Hydraulic Force vs. Pressure and Cylinder Size

The force produced on the rod side (1) of a double acting hydraulic piston - can be expressed as

F₁ = P₁ (π (d₂² - d₁²) / 4)                                    (1)

where

F₁ = rod force (lb, N)

d₁ = rod diameter (in, mm)

d₂= piston diameter (in, mm)

P₁ = pressure in the cylinder on the rod side (psi, N/mm²)

• 1 bar = 105 N/m²= 0.1 Nm/mm²

The force produced on the opposite of rod side (2) - can be expressed as

F₂= P₂ (π d₂² / 4)                  (2)

where

F₂ = rod force (lb, N)

P₂ = pressure in the cylinder (opposite rod) ( psi, N/mm²)

Hydraulic Force Calculator

Imperial Units

Pressure acting on rod side

Piston diameter - d₂(in)

Rod diameter - d₁ (in)

Cylinder pressure - P₁ (psi)

Pressure acting on opposite of rod side

Piston diameter - d₂(in)

Cylinder pressure - d₂(psi)

Metric Units

Pressure acting on rod side

Piston diameter - d₂(mm)

Rod diameter - d₁ (mm)

Cylinder pressure - P₁ (bar)

Pressure acting on opposite of rod side

Piston diameter - d₂(mm)

Cylinder pressure - d₂(bar)

Related Mobile Apps from The Engineering ToolBox

• Hydraulic Force Calculator App

- free apps for offline use on mobile devices.

Rod Force F₂ diagram

- when pressure act on opposite side of rod.

Imperial Units

Metric Units

• 1 psi (lb/in²) = 144 psf (lb_f/ft²) = 6,894.8 Pa (N/m²) = 6.895×10^-3 N/mm² = 6.895×10^-2 bar
• 1 N/m²= 1 Pa = 1.4504×10^-4 lb/in²= 1×10^-5 bar = 4.03×10^-3 in water = 0.336×10^-3 ft water = 0.1024 mm water = 0.295×10^-3 in mercury = 7.55×10^-3 mm mercury = 0.1024 kg/m²= 0.993×10^-5atm
• 1 lb_f (Pound force) = 4.44822 N = 0.4536 kp
• 1 N (Newton) = 0.1020 kp = 7.233 pdl = 7.233/32.174 lb_f = 0.2248 lb_f = 1 (kg m)/s²= 10⁵ dyne = 1/9.80665 kg_f
• 1 in (inch) = 25.4 mm
• 1 m (meter) = 39.37 in = 100 cm = 1000 mm

Rod Force F₁ diagram

- when pressure act on the same side of the rod.

Imperial Units