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MechDatum

Hydraulic cylinder force speed calculation

Standard symbols

Section titled “Standard symbols”
Symbol Description Units
d₂ Piston diameter mm / in
d₁ Rod diameter mm / in
A₂ Effective area on piston side (thrust) mm² / in²
A₁ Annular area on rod side (traction) mm² / in²
P Working pressure bar / psi
F₂ Thrust force (extension) N / lbf
F₁ Traction force (retraction) N / lbf
Q Fluid flow rate L/min / gpm
v Linear velocity of rod m/s / in/s

Calculation formulas

Section titled “Calculation formulas”

Thrust force (piston side, extension):

F₂ = P · A₂ = P · (π · d₂² / 4)

Traction force (rod side, retraction):

F₁ = P · A₁ = P · (π · (d₂² − d₁²) / 4)

Forward or return velocity:

v (m/s) = Q (m³/s) / A (m²)
Imperial system: v (in/min) = 231 · Q (gpm) / A (in²)

Component selection tables

Section titled “Component selection tables”

The following tables show typical forces and velocities for double-acting cylinders with single rod, based on bore diameter, pressure, and flow rate. Values assume 100% efficiency (no friction). For actual calculations, add a friction loss factor of 5–10%.

Thrust and traction forces

Section titled “Thrust and traction forces”
Piston diameter
(mm / in)		 Rod diameter
(mm / in)		 Piston area
(mm² / in²)		 Annular area
(mm² / in²)		 Thrust force at 100 bar / 1450 psi
(kN / lbf)		 Traction force at 100 bar / 1450 psi
(kN / lbf)		 Thrust force at 200 bar / 2900 psi
(kN / lbf)		 Traction force at 200 bar / 2900 psi
(kN / lbf)
25 / 0.98 12 / 0.47 491 / 0.76 333 / 0.52 4.91 / 1100 3.33 / 750 9.82 / 2210 6.66 / 1500
32 / 1.26 14 / 0.55 804 / 1.25 563 / 0.87 8.04 / 1810 5.63 / 1270 16.1 / 3620 11.3 / 2540
40 / 1.57 18 / 0.71 1257 / 1.95 940 / 1.46 12.6 / 2830 9.40 / 2110 25.1 / 5650 18.8 / 4230
50 / 1.97 22 / 0.87 1963 / 3.04 1441 / 2.23 19.6 / 4410 14.4 / 3240 39.3 / 8830 28.8 / 6480
63 / 2.48 28 / 1.10 3117 / 4.83 2223 / 3.45 31.2 / 7010 22.2 / 5000 62.3 / 14000 44.5 / 10000
80 / 3.15 36 / 1.42 5027 / 7.79 3682 / 5.71 50.3 / 11300 36.8 / 8270 101 / 22600 73.6 / 16500
100 / 3.94 45 / 1.77 7854 / 12.2 5661 / 8.78 78.5 / 17700 56.6 / 12700 157 / 35300 113 / 25400
125 / 4.92 56 / 2.20 12272 / 19.0 8621 / 13.4 123 / 27600 86.2 / 19400 245 / 55200 172 / 38700
160 / 6.30 70 / 2.76 20106 / 31.2 14137 / 21.9 201 / 45200 141 / 31700 402 / 90400 283 / 63600
200 / 7.87 90 / 3.54 31416 / 48.7 22235 / 34.5 314 / 70600 222 / 49900 628 / 141000 445 / 100000

Rod velocities

Section titled “Rod velocities”
Piston diameter
(mm / in)		 Piston area
(mm² / in²)		 Flow rate 10 L/min / 2.64 gpm
speed (m/s / in/s)		 Flow rate 30 L/min / 7.93 gpm
speed (m/s / in/s)		 Flow rate 50 L/min / 13.2 gpm
speed (m/s / in/s)
25 / 0.98 491 / 0.76 0.339 / 13.4 1.02 / 40.1 1.70 / 66.8
32 / 1.26 804 / 1.25 0.207 / 8.14 0.621 / 24.4 1.04 / 40.7
40 / 1.57 1257 / 1.95 0.133 / 5.22 0.398 / 15.6 0.663 / 26.1
50 / 1.97 1963 / 3.04 0.085 / 3.34 0.255 / 10.0 0.425 / 16.7
63 / 2.48 3117 / 4.83 0.053 / 2.10 0.160 / 6.31 0.267 / 10.5
80 / 3.15 5027 / 7.79 0.033 / 1.30 0.099 / 3.90 0.166 / 6.50
100 / 3.94 7854 / 12.2 0.021 / 0.83 0.064 / 2.50 0.106 / 4.17
125 / 4.92 12272 / 19.0 0.014 / 0.54 0.041 / 1.61 0.068 / 2.69
160 / 6.30 20106 / 31.2 0.008 / 0.33 0.025 / 0.99 0.042 / 1.65
200 / 7.87 31416 / 48.7 0.005 / 0.21 0.016 / 0.63 0.027 / 1.05

