Laplace Equation Calculator

Posted by Dinesh on

Use this simple health heart stress calculator tool solving Laplace’s equation using cylindrical and spherical vessel wall thickness coordinates.

Laplace Law:

The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid pressure.
For a given vessel radius and internal pressure, a spherical vessel will have half the wall tension of a cylindrical vessel.

The Law of Laplace can also be used to explain why the pressure-overloaded left ventricle (such as that associated with aortic stenosis) will incur a higher myocardial oxygen demand than the volume-overloaded ventricle (as in aortic regurgitation). Laplace stated that wall tension is proportional to PR /2, where P is chamber pressure, and R is chamber radius. The pressure-overloaded ventricle shows a large increase in the pressure variable, which will equate to much higher wall tension, and hence MVO2 . Conversely, in the volume-overloaded ventricle the radius will increase, but not as dramatically as the pressure in the pressure-overload model. Hence the rise in wall stress in the volume overload setting will be less substantial, and the corresponding MVO2 less dramatically elevated.

A simple Laplace equation measuring the tension in the walls of a cyllinder can be related to blood vessels. Properties of this relationship helps to understand the variable thickness of arteries, veins, and capillaries.

Laplace Law Cylindrical, Spherical Vessel Wall Thickness Calculation

Pressure [p] (in mmHg) :
Radius [R] (in cm) :
Cylindrical Vessel Thickness [T] (in mm) :
Spherical Vessel Thickness [T] (in mm) :


i. T = P × R (for Cylindrical Vessel)
ii. T = (P × R / 2) (for Spherical Vessel)

  • T - Wall thickness
  • P - Pressure in mmHg
  • R - Radius