Note: Water is approx 1000 kg/m³, Air is approx 1.225 kg/m³
Please enter valid numeric values.
Calculated Mass Flow Rate
Kilograms per Second:–
Kilograms per Hour:–
Pounds per Second:–
Pounds per Hour:–
Understanding the Volumetric to Mass Flow Rate Conversion
In fluid dynamics, chemical engineering, and HVAC systems, accurately converting between volumetric flow rate and mass flow rate is critical for system sizing, billing, and process control. While volumetric flow measures the space a fluid occupies as it moves, mass flow measures the actual amount of matter moving through the system.
The Physics Formula
The relationship between volumetric flow rate and mass flow rate is governed by the density of the fluid. Since mass is equal to volume multiplied by density, the flow rates follow the same logic:
ṁ = Q × ρ
Where:
ṁ (m-dot): Mass Flow Rate (e.g., kg/s, lb/hr)
Q: Volumetric Flow Rate (e.g., m³/s, CFM, GPM)
ρ (rho): Fluid Density (e.g., kg/m³, lb/ft³)
Why Convert Volumetric Flow to Mass Flow?
Volumetric flow rates can be misleading because the volume of a fluid (especially gases) changes significantly with temperature and pressure. Mass flow rate, however, remains constant regardless of thermodynamic changes. This makes mass flow the preferred metric for:
Combustion control: Fuel must be supplied by mass to maintain the correct stoichiometric ratio.
Custody transfer: Selling natural gas or oil is fairer when done by mass or energy content rather than volume.
Chemical reactions: Reactions occur molecule to molecule (mass-based), not volume to volume.
Common Unit Conversions
Because different industries use different standards (Metric vs. Imperial), converting units is often the hardest part of the calculation. Here are common density values to help with your calculations:
Fluid
Density (kg/m³)
Density (lb/ft³)
Water (4°C)
1000
62.43
Air (20°C, 1 atm)
1.204
0.075
Oil (approx)
800 – 950
50 – 59
Mercury
13534
844.9
Example Calculation
Imagine you have water flowing through a pipe at 500 Liters per minute (L/min). You want to know the mass flow rate in kg/s.
Determine Density: Water is approximately 1000 kg/m³.
When using this calculator, ensure you use the density of the fluid at its actual operating temperature and pressure. Heating a gas decreases its density significantly, which means a constant volumetric flow would result in a lower mass flow rate.
function calculateMassFlow() {
// Get Input Elements
var volFlowInput = document.getElementById("volumetricFlow");
var flowUnitSelect = document.getElementById("flowUnit");
var densityInput = document.getElementById("density");
var densityUnitSelect = document.getElementById("densityUnit");
var errorMsg = document.getElementById("errorMsg");
var resultContainer = document.getElementById("result-container");
// Get Values
var q = parseFloat(volFlowInput.value);
var rho = parseFloat(densityInput.value);
var qUnit = flowUnitSelect.value;
var rhoUnit = densityUnitSelect.value;
// Reset UI
errorMsg.style.display = "none";
resultContainer.style.display = "none";
// Validate Inputs
if (isNaN(q) || isNaN(rho)) {
errorMsg.innerText = "Please enter valid numeric values for Flow Rate and Density.";
errorMsg.style.display = "block";
return;
}
if (q < 0 || rho <= 0) {
errorMsg.innerText = "Flow rate must be positive and density must be greater than zero.";
errorMsg.style.display = "block";
return;
}
// Step 1: Convert Flow Rate (Q) to base unit: Cubic Meters per Second (m³/s)
var q_base = 0; // m³/s
switch (qUnit) {
case "m3_s":
q_base = q;
break;
case "m3_h":
q_base = q / 3600;
break;
case "l_min":
q_base = q / 1000 / 60;
break;
case "l_h":
q_base = q / 1000 / 3600;
break;
case "ft3_min": // CFM
q_base = q * 0.000471947;
break;
case "gal_min": // US GPM
q_base = q * 0.0000630902;
break;
}
// Step 2: Convert Density (rho) to base unit: Kilograms per Cubic Meter (kg/m³)
var rho_base = 0; // kg/m³
switch (rhoUnit) {
case "kg_m3":
rho_base = rho;
break;
case "g_cm3":
rho_base = rho * 1000;
break;
case "lb_ft3":
rho_base = rho * 16.0185;
break;
case "lb_gal":
rho_base = rho * 119.826;
break;
}
// Step 3: Calculate Mass Flow in Base Unit (kg/s)
// Formula: m_dot = Q * rho
var m_dot_kgs = q_base * rho_base;
// Step 4: Convert Base Mass Flow (kg/s) to other units for display
var m_dot_kgh = m_dot_kgs * 3600; // kg/h
var m_dot_lbs = m_dot_kgs * 2.20462; // lb/s
var m_dot_lbh = m_dot_kgs * 2.20462 * 3600; // lb/h
// Display Results
document.getElementById("res_kg_s").innerText = formatNumber(m_dot_kgs) + " kg/s";
document.getElementById("res_kg_h").innerText = formatNumber(m_dot_kgh) + " kg/h";
document.getElementById("res_lb_s").innerText = formatNumber(m_dot_lbs) + " lb/s";
document.getElementById("res_lb_h").innerText = formatNumber(m_dot_lbh) + " lb/h";
resultContainer.style.display = "block";
}
function formatNumber(num) {
// Helper to format numbers nicely (up to 4 decimal places, trimming trailing zeros)
if (num === 0) return "0";
// For very small or large numbers, use scientific notation
if (Math.abs(num) 1000000) {
return num.toExponential(4);
}
// Otherwise fixed decimal
return parseFloat(num.toFixed(4)).toString();
}