Last updated: July 3, 2026
Young-Laplace Equation Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Young-Laplace equation calculator computes the pressure difference across a spherical curved liquid interface. It uses ΔP = 2γ/r for one liquid-gas interface and ΔP = 4γ/r for a soap bubble with two interfaces, implemented as ΔP = 2Nγ/r where N is 1 or 2. Enter surface tension in N/m and radius in m to get pressure in Pa.
For a spherical droplet, the Young-Laplace pressure difference equals two times surface tension divided by radius. For a soap bubble with two interfaces, it equals four times surface tension divided by radius.
Key Takeaways
- For one spherical interface, Young-Laplace pressure is ΔP = 2γ/r.
- A soap bubble has two interfaces, so ΔP = 4γ/r.
- Laplace pressure increases linearly with surface tension and inversely with radius.
- Use SI units: γ in N/m and r in m give ΔP in Pa.
- The general equation for unequal curvature is ΔP = γ(1/R1 + 1/R2).
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
ΔP = 2 × N × γ / r, where N is the number of interfaces
Where:
- ΔP=Pressure difference across the curved interface(Pa)
- γ=Surface tension(N/m)
- r=Spherical radius of curvature(m)
- N=Number of interfaces(dimensionless (1 or 2))
Worked Examples
Water droplet with 1 mm radius
A water droplet has one liquid-air interface and γ = 0.072 N/m.
- 1Use ΔP = 2 × N × γ / r.
- 2Substitute N = 1, γ = 0.072 N/m, and r = 0.001 m.
- 3ΔP = 2 × 1 × 0.072 / 0.001 = 144 Pa.
Low-surface-tension droplet
A small droplet with γ = 0.025 N/m and radius 0.0005 m.
- 1Apply the spherical one-interface equation ΔP = 2γ/r.
- 2Substitute γ = 0.025 N/m and r = 0.0005 m.
- 3ΔP = 2 × 0.025 / 0.0005 = 100 Pa.
Soap bubble with two interfaces
A soap bubble film has inner and outer surfaces, so the Laplace pressure is doubled.
- 1Use N = 2 for a soap bubble, giving ΔP = 4γ/r.
- 2Substitute γ = 0.030 N/m and r = 0.002 m.
- 3ΔP = 4 × 0.030 / 0.002 = 60 Pa.
Introduction
The Young-Laplace equation links surface tension to the pressure jump across a curved interface. For a spherical droplet or bubble, curvature makes the pressure on the concave side higher by ΔP = 2γ/r for one interface. A soap bubble has two liquid-gas surfaces, so the pressure jump becomes ΔP = 4γ/r. This calculator reports Laplace pressure in pascals and pairs naturally with the osmotic pressure calculator and partial pressure calculator when comparing capillary pressure to other pressure effects. The thermodynamic background is discussed in LibreTexts surface chemistry and IUPAC guidance on quantities and units.
Young-Laplace formula for a sphere
The general Young-Laplace equation is ΔP = γ(1/R1 + 1/R2), where R1 and R2 are principal radii of curvature. A sphere has R1 = R2 = r, so ΔP = 2γ/r for one interface. If a thin soap film has both an inner and outer surface, the contribution is doubled: ΔP = 4γ/r.
Higher surface tension increases ΔP linearly.
Smaller radius increases ΔP inversely.
Use one interface for ordinary droplets and gas bubbles.
Use two interfaces for soap bubbles or very thin free films.
How to calculate Laplace pressure
Enter the surface tension in N/m, radius in metres, and whether the object has one or two interfaces. The calculator multiplies 2γ/r by the interface count N. Use SI units throughout so the result is in pascals, because 1 N/m divided by 1 m equals 1 N/m² = 1 Pa.
Measure or look up γ at the experiment temperature.
Convert micrometres or millimetres to metres.
Choose N = 1 for a droplet or single bubble surface.
Choose N = 2 for a soap bubble film.
What the pressure difference means
Surface tension acts like a contractile skin on the interface. Curving that interface inward requires a higher pressure on the concave side to balance the surface force. This is why tiny droplets and bubbles can have surprisingly large internal pressures, while large droplets have almost negligible Laplace pressure.
