# Piston Force Calculator

URL: https://speedycalculator.com/calculators/physics/piston-force/
Last updated: 2026-10-30

> The piston force calculator finds the push and pull force of a hydraulic or pneumatic cylinder from its bore, rod diameter and operating pressure.

## Inputs

- Bore (piston) diameter D (mm, cm, m, in, µm)
- Rod diameter d (mm, cm, m, in, µm)
- Pressure P (bar, MPa, psi, kPa)

## Results

- Piston area
- Push (extend) force
- Pull (retract) force

## Formula

```
F_push = P·π·D²/4,  F_pull = P·π·(D² − d²)/4
```

## Explanation

Hydraulic cylinders lift diggers, presses and car lifts with immense forces from modest pressures. The force is simply pressure times the piston area – smaller on the retract stroke because the rod takes up part of the area.

### How to use the Piston Force Calculator

- **Bore (piston) diameter D**
- **Rod diameter d**
- **Pressure P**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the cylinder bore, rod diameter and pressure.

### Inputs explained

FieldWhat to enterBore (piston) diameter DUnits: mm, cm, m, in, µmRod diameter dUnits: mm, cm, m, in, µmPressure PUnits: bar, MPa, psi, kPa

### What each result means

- **Piston area** = pi×[Bore (piston) diameter D]^2÷4
- **Push (extend) force** = [Pressure P]×pi×[Bore (piston) diameter D]^2÷4
- **Pull (retract) force** = [Pressure P]×pi×([Bore (piston) diameter D]^2 - [Rod diameter d]^2)÷4

### Example values

How the main result changes when **Bore** changes and everything else stays at the example values above:

Bore (piston) diameter D (mm)Push (extend) force (kN)31.57.793147.2517.53456331.172578.7548.70794.570.138126124.6898

## Worked example

Inputs — Bore (piston) diameter D: 63 mm; Rod diameter d: 36 mm; Pressure P: 100 bar.

Results — Piston area = 31.1725 cm²; **Push (extend) force = 31.17245 kN**; Pull (retract) force = 20.99369 kN.

## Key terms

- **Annulus area**: Piston area minus rod area.

## FAQ

**Why is the pull force smaller?**
The rod reduces the effective area on the retract side.

**What pressure do hydraulic systems use?**
Typically 100–350 bar; pneumatic systems 6–10 bar.

**Do I need a safety factor?**
Yes – account for friction and pressure losses (often 10–25%).

**How does area scale with diameter?**
With its square – doubling the bore quadruples the force.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)