Pascal Law Calculator

Pascal law states that pressure applied to an enclosed fluid is transmitted undiminished to all parts. This allows a small force on a small piston to create a large force on a large piston.

🔧 Fluid Mechanics📐 F₁/A₁ = F₂/A₂⚡ Hydraulics
Input Force F₁ (N)
Input Area A₁ (m²)
Output Area A₂ (m²)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
PressurePP = F/APa
Force 2F2F2 = F1 × A2/A1N
Area 1A1Input piston aream²
Area 2A2Output piston aream²
Mechanical AdvantageMAMA = A2/A1—

Step-by-Step Examples

Example 1
Car Hydraulic Jack

Input piston A1=2 cm², output A2=200 cm², input force F1=200 N.

  • P = F1/A1 = 200/0.0002 = 1,000,000 Pa
  • F2 = P × A2 = 1,000,000 × 0.02 = 20,000 N
✓ 20,000 N output — lifts a 2-tonne car with 200 N input
Example 2
Hydraulic Brake

Brake pedal applies 300 N to A1=5 cm². Caliper A2=50 cm².

  • F2 = 300 × (50/5) = 300 × 10 = 3,000 N
✓ 3,000 N on brake pads — 10x mechanical advantage
Example 3
Medical Syringe

Syringe A1=1 cm², needle A2=0.01 cm². Force F1=5 N.

  • P = 5/0.0001 = 50,000 Pa
  • F2 = 50,000 × 0.000001 = 0.05 N
✓ 50,000 Pa pressure in needle

Real-World Applications

🚗
Hydraulic Jacks
Pascal law enables car jacks to lift 2 tonnes with hand force through area ratio amplification.
✈️
Aircraft Controls
Hydraulic actuators in aircraft control surfaces use Pascal law to move large surfaces with small cockpit forces.
🏭
Industrial Presses
Stamping and forming machines use Pascal law to generate forces of thousands of tonnes.
🚲
Bicycle Brakes
Hydraulic disc brakes transmit constant pressure through fluid from lever to caliper.

Common Mistakes to Avoid

⚠️
Confusing force and pressure

Pressure is equal everywhere. Force depends on area: F = P × A. Large piston has large area, so large force.

⚠️
Ignoring piston displacement

MA amplifies force but reduces distance: d2 = d1 × A1/A2. Energy is conserved: F1*d1 = F2*d2.

⚠️
Assuming rigid fluid

Fluid must be incompressible (liquids, not gases) for Pascal law to apply without energy loss to compression.

Frequently Asked Questions

Is pressure really equal everywhere in a fluid? ▾
For static fluid, yes (ignoring gravity effects for height differences). Dynamic flow creates pressure differences via Bernoulli equation.
How is energy conserved in a hydraulic system? ▾
Work in = Work out: F1*d1 = F2*d2. A 10x force amplification gives 1/10x displacement.
Why use oil instead of water in hydraulics? ▾
Oil has better lubrication, higher boiling point, lower freezing point, and corrosion protection for metal surfaces.
What is hydraulic fluid pressure rating? ▾
Industrial hydraulics operate at 200-700 bar (20-70 MPa). Aircraft hydraulics at 3000-5000 psi (200-345 bar).
Can Pascal law amplify power? ▾
No. Power = F*v. Force is amplified but velocity is reduced proportionally. Total power is conserved (minus friction losses).
What happens if there is air in a hydraulic system? ▾
Air is compressible, violating Pascal law assumption. Brakes feel spongy, response is delayed, system is less effective.
How does Pascal law apply to blood pressure? ▾
Heart applies pressure to blood. Due to Pascal law, this pressure is transmitted throughout the vascular system (modified by gravity and vessel resistance).
What is hydrostatic paradox? ▾
A small amount of fluid at height can exert enormous force on a large area below, regardless of fluid volume. Pressure depends on height, not total weight of fluid.

Related Physics Calculators

💨 Bernoulli Equation⚖️ Pressure💧 Hydrostatic Pressure⚙️ Mechanical Advantage💧 Flow Rate

Formula Explorer connections

Interpretation: This relationship connects pressure, velocity, density, viscosity, geometry or transport in a fluid system. Assumption: Check whether flow is steady, incompressible, laminar, fully developed or one-dimensional. Reynolds and Mach regimes determine whether simplified formulas are valid.

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