Pressure–Force–Area (Rearrange)

GCSE Measures pressure triangle
Practice this formula All formulas
\( p=\tfrac{F}{A},\quad F=pA,\quad A=\tfrac{F}{p} \)

Statement

The relationship between pressure, force, and area is given by:

\[ p = \frac{F}{A}, \quad F = pA, \quad A = \frac{F}{p} \]

Why it’s true

  • Pressure is defined as force per unit area.
  • Rearranging gives force = pressure × area, or area = force ÷ pressure.
  • This allows switching between the three depending on which quantities are known.

Recipe (how to use it)

  1. If finding pressure: divide force by area.
  2. If finding force: multiply pressure by area.
  3. If finding area: divide force by pressure.

Spotting it

This formula is used in physics/mechanics problems involving surfaces, hydraulics, or weight spread over an area.

Common pairings

  • Units: pressure in Pascals (Pa), force in Newtons (N), area in m².
  • Applied in fluids, gases, solids contact problems.

Mini examples

  1. Given: Force=200 N, Area=4 m².
    Answer: \(p=200/4=50\) Pa.
  2. Given: Pressure=100 Pa, Area=2 m².
    Answer: \(F=100*2=200\) N.

Pitfalls

  • Forgetting to convert area into square metres (e.g., cm² → m²).
  • Confusing pressure with force (they are not the same).

Exam strategy

  • Always write the correct rearranged version of the formula first.
  • Check units: pressure must be in Pascals (N/m²).
  • Draw a triangle memory aid: F on top, P and A at the bottom corners.

Summary

The formula triangle links pressure, force, and area: \(p=F/A\), \(F=pA\), \(A=F/p\). It is fundamental in mechanics and physics problem-solving.