Hydraulic Pressure Calculator
Enter the force and area for either piston to calculate the hydraulic pressure and the output force on the other piston. The calculator uses Pascal's law - pressure applied to a confined fluid is transmitted equally in all directions - to find the force multiplication ratio of hydraulic systems like car lifts, jacks, and brakes. Switch between metric and imperial units, choose what to solve for, and the results update instantly.
What is hydraulic pressure and Pascal's law?
Hydraulic pressure is the force per unit area exerted by a fluid in a closed system. Pascal's law, stated by French mathematician Blaise Pascal in 1647, says that pressure applied to a confined, incompressible fluid is transmitted undiminished in all directions throughout the fluid. This is the principle that makes hydraulic systems so useful: a small force applied over a small area can produce a very large force at a larger area, because the pressure is the same everywhere in the fluid. The formula is p = F/A, where p is pressure (in Pa or psi), F is force (in N or lbf), and A is the cross-sectional area of the piston (in m^2 or in^2). For a two-piston system: p = F1/A1 = F2/A2.
Mechanical advantage in hydraulic systems
The ratio of the output piston area to the input piston area is the mechanical advantage (MA) of the system: MA = A2/A1 = F2/F1. A car hydraulic jack with a small input cylinder of 1 cm^2 and a large output cylinder of 100 cm^2 has a mechanical advantage of 100, meaning a person pushing with 200 N (about 45 lbf) on the small piston creates 20,000 N (about 4,500 lbf) at the output. There is no free lunch: the output piston moves a proportionally shorter distance. By conservation of energy, the volume of fluid displaced is the same on both sides (A1 x d1 = A2 x d2), so the output piston moves 100 times less than the input piston in the above example. Work in equals work out (ignoring friction losses).
How to use this calculator
Choose whether you want to solve for the output force, input force, system pressure, or one of the piston areas. Enter the known values and the result updates instantly. For the most common case (finding what force you can lift), select 'Output force (F2)', then enter the input force you can apply, the area of the small input piston, and the area of the large output piston. The calculator also computes how far the output piston moves if you provide the input piston travel, and the total work done. Switch between metric (Newtons and cm^2) and imperial (pound-force and in^2) units at any time. Pressure is shown in Pa, kPa, or MPa (metric) and psi (imperial).
Real-world losses and system efficiency
This calculator assumes a perfect, lossless hydraulic system. In practice, some efficiency is lost to seal friction, fluid compressibility, pipe resistance, and leakage. Typical hydraulic system efficiency ranges from 80% to 95% for well-maintained industrial systems, and can be lower in older or poorly fitted systems. To account for these losses, multiply the theoretical output force by the efficiency factor. For example, if your calculation gives 10,000 N but your system is 90% efficient, the actual output force will be about 9,000 N. Always add a safety factor when designing hydraulic systems for lifting or safety-critical applications.
Typical hydraulic system pressures by application
| Application | Typical pressure | Mechanical advantage range |
|---|---|---|
| Hydraulic jack (floor jack) | 5,000-10,000 psi (34-69 MPa) | 10:1 to 100:1 |
| Automotive power steering | 1,000-1,500 psi (7-10 MPa) | 20:1 to 80:1 |
| Automotive brake system | 1,000-3,000 psi (7-21 MPa) | 5:1 to 40:1 |
| Industrial hydraulic press | 2,000-5,000 psi (14-34 MPa) | 50:1 to 500:1 |
| Construction equipment (excavator) | 3,000-5,000 psi (21-34 MPa) | 30:1 to 200:1 |
| Aircraft landing gear | 3,000-5,000 psi (21-34 MPa) | 100:1 to 1000:1 |
| Dental chair / barber chair | 100-200 psi (0.7-1.4 MPa) | 5:1 to 20:1 |
| Bicycle hydraulic disc brake | 50-150 psi (0.3-1.0 MPa) | 3:1 to 10:1 |
Common operating pressure ranges for hydraulic systems. Industrial and mobile equipment often exceeds these typical values.
Frequently asked questions
What is Pascal's law in hydraulics?
Pascal's law states that pressure applied to a confined fluid is transmitted undiminished to all parts of the fluid and the walls of the container. In a hydraulic system with two pistons, this means the pressure at piston 1 equals the pressure at piston 2 (F1/A1 = F2/A2). This principle allows a small force on a small piston to produce a large force on a larger piston, which is the basis of hydraulic jacks, car lifts, brake systems, and construction equipment.
How do I calculate hydraulic pressure?
Hydraulic pressure is calculated using p = F/A, where F is the applied force (in Newtons or pound-force) and A is the cross-sectional area of the piston (in m^2 or in^2). For example, a force of 100 N applied to a piston with an area of 10 cm^2 (0.001 m^2) creates a pressure of 100/0.001 = 100,000 Pa = 100 kPa = 14.5 psi. This same pressure then acts on any connected piston to produce an output force equal to the pressure multiplied by that piston's area.
What is the mechanical advantage of a hydraulic system?
Mechanical advantage (MA) is the ratio of output force to input force, which equals the ratio of the output piston area to the input piston area: MA = F2/F1 = A2/A1. An MA of 10 means a 100 N push on the input produces 1,000 N at the output. The trade-off is that the output piston moves 10 times less distance than the input piston, so the total work (force times distance) is the same on both sides, as required by conservation of energy.
Why does the output piston move less than the input piston?
By conservation of energy, the volume of fluid displaced on both sides must be equal: A1 x d1 = A2 x d2. If the output piston is 5 times larger in area than the input piston, it moves 5 times less distance. This is the fundamental trade-off in hydraulics: you can multiply force, but not energy. The same amount of work (force x distance) enters and leaves the system.
What units are used for hydraulic pressure?
In SI (metric) units, pressure is measured in Pascals (Pa), kilopascals (kPa = 1,000 Pa), or megapascals (MPa = 1,000,000 Pa). In imperial units, the common unit is pounds per square inch (psi). Common conversions: 1 psi = 6,894.76 Pa = 6.895 kPa; 1 MPa = 145.038 psi; 1 bar = 100,000 Pa = 14.5 psi. Industrial hydraulic systems typically operate at 1,000 to 5,000 psi (7 to 34 MPa).
Can I use this calculator for hydraulic cylinder force?
Yes. To find the push force of a hydraulic cylinder, enter the system pressure and the bore (internal cylinder) area, and solve for output force. The bore area of a cylinder with diameter d is A = pi x (d/2)^2. For a pull (retract) stroke, the rod reduces the effective area: A_pull = pi x ((d_bore/2)^2 - (d_rod/2)^2). This calculator works for any linear hydraulic application where the piston area and pressure are known.