Please enter valid numeric values. Rod diameter must be smaller than bore diameter.
Required Flow (Extension)
0.00 GPM
Required Flow (Retraction)
0.00 GPM
(To match extension time)
Piston Area (Blind End)
0.00 sq in
Annulus Area (Rod End)
0.00 sq in
Fluid Volume Per Stroke
Extend: 0.00gal
Retract: 0.00gal
Resulting Velocity
0.00 in/sec
Understanding Cylinder Flow Rate Calculations
Calculating the flow rate for hydraulic cylinders is a fundamental step in designing fluid power systems. The flow rate determines how fast the cylinder piston extends and retracts. Because the volume of the cylinder chambers differs between the cap end (blind end) and the rod end, the flow requirements and speeds will vary even if the pump output remains constant.
Key Formulas Used
The relationship between Flow Rate ($Q$), Velocity ($v$), and Area ($A$) is defined by the formula: $Q = A \times v$. However, in practical applications, we often solve for Flow Rate based on a desired cycle time.
1. Calculate Areas
First, determine the effective area for the fluid to push against:
Multiply the area by the stroke length to get the total volume of fluid required for one full movement.
3. Calculate Flow Rate
Finally, divide the volume by the desired time. In the Imperial system, we use conversion factors to get Gallons Per Minute (GPM):
Flow (GPM) = (Volume in cubic inches ÷ 231) × (60 ÷ Time in seconds)
Why Retraction is Faster
You will notice in the calculator results that the Retraction Flow required to meet the same time target is lower than the Extension Flow. Conversely, if you supply a constant flow rate to the cylinder, it will retract faster than it extends. This is due to the Rod Volume occupying space in the cylinder, reducing the volume of fluid needed to fill the rod-end chamber.
Metric vs. Imperial Hydraulic Units
This calculator supports both standard industrial unit systems:
Imperial: Bore/Stroke in inches, Flow in GPM (Gallons Per Minute).
Metric: Bore/Stroke in millimeters, Flow in LPM (Liters Per Minute).
Ensure you select the correct system before entering your dimensions to ensure accurate pump sizing and system performance analysis.
var currentUnit = 'imperial';
function updateUnits() {
var select = document.getElementById("unitToggle");
currentUnit = select.value;
var boreLabel = document.getElementById("boreUnit");
var rodLabel = document.getElementById("rodUnit");
var strokeLabel = document.getElementById("strokeUnit");
if (currentUnit === 'imperial') {
boreLabel.innerText = "(in)";
rodLabel.innerText = "(in)";
strokeLabel.innerText = "(in)";
} else {
boreLabel.innerText = "(mm)";
rodLabel.innerText = "(mm)";
strokeLabel.innerText = "(mm)";
}
// Clear results when switching units to avoid confusion
document.getElementById("results").style.display = "none";
}
function calculateHydraulics() {
// 1. Get Inputs
var bore = parseFloat(document.getElementById("boreDiameter").value);
var rod = parseFloat(document.getElementById("rodDiameter").value);
var stroke = parseFloat(document.getElementById("strokeLength").value);
var time = parseFloat(document.getElementById("cycleTime").value);
var errorMsg = document.getElementById("error-msg");
var resultsDiv = document.getElementById("results");
// 2. Validation
if (isNaN(bore) || isNaN(rod) || isNaN(stroke) || isNaN(time) || time <= 0 || bore = bore) {
errorMsg.innerText = "Rod diameter must be smaller than the Bore diameter.";
errorMsg.style.display = "block";
resultsDiv.style.display = "none";
return;
}
errorMsg.style.display = "none";
resultsDiv.style.display = "block";
var pi = Math.PI;
var areaExt, areaRet, volExt, volRet, flowExt, flowRet, velocity;
// 3. Calculation Logic
if (currentUnit === 'imperial') {
// Imperial Calculations (Inches, Gallons, GPM)
// Areas in Square Inches
areaExt = pi * Math.pow((bore / 2), 2);
areaRet = areaExt – (pi * Math.pow((rod / 2), 2));
// Volumes in Cubic Inches
var volExtCuIn = areaExt * stroke;
var volRetCuIn = areaRet * stroke;
// Convert Volume to Gallons (1 gal = 231 cu in)
volExt = volExtCuIn / 231;
volRet = volRetCuIn / 231;
// Flow Rate in GPM
// Flow = Volume (gal) / (Time (sec) / 60)
flowExt = volExt / (time / 60);
flowRet = volRet / (time / 60);
// Velocity in Inches/Sec
velocity = stroke / time;
// Update Unit Labels for Output
document.getElementById("resFlowExtUnit").innerText = "GPM";
document.getElementById("resFlowRetUnit").innerText = "GPM";
document.getElementById("resAreaExtUnit").innerText = "in²";
document.getElementById("resAreaRetUnit").innerText = "in²";
document.getElementById("resVolExtUnit").innerText = "gallons";
document.getElementById("resVolRetUnit").innerText = "gallons";
document.getElementById("resVelocityUnit").innerText = "in/sec";
} else {
// Metric Calculations (mm, Liters, LPM)
// Areas in Square Millimeters
areaExt = pi * Math.pow((bore / 2), 2);
areaRet = areaExt – (pi * Math.pow((rod / 2), 2));
// Volumes in Cubic Millimeters
var volExtCuMm = areaExt * stroke;
var volRetCuMm = areaRet * stroke;
// Convert Volume to Liters (1 Liter = 1,000,000 mm^3)
volExt = volExtCuMm / 1000000;
volRet = volRetCuMm / 1000000;
// Flow Rate in LPM
// Flow = Volume (L) / (Time (sec) / 60)
flowExt = volExt / (time / 60);
flowRet = volRet / (time / 60);
// Velocity in mm/sec (display as cm/sec or m/sec might be better, sticking to mm/sec for consistency with input)
// Actually, let's output mm/sec
velocity = stroke / time;
// Update Unit Labels for Output
document.getElementById("resFlowExtUnit").innerText = "LPM";
document.getElementById("resFlowRetUnit").innerText = "LPM";
document.getElementById("resAreaExtUnit").innerText = "mm²";
document.getElementById("resAreaRetUnit").innerText = "mm²";
document.getElementById("resVolExtUnit").innerText = "Liters";
document.getElementById("resVolRetUnit").innerText = "Liters";
document.getElementById("resVelocityUnit").innerText = "mm/sec";
}
// 4. Update DOM
document.getElementById("resFlowExt").innerText = flowExt.toFixed(2);
document.getElementById("resFlowRet").innerText = flowRet.toFixed(2);
document.getElementById("resAreaExt").innerText = areaExt.toFixed(2);
document.getElementById("resAreaRet").innerText = areaRet.toFixed(2);
document.getElementById("resVolExt").innerText = volExt.toFixed(3);
document.getElementById("resVolRet").innerText = volRet.toFixed(3);
document.getElementById("resVelocity").innerText = velocity.toFixed(2);
}