How to calculate hydraulic cylinder bore size？

The cylinder bore and rod diameter can be calculated from a hydraulic calculator once the pressure is known.
After choosing a good design pressure, that is, P is known, the load size （F） is also calculable; being calculated according to the formula of the force area, and then according to the force area to calculate the hydraulic cylinder bore.

Thrust F1 = A1 * P1 *β
A1: Push side piston pressurized area cm²
A2: Pull side piston pressurized area cm²
D: Hydraulic cylinder bore diameter, i.e. piston diameter cm
d: piston rod diameter cm
P1: Push side acting pressure kgf/cm²
P2: Pull-side operating pressure kgf/cm²
β: load ratio

Pull F2 = A2 * P2 *β
A1= π/4D²=0.785D²
A2=π/4（D²-d²）=0.785（D²- d ²）

1. The actual output of the hydraulic cylinder is lower than the theoretical output
2. Load ratio β value, in the case of small inertia force take 80%, inertia force occasions take 6

Example: 
Set the hydraulic cylinder force of 1000 kg, the operating pressure of 70kgf/cm², what is the hydraulic cylinder bore size？

F1=1000kg
P1=70kgf/cm² 
β=0.8
F1=A1*P1*β
A1=F1/（β*P1）=1000/（70*0.8）=17.86cm²
A1= π/4D²=0.785D²
D²=17.86/0.785=22.75cm²
D=4.8cm=48mm

The bore diameter of the cylinder is 50 mm