Hydraulic Pressure Calculator
Hydraulics turn a small force into a large one by transmitting pressure through a fluid. This calculator works from two exact principles: pressure equals force divided by area, and Pascal's law, which says pressure in a confined fluid is the same everywhere. Enter the input force and the input piston area to get the system pressure in psi and bar, then enter an output piston area to see the multiplied output force of a hydraulic press. The relationships are exact physics for an ideal fluid, with friction and losses set aside.
Hydraulic pressure formula
Pressure (psi) = input force / input area
Pressure (bar) = pressure (psi) / 14.5037738
Output force = pressure * output area
Force ratio = output area / input area
Pressure is force over area. By Pascal's law the same pressure acts on the output piston, so the output force is pressure times output area, equal to the input force scaled by the area ratio.
Hydraulics context
- Pressure equals force divided by area; this defines the pressure unit.
- Pascal's law: pressure in a confined fluid is transmitted equally in all directions.
- A larger output piston multiplies force but moves a shorter distance for the same fluid volume.
- One bar equals 14.5037738 psi by definition.
- The ideal model ignores friction, fluid compressibility, and leakage.
Hydraulic pressure: frequently asked questions
How do I calculate hydraulic pressure?
Pressure equals force divided by area. With force in pounds-force and piston area in square inches, the pressure comes out in pounds per square inch (psi). This is the definition of pressure and applies to any hydraulic cylinder.
What is Pascal's law?
Pascal's law states that pressure applied to a confined fluid is transmitted equally throughout. In a hydraulic press the same pressure acts on both pistons, so the output force equals the input force times the ratio of the output piston area to the input piston area.
How does a hydraulic press multiply force?
Because pressure is equal on both pistons, a larger output piston produces a larger force. Output force equals input force times output area divided by input area. A press with a 10 to 1 area ratio multiplies force tenfold, at the cost of proportionally more travel on the input side.
How do I convert psi to bar?
One bar equals 14.5037738 psi by definition, so psi divided by 14.5037738 gives bar. The calculator reports pressure in both units using this exact conversion factor.
Are these formulas exact?
Yes. Pressure equals force over area and Pascal's law are exact physical relationships, and the unit conversions are defined constants. The calculator assumes an ideal incompressible fluid and ignores friction and losses, which is the standard idealisation.
Official sources
- NASA Glenn Research Center: Pressure definition.
- National Institute of Standards and Technology: Pressure unit definitions (psi, bar).
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.