Pascal's Law
Pressure applied to a confined fluid transmits equally in all directions.
Formula
Variables
Example
A hydraulic jack lets a small force on a small piston lift a car on a large piston.
How it works
Pascal’s Law says that if a fluid is trapped in a sealed container, any pressure added at one point is passed through the fluid without being lost, so the pressure is the same at all connected points. Since pressure is force per unit area, this means a small force on a small area can produce a larger force on a larger area while keeping the pressure equal. The law works because liquids are nearly incompressible, so the fluid can only transmit the applied pressure rather than absorb it.
When to use it
Use this formula when analyzing hydraulic systems such as brakes, presses, lifts, and jacks. It is also useful for comparing forces on different piston sizes in any enclosed fluid system.
Worked example, step by step
A hydraulic press has a small piston with area A1 = 0.020 m^2 and a large piston with area A2 = 0.50 m^2. A force of F1 = 120 N is applied to the small piston. Using Pascal’s Law: F1 / A1 = F2 / A2 Substitute the values: 120 / 0.020 = F2 / 0.50 Compute the pressure: 120 ÷ 0.020 = 6000 Pa So, F2 / 0.50 = 6000 Multiply both sides by 0.50: F2 = 6000 × 0.50 = 3000 N Final answer: the large piston exerts 3000 N.
Common mistakes to avoid
- Forgetting that the fluid must be confined in a closed system
- Using the wrong area units, such as mixing cm^2 with m^2
- Assuming the force stays the same instead of the pressure staying the same
Did You Know?
Pascal's law lets a car's tiny brake pedal generate enough force to stop two tons — hydraulics multiply force.
Share this formula
More in Physics Laws & Theorems
View allNewton's First Law (Inertia)
BasicAn object stays at rest or in uniform motion unless acted on by a net force.
Newton's Second Law
BasicNet force equals mass times acceleration (rate of change of momentum).
Newton's Third Law
BasicFor every action there is an equal and opposite reaction.
Conservation of Momentum
IntermediateTotal momentum of an isolated system stays constant.
Conservation of Energy
BasicEnergy cannot be created or destroyed, only transformed.
Archimedes' Principle
IntermediateBuoyant force equals the weight of fluid displaced.