Standard working pressures

Section titled “Standard working pressures”

Working pressures in hydraulic systems are typically classified according to the application type. The most common design values are shown below.

Pressure class Typical range (bar / psi) Common applications
Low pressure 10 – 70 bar / 145 – 1015 psi Lubrication systems, fluid transfer, light drives
Medium pressure 70 – 210 bar / 1015 – 3045 psi Agricultural machinery, low-capacity hydraulic presses, light mobile equipment
High pressure 210 – 350 bar / 3045 – 5075 psi Excavators, construction machinery, heavy industrial equipment
Very high pressure 350 – 700 bar / 5075 – 10150 psi Special applications: rescue hydraulics, cutting tools, high-tonnage cylinders

Calculation example

Section titled “Calculation example”

Cylinder data:
Piston diameter d₂ = 80 mm / 3.15 in
Rod diameter d₁ = 40 mm / 1.57 in
Working pressure P = 200 bar / 2900 psi
Flow rate Q = 30 L/min / 7.93 gpm

1. Effective areas
A₂ = π · (80 mm)² / 4 = 5027 mm² / 7.79 in²
A₁ = π · (80² − 40²) / 4 = 3770 mm² / 5.84 in²

2. Thrust force (extension)
F₂ = 200 bar · 10 N/(cm²·bar) · 50.27 cm² = 100 540 N ≈ 100.5 kN / 22 600 lbf

3. Traction force (retraction)
F₁ = 200 bar · 10 N/(cm²·bar) · 37.70 cm² = 75 400 N ≈ 75.4 kN / 16 950 lbf

4. Extension speed
A₂ = 5027 mm² = 0.005027 m²
Q = 30 L/min = 0.0005 m³/s
v = 0.0005 / 0.005027 = 0.0995 m/s / 3.92 in/s

Frequently Asked Questions (FAQ)

Section titled “Frequently Asked Questions (FAQ)”

What thrust force does a cylinder with 100 mm diameter generate at 250 bar?

Section titled “What thrust force does a cylinder with 100 mm diameter generate at 250 bar?”

A cylinder with piston diameter of 100 mm (3.94 in) operated at 250 bar (3626 psi) develops a thrust force of 196.3 kN (44,100 lbf), neglecting friction.

How does rod diameter affect retraction force?

Section titled “How does rod diameter affect retraction force?”

Retraction force is always less than thrust force because the annular area is smaller. For example, with a 45 mm (1.77 in) rod in a 100 mm (3.94 in) cylinder, the traction force at 200 bar (2900 psi) is 113 kN (25,400 lbf), 28% lower than the thrust force.

What speed does a cylinder with 80 mm diameter achieve with a flow rate of 40 L/min?

Section titled “What speed does a cylinder with 80 mm diameter achieve with a flow rate of 40 L/min?”

With a flow rate of 40 L/min (10.6 gpm), the extension speed of an 80 mm (3.15 in) bore cylinder is approximately 0.133 m/s (5.22 in/s).

What pressure is required to lift a load of 50 kN with a 63 mm cylinder?

Section titled “What pressure is required to lift a load of 50 kN with a 63 mm cylinder?”

For a cylinder with piston diameter of 63 mm (2.48 in) that must exert 50 kN (11,240 lbf) of thrust, a working pressure of approximately 160 bar (2320 psi) is required.

Is the force formula valid for single-acting cylinders?

Section titled “Is the force formula valid for single-acting cylinders?”

Yes, in a single-acting cylinder the thrust force is calculated with the same formula F = P · A, but the return stroke depends on a spring or external load, not on opposing hydraulic pressure.

Section titled “What margin is recommended to add for friction in force calculations?”

Friction from seals and bearings can consume between 5% and 20% of the theoretical force. For preliminary calculations, an increase factor of 10% over the required load is typically applied.

References

Section titled “References”