Note: Calculations assume Ideal Gas Law behavior at constant temperature.
Understanding Vacuum Leak Rate Calculations
In vacuum engineering, determining the integrity of a vacuum chamber is critical for process control and safety. The most common method for quantifying air leakage in a sealed system is the Pressure Rise Method (often called the Rate-of-Rise test). This calculator helps engineers and technicians quickly determine the leak rate ($Q$) based on the volume of the system and the change in pressure over a specific time interval.
The Leak Rate Formula
The calculation is derived from the Ideal Gas Law. Assuming the temperature remains constant during the test, the leak rate ($Q_{leak}$) is calculated as:
Qleak = V × ( (P2 – P1) / Δt )
Where:
V = Total internal volume of the vacuum chamber and connected piping.
P1 = Initial pressure at the start of the test (after isolating the pump).
P2 = Final pressure at the end of the test.
Δt = Time duration between the measurement of P1 and P2.
How to Perform a Rate-of-Rise Test
Evacuate: Pump the chamber down to its base pressure or the desired operating pressure.
Isolate: Close the valve connecting the vacuum pump to the chamber. The chamber is now isolated.
Measure P1: Record the pressure ($P_1$) immediately after isolation.
Wait: Allow the system to sit for a set duration ($\Delta t$). Common durations range from 1 minute for rough vacuum to 1 hour or more for high vacuum systems.
Measure P2: Record the final pressure ($P_2$).
Calculate: Input these values into the calculator above to determine the leak rate.
Interpreting the Results
The resulting leak rate includes both real leaks (air entering from outside) and virtual leaks (outgassing from internal surfaces).
Unit
Typical Usage
mbar·L/s
The standard metric unit for vacuum engineering in Europe and scientific applications.
Torr·L/s
Commonly used in the US semiconductor and industrial vacuum sectors.
Pa·m³/s
The SI standard unit, often used in academic physics.
SCCM
Standard Cubic Centimeters per Minute. Often used when comparing leaks to mass flow controller settings.
Leak Rate Guidelines
10-2 to 10-4 mbar·L/s: Generally indicates a gross leak or poor seal (O-ring issue).
10-5 to 10-6 mbar·L/s: Acceptable for many industrial rough/medium vacuum processes.
< 10-9 mbar·L/s: Required for UHV (Ultra-High Vacuum) systems, usually requires helium leak detection to locate.
function calculateLeakRate() {
// 1. Get Input Elements
var sysVolumeInput = document.getElementById('sysVolume');
var volUnitInput = document.getElementById('volUnit');
var timeDurationInput = document.getElementById('timeDuration');
var timeUnitInput = document.getElementById('timeUnit');
var initPressureInput = document.getElementById('initPressure');
var finalPressureInput = document.getElementById('finalPressure');
var pressUnitInput = document.getElementById('pressUnit1'); // Unit applies to both
var errorDiv = document.getElementById('errorMsg');
var resultDiv = document.getElementById('result-container');
// 2. Parse Values
var volume = parseFloat(sysVolumeInput.value);
var timeVal = parseFloat(timeDurationInput.value);
var p1 = parseFloat(initPressureInput.value);
var p2 = parseFloat(finalPressureInput.value);
// 3. Validation
errorDiv.style.display = 'none';
resultDiv.style.display = 'none';
if (isNaN(volume) || isNaN(timeVal) || isNaN(p1) || isNaN(p2)) {
errorDiv.textContent = "Please enter valid numeric values for all fields. (Scientific notation e.g., 1.2e-3 is supported)";
errorDiv.style.display = 'block';
return;
}
if (volume <= 0 || timeVal <= 0) {
errorDiv.textContent = "Volume and Time must be greater than zero.";
errorDiv.style.display = 'block';
return;
}
if (p1 < 0 || p2 < 0) {
errorDiv.textContent = "Pressure cannot be negative.";
errorDiv.style.display = 'block';
return;
}
if (p2 Liters (L)
// Pressure -> mbar
// Time -> seconds (s)
var volLiters = 0;
switch(volUnitInput.value) {
case 'liters': volLiters = volume; break;
case 'm3': volLiters = volume * 1000; break;
case 'ft3': volLiters = volume * 28.3168; break;
case 'cc': volLiters = volume / 1000; break;
}
var timeSeconds = 0;
switch(timeUnitInput.value) {
case 'seconds': timeSeconds = timeVal; break;
case 'minutes': timeSeconds = timeVal * 60; break;
case 'hours': timeSeconds = timeVal * 3600; break;
}
var p1Mbar = 0;
var p2Mbar = 0;
// Conversion factors to mbar
var factorToMbar = 1;
switch(pressUnitInput.value) {
case 'mbar': factorToMbar = 1; break;
case 'torr': factorToMbar = 1.33322; break;
case 'pa': factorToMbar = 0.01; break;
case 'atm': factorToMbar = 1013.25; break;
}
p1Mbar = p1 * factorToMbar;
p2Mbar = p2 * factorToMbar;
// 5. Calculate Leak Rate in Base Unit (mbar·L/s)
// Formula: Q = V * (dP / dt)
var pressureDiff = p2Mbar – p1Mbar;
var leakRateMbarLS = volLiters * (pressureDiff / timeSeconds);
// 6. Convert Results
var leakRateTorrLS = leakRateMbarLS / 1.33322;
var leakRatePaM3S = leakRateMbarLS * 0.0001; // (mbar to Pa is *100, L to m3 is /1000 -> net /10)
// Actually: 1 mbar L/s = 100 Pa * 0.001 m^3/s = 0.1 Pa m^3/s
var leakRatePaM3S_Corrected = leakRateMbarLS * 0.1;
// SCCM Conversion (Standard Cubic Centimeters per Minute)
// 1 mbar L/s approx 59.2 sccm (at std conditions 0C, 1 atm)
// More precisely: 1 std atm = 1013.25 mbar.
// Q(sccm) = Q(mbar L/s) * (60 s/min) * (1000 cc/L) / 1013.25 mbar
var leakRateSCCM = leakRateMbarLS * (60000 / 1013.25);
// 7. Display Results
// Helper to format scientific notation cleanly
function formatNumber(num) {
if (num === 0) return "0";
if (num 10000) {
return num.toExponential(3);
}
return num.toFixed(4);
}
document.getElementById('resMbarLS').textContent = formatNumber(leakRateMbarLS);
document.getElementById('resTorrLS').textContent = formatNumber(leakRateTorrLS);
document.getElementById('resPaM3S').textContent = formatNumber(leakRatePaM3S_Corrected);
document.getElementById('resSCCM').textContent = formatNumber(leakRateSCCM);
resultDiv.style.display = 'block';
}
function resetCalculator() {
document.getElementById('sysVolume').value = ";
document.getElementById('timeDuration').value = ";
document.getElementById('initPressure').value = ";
document.getElementById('finalPressure').value = ";
document.getElementById('errorMsg').style.display = 'none';
document.getElementById('result-container').style.display = 'none';
}