The main formulas used in hydraulic cylinder calculations are:

- Extend Force: \(F_e = P \times A_b\)
- Retract Force: \(F_r = P \times (A_b - A_r)\)
- Cylinder Volume: \(V = A_b \times L\)

Where:

- \(F_e\): Extend force (lbs)
- \(F_r\): Retract force (lbs)
- \(P\): Operating pressure (psi)
- \(A_b\): Bore area (sq in)
- \(A_r\): Rod area (sq in)
- \(V\): Cylinder volume (cubic inches)
- \(L\): Stroke length (inches)

- Calculate the bore area: \(A_b = \pi \times (D_b / 2)^2\)
- Calculate the rod area: \(A_r = \pi \times (D_r / 2)^2\)
- Calculate the extend force: \(F_e = P \times A_b\)
- Calculate the retract force: \(F_r = P \times (A_b - A_r)\)
- Calculate the cylinder volume: \(V = A_b \times L\)

Let's calculate for a cylinder with 4" bore diameter, 2" rod diameter, 12" stroke length, and 1000 psi operating pressure:

- Bore area: \(A_b = \pi \times (4 / 2)^2 = 12.57\) sq in
- Rod area: \(A_r = \pi \times (2 / 2)^2 = 3.14\) sq in
- Extend force: \(F_e = 1000 \times 12.57 = 12,570\) lbs
- Retract force: \(F_r = 1000 \times (12.57 - 3.14) = 9,430\) lbs
- Cylinder volume: \(V = 12.57 \times 12 = 150.84\) cubic inches

This calculator helps engineers and technicians quickly determine the performance characteristics of hydraulic cylinders, which is crucial for designing and troubleshooting hydraulic systems.

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