The sign of ΔP depends on which side you call inside; this calculator reports the positive pressure magnitude.
Typical surface-tension and radius scales
Laplace pressure becomes important whenever a radius is small enough that capillary forces compete with hydrostatic, gas, or osmotic pressure. Compare micron-scale droplets to macroscopic drops before deciding whether ΔP can be ignored.
| System | Typical γ | Typical radius | Pressure scale |
|---|---|---|---|
| Water-air at room temperature | 0.072 N/m | 1 mm | 144 Pa |
| Water-air microdroplet | 0.072 N/m | 10 µm | 14.4 kPa |
| Surfactant solution | 0.025–0.040 N/m | 0.5 mm | 100–160 Pa |
| Soap bubble | 0.025–0.035 N/m | 2 mm | 50–70 Pa |
Applications in chemistry and materials science
Young-Laplace pressure appears in emulsions, foams, aerosols, capillary rise, nucleation, inkjet droplets, porous catalysts, and microfluidic devices. It is also central to interpreting pressure-driven flow in small pores, where the relevant radius may be a meniscus radius rather than a physical tube radius. For transport comparisons, see the diffusion coefficient calculator and Langmuir isotherm calculator.
Assumptions and limitations
This calculator implements the spherical case. Real interfaces may have two unequal principal curvatures, contact-angle effects, gravity, dynamic surfactant adsorption, electric fields, or nonuniform temperature. For a nonspherical interface you need the general equation ΔP = γ(1/R1 + 1/R2), with signs chosen by a consistent curvature convention.
If gravity deforms a large droplet, use a capillary length or full shape analysis rather than the simple spherical formula.
Quick Reference Card
Young-Laplace Equation — Quick Reference
Quick reference • Young-Laplace Equation Calculator
ΔP = 2Nγ/r; N = 1 for one interface, N = 2 for a soap bubbleValid range: Best for spherical interfaces with uniform surface tension and radii small enough that gravity does not strongly deform the shape.
Common Values
⚠ Watch Out
- •Do not enter radius in millimetres or micrometres without converting to metres.
- •Use two interfaces only for thin films such as soap bubbles, not ordinary liquid droplets.
- •The spherical formula is not exact for flattened, pendant, or strongly gravity-deformed droplets.
- •Surface tension depends strongly on temperature, surfactants, impurities, and composition.
- •For nonspherical interfaces, use the general two-radius Young-Laplace equation.
Pro Tips
- →For quick water estimates, ΔP ≈ 0.144/r_mm Pa for one interface with r in millimetres.
- →Check whether surfactants are present before using pure-water surface tension.
- →If two principal radii differ, calculate γ(1/R1 + 1/R2) instead of forcing one radius.
- →Use pressure magnitude for comparison, then assign sign based on your curvature convention.
- →Compare ΔP with hydrostatic pressure ρgh when deciding if gravity can be ignored.
FAQs
What is the Young-Laplace equation?
It is the relation between surface tension, interface curvature, and pressure difference: ΔP = γ(1/R1 + 1/R2). For a spherical interface this becomes ΔP = 2γ/r.
Why does a soap bubble use 4γ/r instead of 2γ/r?
A soap bubble is a thin liquid film with two gas-liquid interfaces, one on the outside and one on the inside. Each contributes 2γ/r for a spherical film, so the total is 4γ/r.
What units should I enter?
Enter surface tension in newtons per metre and radius in metres. The result is then in pascals because N/m divided by m is N/m².
Does smaller radius increase pressure?
Yes. Laplace pressure is inversely proportional to radius, so halving the radius doubles the pressure difference for the same surface tension and interface count.
Can I use this for nonspherical droplets?
Only as an approximation. For nonspherical shapes use the general form with two principal radii of curvature, ΔP = γ(1/R1 + 1/R2).
Which side has the higher pressure?
For a spherical droplet in air, the pressure inside the droplet is higher than outside by the calculated ΔP. The calculator reports the positive magnitude of that pressure jump.