Hydraulic Pressure Calculator

Created by Gabriela Diaz
Last updated: Nov 05, 2022

With this hydraulic pressure calculator, you can study the force and area on both pistons of a hydraulic press.

Did you know that a hydraulic system powers the elevators of the Eiffel Tower? Or that hydraulic systems are also used in car and aircraft brakes or even for some doors' hinges? The fact is that this type of technology surrounds us. Pascal's law, or Pascal's principle, is the foundation of this technology. Keep reading to learn:

  • What Pascal's principle is about;
  • The hydraulic pressure formula or Pascal's law formula;
  • How to calculate the hydraulic pressure in a basic hydraulic system.

💡 Aside from hydraulic elevators, there're also traction elevators. This ones work with pulley systems, check our pulley calculator to learn about how pulley systems!

What is Pascal's principle?

Hydraulic systems use an incompressible fluid to transmit forces from one point to another within the fluid — usually petroleum-based or water-based fluids. The main advantage of this technology is that it allows the amplification of a small force into a larger one, i.e., consider a hydraulic vehicle lift, the kind that is used at car service centers. With this machine is possible to elevate a heavy car by employing a relatively small force.

We can also encounter this technology in a variety of applications, including automotive brakes, construction equipment, hydraulic jacks, robotics, aircraft landing gear, hydraulic presses, and more.

All of this is based on Pascals's principle or Pascal's law, which states that:

When there is an increase in pressure at any point in a confined fluid, this pressure is transmitted equally and undiminished to all points in the fluid, resulting in an equal increase at every other point in the container.

We can mathematically represent this as:

Δp=ρgΔh\small \Delta p = \rho g \Delta h


  • Δp\Delta p – Hydrostatic pressure difference between two points in a column of liquid;
  • ρ\rho – Density of the fluid;
  • gg – Gravitational acceleration; and
  • Δh\Delta h – Difference in height between two points in a column of liquid.

🙋 Learn more about hydrostatic pressure and its applications with the hydrostatic pressure calculator and about differential pressure with the differential pressure calculator.

How to calculate the hydraulic pressure - Hydraulic pressure formula

From the previous, we can see that if we were to pick any two points in a particular hydraulic system, the pressure would be the same at both points. We can express this as:

P1=P2\small P_1 = P_2

If we recall from the pressure definition (check the pressure calculator for more), we know that this one is equal to the ratio between the exerted force and the area at which it is applied, then:

F1A1=F2A2\small \cfrac{F_1}{A_1} = \cfrac{F_2}{A_2}

This is known as the hydraulic pressure formula or Pascal's law formula.

Two pistons hydraulic system with areas one and two, and forces one and two.
Source: Wikipedia.org


  • F1F_1 – Force applied to the first piston;
  • F2F_2 – Force applied to the second piston;
  • A1A_1 – Area of the first piston; and
  • A2A_2 – Area of the second piston.

Then, if we'd like to determine the required force F1F_1 that we'd need to apply in order to raise an object on known weight F2F_2 placed over the area two A2A_2, we simply rearrange the last expression into:

F1=F2A1A2\small F_1 = F_2 \cfrac{A_1}{A_2}

Using the hydraulic pressure calculator

You can calculate the area and force for both pistons in a hydraulic press with this hydraulic pressure calculator. Let's see how to use this tool:

  1. In the First piston section, enter the Area and Force applied.
  2. In the case that you know the dimensions of the other piston, enter the Area of the Second piston.
  3. The calculator will show you the required Force to equate the force applied on the first piston.
  4. On the Advanced mode of this calculator, you can also determine the traveled distance of the pistons Lifting distance and the Work done.

💡 Did you know that our tools work in any order? This means that you could also use this tool to get the other values. Give it a try!

Gabriela Diaz
First piston
Second piston
Liquid pressure
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