Hydraulic Calculator

Calculate hydraulic cylinder force (Pascal's law)

Hydraulic Force

F = P x A

Formula
F = P x pi x (d/2)^2

What Is Hydraulics?

Hydraulics is the science of using pressurized liquid to transmit force and motion. A hydraulic system converts mechanical energy into fluid pressure, then uses that pressure to do work at another location. The key principle is Pascal's Law: pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid.

Hydraulic systems are everywhere in heavy machinery: excavators, forklifts, car lifts, aircraft landing gear, and brake systems. They offer a major advantage over mechanical systems — a small input force on a small piston can produce a very large output force on a large piston, with the pressure being the connecting link between them.

How to Use This Calculator

  1. Select what you want to calculate: Force (F), Pressure (P), or Piston Area (A).
  2. Enter the two known values with their units (newtons, pascals, or square meters).
  3. Click Calculate to see the result instantly.
  4. Use Reset to clear the fields and start over.

Formula & Explanation

P = F / A F = P × A A = F / P Pascal's Law: F2/F1 = A2/A1 Mechanical advantage = A2 / A1

P = Pressure (Pa), F = Force (N), A = Piston area (m²). For a two-piston system: the force multiplication equals the area ratio. A piston 10× larger in area generates 10× more force at the same pressure.

Worked Examples

Example 1 — Car Hydraulic Lift

A lift uses 150 bar (15,000,000 Pa) pressure on a 0.025 m² piston. F = P × A = 15,000,000 × 0.025 = 375,000 N = 375 kN (can lift ~38 tonnes).

Example 2 — Force Multiplication

Input piston: area = 0.001 m², force = 100 N. Pressure = 100 / 0.001 = 100,000 Pa. Output piston: area = 0.05 m². Output force = 100,000 × 0.05 = 5,000 N. Mechanical advantage = 50.

Example 3 — Hydraulic Brake

Master cylinder piston: 0.0003 m², pedal force = 300 N. Pressure = 300 / 0.0003 = 1,000,000 Pa = 10 bar. Caliper piston: 0.002 m². Brake force = 1,000,000 × 0.002 = 2,000 N per caliper.

Frequently Asked Questions

What is Pascal's Law?▾
Pascal's Law states that pressure applied to an enclosed, static fluid is transmitted undiminished to every part of the fluid and to the walls of the container. This allows a small force on a small area to create the same pressure that acts on a much larger area, producing a proportionally larger force.
What is the difference between hydraulics and pneumatics?▾
Hydraulics uses incompressible liquid (usually oil or water) as the working fluid. Pneumatics uses compressible gas (usually air). Hydraulic systems provide much higher force and more precise position control; pneumatic systems are faster, cleaner, and simpler but limited in force output.
Why is hydraulic fluid usually oil?▾
Hydraulic oil serves multiple functions: transmitting pressure, lubricating moving parts, removing heat, and preventing corrosion and rust. Compared to water, oil has better lubrication, does not freeze at moderate temperatures, and does not corrode metal components.
What causes hydraulic system failure?▾
Common causes: contaminated fluid (particles damage seals and valves), air entrainment (causes cavitation and spongy response), overheating (degrades fluid and seals), seal leakage, and excessive pressure spikes. Regular fluid changes and filtration maintenance prevent most failures.
How do I calculate the cylinder bore size I need?▾
First determine the required force and available pressure. Area = Force / Pressure. Then bore diameter = 2 × √(Area / π). For example, to generate 50,000 N at 200 bar (20,000,000 Pa): Area = 50,000 / 20,000,000 = 0.0025 m². Bore = 2 × √(0.0025/π) ≈ 56.4 mm.