Enter the internal pressure, external pressure, and the surface area into the calculator to determine the net force from a pressure difference across a surface (ΔP · A).

Pressure Difference Force (ΔP·A) Calculator

Enter any 3 values to calculate the missing variable. Note: this calculator treats the force as a magnitude (non-negative). When solving for a missing pressure, it assumes the internal pressure is the higher pressure.

Pressure Difference Force (ΔP·A) Formula

The following equation is used to calculate the force magnitude on a surface caused by a pressure difference between the two sides (often written as ΔP · A).

F = |IP - EP| * A
  • Where F is the force magnitude (N or lbf)
  • IP is the internal pressure (any pressure unit)
  • EP is the external pressure (same unit as IP)
  • A is the surface area (units consistent with the pressure unit)

To calculate the force magnitude from a pressure difference, subtract the external pressure from the internal pressure, take the absolute value, then multiply by the surface area. For example, using psi with in² gives lbf, and using Pa with m² gives N.

What is Force From a Pressure Difference?

Definition:

Force from a pressure difference (also called pressure differential force) is the net force on a surface when the pressure on one side differs from the pressure on the other side. If the pressure is approximately uniform over the surface, the force magnitude is the pressure difference times the area: F = |ΔP| · A.

If pressure varies across the surface, the more general relationship is an area integral: F = ∬(pinternal − pexternal) dA. In fluid dynamics and meteorology, the term “pressure-gradient force” usually refers to the body-force density −∇p (force per unit volume). This calculator uses the common engineering surface-force approximation based on a pressure difference across a defined area.

How to Calculate Pressure Difference Force?

Example Problem:

The following example outlines the steps and information needed to calculate the force from a pressure difference across a surface.

First, determine the internal pressure. For this example problem, the internal pressure is measured to be 50 psi.

Next, determine the external pressure. In this case, the external pressure is 25 psi.

Next, determine the total surface area the pressure difference is acting on. For this problem, the area is 5 square inches (in²).

Finally, calculate the force using the formula above:

F = |IP – EP| * A

F = |50 − 25| psi × 5 in²

F = 125 lbf

FAQ

What units are used to measure pressure in the context of calculating force from a pressure difference?

Any consistent pressure units can be used (for example, Pa, psi, bar, or atm). Just ensure the area unit is compatible so the resulting force unit makes sense (e.g., Pa with m² gives N; psi with in² gives lbf).

Can the pressure difference force formula be applied to any fluid?

Yes. The relationship F = |ΔP| · A applies to gases and liquids when you have (approximately) uniform pressures on each side of a surface. If pressure varies over the surface, use an integral over area.

How does the surface area affect the force?

The surface area directly affects the magnitude of the force. A larger surface area subjected to the same pressure difference results in a greater force because force scales linearly with area.