch off droplets and prevent satellite formation. Reporting ΔP in kPa, bar, or mmHg helps match instrument readouts
6) Biomedical and environmental examples
Biology uses the same physics. Alveoli in lungs require surfactants to lower γ and reduce ΔP, supporting inflation at reasonable pressures. In foams and sea spray aerosols, curvature-driven pressure influences gas exchange and bubble lifetimes. The calculator’s sign option helps align with different textbook conventions.
7) Interpreting sign and absolute pressures
Many references define ΔP as Pinside − Poutside, meaning a convex droplet interior is higher pressure. If you select the opposite convention, the calculator flips the sign while keeping magnitudes consistent. When you enter outside pressure, the tool also estimates inside absolute pressure
8) Quality checks and good measurement habits
For reliable results, confirm radius units, keep γ consistent with your temperature, and avoid using R values near zero. If the interface is not static, viscous and dynamic effects can add to measured pressure differences. Use the conversion panel to sanity-check whether the magnitude is physically plausible.
FAQs
1) What is the difference between a bubble and a droplet here?
A droplet has one liquid–gas interface. A soap bubble has two interfaces (inner and outer films), so some texts use ΔP = 4γ/R. This calculator uses the single-interface Laplace relation unless you model the bubble explicitly.
2) Can R1 or R2 be negative?
Yes. A negative principal radius represents curvature in the opposite direction based on your chosen “inside.” Mixed signs can occur on saddle-shaped surfaces and can reduce ΔP if the curvatures partially cancel.
3) Why does a cylinder use an infinite second radius?
A perfect cylinder is curved in one direction and flat in the other. Flat curvature corresponds to 1/R = 0, which is represented by R → ∞. That is why the second term drops out.
4) What units should I use for surface tension?
Use N/m. If your data is in mN/m, divide by 1000 before entering it. Keeping γ in N/m and radii in meters ensures ΔP is calculated in pascals and converted correctly.
5) Does temperature matter?
Yes. Surface tension generally decreases as temperature increases. Even small contamination can change γ significantly, especially for water. For high-accuracy work, use measured γ values at the same temperature and composition as your experiment.
6) When is Laplace pressure not enough?
When the interface moves quickly, dynamic pressure, viscosity, and inertial effects can contribute. Contact angle and confinement can also modify curvature. Use Laplace pressure as the static baseline, then add flow or wetting models if needed.
7) Why are my results much larger at micron scales?
Because ΔP scales as 1/R. Reducing radius from 1 mm to 10 µm increases curvature by 100×, so ΔP increases by about 100×. This is why microbubbles can require surprisingly high internal pressures.
Notes and assumptions
- Valid for static interfaces with well-defined curvature.
- Radii may be negative if curvature orientation is reversed.
- Extremely small radii can yield large pressures; verify inputs.
- Surface tension depends on temperature and contamination.
Measure wisely, verify units, and document your assumptions.