Hydraulic Pressure Force Calculator
Hydraulic systems use Pascal's principle, which states that pressure applied to a confined fluid is transmitted equally in all directions. The fundamental relationship is F = P x A: force (N) equals pressure (Pa) multiplied by area (m^2). This calculator solves for force, pressure, or area given the other two values. The same principle is used in hydraulic jacks, brakes, presses, and actuators in industrial machinery. It explains how a small force on a small piston can create a large force on a large piston when both are connected by a fluid.
Pascal's principle formula
F = P × A
F is force in Newtons (N), P is pressure in Pascals (Pa = N/m^2), A is area in m^2. Rearranges to P = F/A and A = F/P. For hydraulic advantage: F(out)/F(in) = A(out)/A(in) at constant pressure.
Hydraulic advantage example
- Input piston area: 0.001 m^2 (10 cm^2), input force: 100 N.
- Pressure: P = 100 / 0.001 = 100,000 Pa.
- Output piston area: 0.1 m^2 (1,000 cm^2).
- Output force: F = 100,000 x 0.1 = 10,000 N (100x amplification).
Frequently asked questions
What is Pascal's principle?
Pascal's principle states that pressure applied to a confined fluid is transmitted undiminished in all directions throughout the fluid and to the walls of the container. This is the basis for hydraulic systems, which can amplify force.
What is the formula for hydraulic force?
F = P x A, where F is force in Newtons (N), P is pressure in Pascals (Pa = N/m^2), and A is area in square meters (m^2). A hydraulic system can multiply force: if F1/A1 = F2/A2 = P, then a small force on a small piston creates a large force on a large piston.
What units should I use?
SI units: pressure in Pascals (Pa) or kilopascals (kPa = 1,000 Pa), area in m^2, and force in Newtons (N). To convert psi to Pa, multiply by 6,894.76. To convert from N to pounds-force, divide by 4.44822.
How does a hydraulic jack work?
A hydraulic jack uses Pascal's principle. A small force on a small-area input piston creates pressure P = F1/A1. That same pressure acts on a large-area output piston: F2 = P x A2. The mechanical advantage is F2/F1 = A2/A1.
What is hydrostatic pressure?
Hydrostatic pressure at depth h in a fluid of density rho is P = rho g h. This is different from applied pressure; it is the pressure due to the weight of fluid above a point. For water at 10 m depth: P = 1,000 x 9.807 x 10 = 98,070 Pa (about 1 atm extra).
Official sources
- NIST: NIST Standard Atmosphere.
- OpenStax University Physics: 14.3 Pascal's Principle and Hydraulics.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.