Hydraulic Pressure Formula (Pascal's Law)
Calculate hydraulic press force multiplication using Pascal's law.
F1/A1 = F2/A2 with worked examples.
The Formula
Pascal's law states that pressure applied to a confined fluid is transmitted equally in all directions. This principle is the foundation of all hydraulic systems.
In a hydraulic press, a small force on a small piston creates the same pressure as a large force on a large piston. This allows you to multiply force.
Variables
| Symbol | Meaning |
|---|---|
| F₁ | Force applied to the small piston (Newtons or lbs) |
| A₁ | Area of the small piston (m² or in²) |
| F₂ | Force produced by the large piston (Newtons or lbs) |
| A₂ | Area of the large piston (m² or in²) |
Rearranged Forms
| Solve For | Formula |
|---|---|
| Output force (F₂) | F₂ = F₁ × (A₂ / A₁) |
| Input force needed (F₁) | F₁ = F₂ × (A₁ / A₂) |
| Mechanical advantage | MA = A₂ / A₁ = F₂ / F₁ |
Example 1 — Hydraulic Car Lift
A hydraulic car lift has a small piston (area = 10 cm²) and a large piston (area = 500 cm²). You push with 200 N on the small piston.
F₂ = F₁ × (A₂ / A₁)
F₂ = 200 × (500 / 10)
F₂ = 10,000 N (enough to lift a small car)
Example 2 — Hydraulic Brake System
A brake pedal applies 50 N to a master cylinder (area = 2 cm²). The brake caliper piston has an area of 20 cm².
F₂ = 50 × (20 / 2)
F₂ = 500 N (10× force multiplication at each wheel)
Example 3 — Imperial Units
A hydraulic press has pistons of 2 in² and 50 in². You apply 100 lbs of force.
F₂ = 100 × (50 / 2)
F₂ = 2,500 lbs of output force
The Trade-Off: Force vs. Distance
Hydraulic systems multiply force but NOT energy. The small piston must travel a greater distance than the large piston moves.
If you multiply force by 50×, the large piston moves only 1/50th the distance. This is why hydraulic jacks require many pump strokes to lift something a few inches.
When to Use It
- Designing hydraulic presses and lifts
- Understanding car brake systems
- Sizing hydraulic cylinders for construction equipment
- Calculating force in hydraulic jacks
- Engineering heavy machinery (excavators, forklifts, airplane landing gear)
Real-World Applications
- Car brakes: Multiply foot pedal force to stop a 2-ton vehicle
- Hydraulic car lifts: One person can lift a car with a hand pump
- Construction excavators: Convert small pump pressure into massive digging force
- Aircraft flight controls: Allow pilots to move large control surfaces with manageable effort
- Hydraulic presses: Crush, bend, or stamp metal parts in manufacturing