Pressure, force, area and cylinder calculator
Choose the unknown, enter values and units, then apply optional engineering adjustments.
Common pressure reference table
Approximate values are provided for convenient comparison.
| Pressure | PSI | Typical context |
|---|---|---|
| 1 atmosphere | 14.6959 | Standard sea-level atmospheric pressure |
| 1 bar | 14.5038 | Industrial and meteorological pressure |
| 100 kPa | 14.5038 | Near one bar |
| 1 MPa | 145.038 | Structural and hydraulic calculations |
| 2,000 PSI | 2,000 | Moderate hydraulic system |
| 3,000 PSI | 3,000 | Common mobile hydraulic system |
| 5,000 PSI | 5,000 | High-pressure hydraulic application |
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Formula used
The central relationship connects force, area, and pressure. A pound-force describes a load, while PSI describes how concentrated that load is. The same force creates greater pressure when it acts on a smaller area and lower pressure when it spreads across a larger area.
Reverse formulas
Circular piston formula
Hydraulic cylinder formulas
For extension, the fluid generally acts across the full piston area. During retraction, the rod occupies part of that area. Therefore, retraction force is lower than extension force at the same pressure.
How to use this calculator
Choose the unknown
Select whether you need pressure, force, required area, hydraulic cylinder output, or distributed contact pressure. The form automatically shows the sections relevant to that mode.
Enter values with correct units
Enter force as pound-force, ounce-force, newtons, kilonewtons, kilogram-force, or metric ton-force. Enter pressure in PSI or another available unit. Enter area directly or calculate it from common geometric dimensions.
Set pressure reference
Gauge pressure is measured relative to local atmospheric pressure. Absolute pressure is measured relative to a perfect vacuum. When absolute pressure is selected, the calculator estimates local atmosphere from the entered altitude.
Apply practical adjustments
Efficiency accounts for mechanical losses. Count represents multiple cylinders, contacts, or fasteners. Load distribution represents the portion of the total load reaching the group. Safety factor produces a more conservative design result, but it does not replace applicable codes or professional review.
Review calculations
The result includes the primary value, supporting quantities, formula substitutions, conversions, and warnings. Use the print option to create a paper copy or save the page as a PDF through your browser.
Understanding pounds-force and PSI
Pounds-force and PSI are not interchangeable units. Pounds-force measures total force. PSI means pounds-force per square inch and therefore measures pressure or stress. A direct conversion is impossible unless contact area is known. For example, 100 lbf applied to 10 in² equals 10 PSI, while the same 100 lbf applied to 1 in² equals 100 PSI.
This distinction matters in hydraulic cylinders, presses, clamps, structural bearing surfaces, tires, seals, bolted joints, lifting equipment, and material testing. A total load may be acceptable, but a small contact area can create damaging local pressure.
PSI, PSIG, and PSIA
PSI is often used loosely, so the reference should be stated. PSIG is gauge pressure and reads zero when exposed to the surrounding atmosphere. PSIA is absolute pressure and reads approximately 14.696 PSI at standard sea-level conditions even when a gauge reads zero. The relationship is approximately PSIA = PSIG + atmospheric pressure.
Atmospheric pressure changes with altitude and weather. This calculator uses a standard-atmosphere approximation based on altitude. Use measured barometric pressure when a precise absolute-pressure conversion is required.
Engineering notes and limitations
The equations assume uniform pressure and ideal force transfer. Real systems may include friction, seal drag, side loading, fluid compressibility, pressure drop, hose expansion, dynamic impact, misalignment, uneven contact, temperature effects, material deformation, leakage, and manufacturing tolerances. Efficiency input can approximate some losses, but detailed system analysis may require measured data.
Never use a calculated value as the only basis for selecting pressure vessels, cylinders, hoses, fittings, valves, fasteners, lifting equipment, or safety-critical structures. Verify working pressure, proof pressure, burst pressure, fatigue rating, material strength, applicable standards, and required design factors.
Worked examples
Example 1: force over a flat area
A 600 lbf load acts uniformly over 12 in². Pressure equals 600 ÷ 12, producing 50 PSI.
Example 2: circular piston
A 4-inch bore has an area of π × 4² ÷ 4, or approximately 12.566 in². At 2,000 PSI, ideal extension force is approximately 25,133 lbf before losses and design adjustments.
Example 3: required area
A design must support 10,000 lbf while limiting pressure to 500 PSI. Required area equals 10,000 ÷ 500, or 20 in². An equivalent circular diameter is approximately 5.05 inches.
Example 4: multiple contacts
A 4,000 lbf load is shared equally by four pads, each measuring 2 in². Each pad carries 1,000 lbf, producing 500 PSI before any safety factor.
Frequently asked questions
Can pounds be converted directly to PSI?
No. PSI is pounds-force per square inch. You must know the loaded area.
Does lb mean mass or force?
In pressure calculations, use pound-force. Pounds-mass requires a gravity or acceleration relationship before it becomes force.
Why is hydraulic retraction force lower?
The piston rod reduces the fluid-acting area on the rod side, so the same pressure generates less retraction force.
Should I use gauge or absolute pressure?
Most hydraulic gauges and common shop calculations use gauge pressure. Thermodynamic, vacuum, and gas-law calculations often require absolute pressure.
What efficiency should I enter?
Use 100% for ideal output. For practical equipment, use manufacturer data or measured performance. Do not guess for safety-critical work.
How does the safety factor work?
It increases required area or design pressure and reduces reported available design force, providing a conservative calculation.
Can this calculate bolt bearing pressure?
It can estimate average pressure from force and projected area, but detailed joint design may require shear, tensile, bearing, fatigue, preload, and code checks.
Can I save results?
Submitted results are added to browser-local history. You can also copy, export CSV, print, or save as PDF through the browser.