Hydraulic Pressure Calculator
Calculate forces, pressures, and distances in hydraulic systems using Pascal's principle
Calculate Hydraulic System Parameters
Piston 1 (Small/Input)
Piston 2 (Large/Output)
Hydraulic System Results
Pascal's Law: P = F₁/A₁ = F₂/A₂ (Pressure is equal throughout the fluid)
Force Relationship: F₁/F₂ = A₁/A₂ (Force amplification is proportional to area ratio)
Distance Relationship: d₁/d₂ = A₂/A₁ (Distance is inversely proportional to area ratio)
System Analysis
Example: Car Lift Calculation
Hydraulic Car Lift System
Small piston diameter: 3 cm (A₁ = 7.07 cm²)
Large piston diameter: 30 cm (A₂ = 706.9 cm²)
Car weight: 1000 kg (F₂ = 9,807 N)
Required input force: F₁ = F₂ × A₁/A₂ = 98.1 N
Mechanical advantage: 100× force multiplication
Energy Conservation
To lift the car 1 meter, the small piston must move 100 meters
Work input = Work output (conservation of energy)
Force gained = Distance sacrificed
Pascal's Principle
Pressure Transmission
Pressure applied to a confined fluid is transmitted equally in all directions
Force Multiplication
Small force on small area creates large force on large area
Energy Conservation
Work input equals work output (W = F × d)
Common Applications
Car lifts and jacks
Construction machinery
Aircraft control systems
Truck braking systems
Industrial presses
Hydraulic Tips
Larger area ratio = greater force multiplication
Incompressible fluids work best (oils, water)
System must be sealed to maintain pressure
Work output cannot exceed work input
Understanding Hydraulic Pressure Systems
What is Pascal's Principle?
Pascal's principle states that pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid. This principle forms the foundation of hydraulic systems, allowing small forces to be amplified into much larger forces.
How Hydraulic Systems Work
- •Force applied to small piston creates pressure in fluid
- •Pressure transmits equally throughout the system
- •Large piston experiences same pressure over larger area
- •Results in force multiplication proportional to area ratio
Key Formulas
P = F₁/A₁ = F₂/A₂
F₁/F₂ = A₁/A₂
d₁/d₂ = A₂/A₁
W = F × d
- P: Pressure (same throughout system)
- F₁, F₂: Forces on pistons 1 and 2
- A₁, A₂: Areas of pistons 1 and 2
- d₁, d₂: Distances moved by pistons
- W: Work done (energy transfer)
Note: Mechanical advantage = A₂/A₁. A system with 10:1 area ratio provides 10× force multiplication.