# Hydraulic Cylinder Calculations

### Cylinder Blind End Area (in square inches)

PI X (Cylinder Radius) ^2
What is the area of a 6" diameter cylinder?

Diameter = 6"
Radius is 1/2 of diameter = 3"
Radius ^2 = 3" X 3" = 9"
PI X (Cylinder Radius )^2 = 3.14 X (3)^2 = 3.14 X 9 = 28.26 square inches

### Cylinder Rod End Area (in square inches)

Blind End Area - Rod Area
What is the rod end area of a 6" diameter cylinder which has a 3" diameter rod?

Cylinder Blind End Area = 28.26 square inches
Rod Diameter = 3"
Radius is 1/2 of rod diameter = 1.5"
Radius ^2 = 1.5" X 1.5" = 2.25"
PI X Radius ^2 = 3.14 X 2.25 = 7.07 square inches
Blind End Area - Rod Area = 28.26 - 7.07 = 21.19 square inches

### Cylinder Output Force (in Pounds)

Pressure (in PSI) X Cylinder Area
What is the push force of a 6" diameter cylinder operating at 2,500 PSI?

Cylinder Blind End Area = 28.26 square inches
Pressure = 2,500 psi
Pressure X Cylinder Area = 2,500 X 28.26 = 70,650 pounds

What is the pull force of a 6" diameter cylinder with a 3" diameter rod operating at 2,500 PSI?

Cylinder Rod End Area = 21.19 square inches
Pressure = 2,500 psi
Pressure X Cylinder Area = 2,500 X 21.19 = 52,975 pounds

### Fluid Pressure in PSI Required to Lift Load (in PSI)

Pounds of Force Needed / Cylinder Area
What pressure is needed to develop 50,000 pounds of push force from a 6" diameter cylinder?

Pounds of Force = 50,000 pounds
Cylinder Blind End Area = 28.26 square inches
Pounds of Force Needed / Cylinder Area = 50,000 / 28.26 = 1,769.29 PSI

What pressure is needed to develop 50,000 pounds of pull force from a 6" diameter cylinder which has a 3" diameter rod?

Pounds of Force = 50,000 pounds
Cylinder Rod End Area = 21.19 square inches
Pounds of Force Needed / Cylinder Area = 50,000 / 21.19 = 2,359.60 PSI

### Cylinder Speed (in inches per second)

(231 X GPM) / (60 X Net Cylinder Area)
How fast will a 6" diameter cylinder with a 3" diameter rod extend with 15 gpm input?

GPM = 6
Net Cylinder Area = 28.26 square inches
(231 X GPM) / (60 X Net Cylinder Area) = (231 X 15) / (60 x 28.26) = 2.04 inches per second

How fast will it retract?

Net Cylinder Area = 21.19 square inches
(231 X GPM) / (60 X Net Cylinder Area) = (231 X 15) / (60 x 21.19) = 2.73 inches per second

### GPM of Flow Needed for Cylinder Speed

Cylinder Area X Stroke Length in Inches / 231 X 60 / Time in seconds for one stroke
How many GPM are needed to extend a 6" diameter cylinder 8 inches in 10 seconds?

Cylinder Area = 28.26 square inches
Stroke Length = 8 inches
Time for 1 stroke = 10 seconds
Area X Length / 231 X 60 / Time = 28.26 X 8 / 231 X 60 / 10 = 5.88 gpm
If the cylinder has a 3" diameter rod, how many gpm is needed to retract 8 inches in 10 seconds?
Cylinder Area = 21.19 square inches
Stroke Length = 8 inches
Time for 1 stroke = 10 seconds
Area X Length / 231 X 60 / Time = 21.19 X 8 / 231 X 60 / 10 = 4.40 gpm

### Cylinder Blind End Output (GPM)

Blind End Area / Rod End Area X GPM In
How many GPM come out the blind end of a 6" diameter cylinder with a 3" diameter rod when there is 15 gallons per minute put in the rod end?

Cylinder Blind End Area =28.26 square inches
Cylinder Rod End Area = 21.19 square inches
GPM Input = 15 gpm
Blind End Area / Rod End Area X GPM In = 28.26 / 21.19 * 15 = 20 gpm
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