Calculate Force, Speed, and Volume (Imperial Units)
inches
inches
inches
PSI
GPM
Calculation Results
Piston Area (Push)–
sq. in.
Annulus Area (Pull)–
sq. in.
Extension Force–
lbs
(– Tons)
Retraction Force–
lbs
(– Tons)
Extension Speed–
in/sec
Retraction Speed–
in/sec
Total Volume Required for Full Stroke–
Gallons
function calculateHydraulics() {
// Get input values
var bore = parseFloat(document.getElementById('boreDiameter').value);
var rod = parseFloat(document.getElementById('rodDiameter').value);
var stroke = parseFloat(document.getElementById('strokeLength').value);
var pressure = parseFloat(document.getElementById('pressure').value);
var flow = parseFloat(document.getElementById('flowRate').value);
var errorDiv = document.getElementById('error-message');
var resultsDiv = document.getElementById('results');
// Reset display
errorDiv.style.display = 'none';
resultsDiv.style.display = 'none';
// Validation
if (isNaN(bore) || isNaN(rod) || isNaN(stroke) || isNaN(pressure) || isNaN(flow)) {
errorDiv.innerText = "Please fill in all fields with valid numbers.";
errorDiv.style.display = 'block';
return;
}
if (rod >= bore) {
errorDiv.innerText = "Error: Rod diameter cannot be larger than or equal to Bore diameter.";
errorDiv.style.display = 'block';
return;
}
if (bore <= 0 || rod < 0 || stroke <= 0 || pressure <= 0 || flow <= 0) {
errorDiv.innerText = "Please enter positive values for all dimensions and rates.";
errorDiv.style.display = 'block';
return;
}
// Calculations
// 1. Areas (sq in) = PI * r^2
var boreRadius = bore / 2;
var rodRadius = rod / 2;
var boreArea = Math.PI * Math.pow(boreRadius, 2);
var rodArea = Math.PI * Math.pow(rodRadius, 2);
var annulusArea = boreArea – rodArea; // Area for retraction
// 2. Forces (lbs) = Pressure (PSI) * Area (sq in)
var pushForceLbs = pressure * boreArea;
var pullForceLbs = pressure * annulusArea;
// Convert to Tons (1 Ton = 2000 lbs)
var pushForceTons = pushForceLbs / 2000;
var pullForceTons = pullForceLbs / 2000;
// 3. Cylinder Volume (cubic inches) = Area * Stroke
// We calculate volume to extend the full stroke.
// Note: Retract volume would be less, but typically sizing is based on capacity needed.
// Let's calculate total fluid volume to fill the blind end (Extension).
var volumeCubicInches = boreArea * stroke;
var volumeGallons = volumeCubicInches / 231; // 231 cu in = 1 Gallon
// 4. Speeds (in/sec)
// Flow (GPM) * 231 = Cubic Inches per Minute
// Cubic Inches per Minute / 60 = Cubic Inches per Second
// Velocity = Q / A
var flowCuInPerSec = (flow * 231) / 60;
var extSpeed = flowCuInPerSec / boreArea;
var retSpeed = flowCuInPerSec / annulusArea;
// Display Results
document.getElementById('res-bore-area').innerText = boreArea.toFixed(2);
document.getElementById('res-annulus-area').innerText = annulusArea.toFixed(2);
document.getElementById('res-push-force-lbs').innerText = Math.round(pushForceLbs).toLocaleString();
document.getElementById('res-push-force-tons').innerText = pushForceTons.toFixed(2);
document.getElementById('res-pull-force-lbs').innerText = Math.round(pullForceLbs).toLocaleString();
document.getElementById('res-pull-force-tons').innerText = pullForceTons.toFixed(2);
document.getElementById('res-ext-speed').innerText = extSpeed.toFixed(2);
document.getElementById('res-ret-speed').innerText = retSpeed.toFixed(2);
document.getElementById('res-volume-gal').innerText = volumeGallons.toFixed(3);
resultsDiv.style.display = 'block';
}
Comprehensive Guide to Hydraulic Cylinder Calculations
Designing or maintaining a hydraulic system requires precise calculations to ensure your components can handle the required loads and operate at the desired speeds. This hydraulic cylinder calculator helps engineers and technicians quickly determine the fundamental performance metrics of a double-acting cylinder.
Key Concepts in Hydraulics
Before using the calculator, it is essential to understand the variables that affect cylinder performance:
Bore Diameter: The inner diameter of the cylinder barrel. This determines the area available for the fluid to push against during extension.
Rod Diameter: The thickness of the piston rod. This reduces the available surface area on the retraction side (annulus area), resulting in less force but higher speed during retraction.
Stroke Length: The total distance the cylinder travels from fully retracted to fully extended.
System Pressure (PSI): The maximum pressure the hydraulic pump can supply to the cylinder. Force is directly proportional to pressure.
Flow Rate (GPM): The volume of fluid the pump delivers per minute. This determines how fast the cylinder moves.
Hydraulic Formulas Used
Understanding the math behind the tool allows for better system troubleshooting. Here are the standard formulas used in hydraulic engineering:
1. Calculating Area
Blind End Area (Extension) = π × (Bore Diameter / 2)²
Rod End Area (Retraction) = Blind End Area – (π × (Rod Diameter / 2)²)
2. Calculating Force
Force is the product of pressure and area. Note that because the rod takes up space inside the cylinder, the retraction force is always lower than the extension force for the same pressure.
Extension Force (lbs) = Pressure (PSI) × Blind End Area
Retraction Force (lbs) = Pressure (PSI) × Rod End Area
To convert Pounds (lbs) to Tons, divide by 2,000.
3. Calculating Speed
Speed is determined by the flow rate of the fluid filling the cylinder volume. Since 1 gallon equals 231 cubic inches:
Because the Rod End Area is smaller, a cylinder will typically retract faster than it extends given the same flow rate.
Common Troubleshooting Scenarios
Problem
Potential Cause
Calculation Check
Cylinder moves too slowly
Insufficient Flow Rate (GPM) or Pump Wear
Check "Extension Speed" output. If the theoretical speed is higher than actual, check pump efficiency.
Cylinder stalls under load
Pressure too low or Cylinder undersized
Check "Extension Force". Ensure calculated force exceeds the load weight by at least 20%.
Retraction is weak
Large Rod Diameter relative to Bore
Check "Annulus Area". A large rod significantly reduces retraction force.
Why the Rod Diameter Matters
Many novices overlook the rod diameter when sizing a cylinder. If your application involves pulling a load (retraction), you are working with the Annulus Area, not the full bore area. For example, in a cylinder with a 4-inch bore and a 2-inch rod, you lose 25% of your force on the retraction stroke compared to the extension stroke. This calculator automatically accounts for this differential.