Mass Flow Rate Calculator
Mass flow rate answers a plain question with expensive consequences when it is wrong: how much mass moves through this pipe, duct or channel every second? It is the number behind pump sizing, HVAC duct design, chemical feed rates and fuel-system work. This calculator works in the two forms engineers actually use, density × velocity × area or density × volumetric flow, converts every input to SI units for you so metric and imperial can be mixed freely, and includes a pipe-diameter helper for the common case where you know the diameter but not the area.
Know the pipe diameter instead? Enter it above and the area is computed as πd²/4.
Mass flow rate
Quick Answer
Water (ρ = 1,000 kg/m³) flowing at 2 m/s through an area of 0.05 m² has a mass flow rate of 100.00 kg/s: ρ × v × A = 1,000 × 2 × 0.05. That is 360,000 kg/h, or 220.46 lb/s. This exact run is pre-filled in the calculator above.
Key takeaways
- Two modes cover the two ways the inputs arrive: density with velocity and area, or density with a volumetric flow reading from a meter.
- Every input carries its own unit selector and is converted to SI before the math, so ft/s with in² and lb/ft³ works directly, with no hand conversion.
- If you know the pipe diameter, enter it: the tool computes the area as πd²/4, and a valid diameter overrides the area field.
- One run returns five units: kg/s, kg/h, g/s, lb/s and tonnes/h, plus the volumetric flow in the first mode.
- Quick Answer
- How to use the mass flow rate calculator
- The formula: ṁ = ρ × v × A = ρ × Q
- Worked examples, verified against the tool
- The conversion factors this tool uses, stated plainly
- Mass flow vs volumetric flow: why density is the whole game
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the mass flow rate calculator
Pick the mode that matches the numbers you have, enter them in whatever units they arrived in, and click Calculate. The result stays hidden until you click, and switching modes hides it again.
- Density × velocity × area mode: enter the fluid density, the average flow velocity and the cross-sectional area. Water at 1,000 kg/m³, 2 m/s and 0.05 m² is pre-filled as the worked example.
- Pipe diameter instead of area: type the diameter into the optional field, in m, cm or inches. A valid positive diameter replaces the area with πd²/4; clear the field to go back to your entered area.
- Density × volumetric flow mode: if a meter already gives you the volumetric flow, enter density and that flow in m³/s, L/s or gal/min. The pre-filled run is 1,000 kg/m³ at 0.2 m³/s, which gives 200.00 kg/s.
- Read all five units: the main figure is kg/s; underneath you get kg/h, g/s, lb/s and tonnes/h from the same calculation, plus the volumetric flow line in the first mode.
- Fixing errors: each field validates on its own. A missing value says “Enter the…” and a zero or negative value says it “must be greater than zero,” with the offending field outlined in red.
Neighbouring jobs have their own tools: if your known quantity is a hose and a pressure-driven flow, the hose flow rate calculator starts from the hose instead, and drainage work is covered by the drain flow rate calculator.
The formula: ṁ = ρ × v × A = ρ × Q
Mass flow rate (ṁ) equals fluid density (ρ) times flow velocity (v) times cross-sectional area (A). Since volumetric flow Q = v × A, the same answer comes from density times volumetric flow.
Volumetric flow Q = v × A, so ṁ = ρ × Q
Circular pipe area A = πd²/4
The units check is built into the formula: (kg/m³) × (m/s) × (m²) cancels down to kg/s, mass per time, which is the whole point. This is the steady-flow form of conservation of mass: in a pipe with one inlet and one outlet and no accumulation, the mass flow in equals the mass flow out, even where the pipe narrows and the velocity rises. Industry references such as the Kytola guide to calculating flow rates build on the same pair of equations, Q = A × v and ṁ = ρ × Q, and typical water velocities in pipes sit in the range surveyed by the Engineering ToolBox flow velocity recommendations for water pipes, which is a useful sanity check on the velocity you enter: a figure far outside the usual band usually means a unit slip, not a remarkable pipe.
Worked examples, verified against the tool
Every row was produced by running the calculator above on the stated inputs, formatting included.
| Run | Inputs | Tool output |
|---|---|---|
| Pre-filled example | Water 1,000 kg/m³, 2 m/s, 0.05 m² | 100.00 kg/s (Q = 0.1000 m³/s; 360,000 kg/h; 220.46 lb/s) |
| Diameter helper | Water, 2 m/s, diameter 0.1 m, area field empty | 15.708 kg/s (Q = 0.0157 m³/s, area from pipe diameter) |
| Mixed units | 62.4 lb/ft³, 10 ft/s, 2 in² | 3.931 kg/s (14,152 kg/h; 8.667 lb/s) |
| Volumetric mode | Water 1,000 kg/m³, flow 60 gal/min | 3.785 kg/s (13,627 kg/h) |
The mixed-units row is the one to test other calculators with. Converted by hand, 62.4 lb/ft³ is 999.55 kg/m³, 10 ft/s is 3.048 m/s and 2 in² is 0.00129032 m², and 999.55 × 3.048 × 0.00129032 = 3.931 kg/s. A tool that skips any one of those conversions lands somewhere else entirely, and the error is silent.
The conversion factors this tool uses, stated plainly
Each selector carries the factor that converts its unit to SI, and the tool multiplies by exactly these numbers. Two of them are rounded, and you deserve to know which.
| Input | Units and factors to SI |
|---|---|
| Density | kg/m³ ×1, g/cm³ ×1,000, lb/ft³ ×16.0185 |
| Velocity | m/s ×1, ft/s ×0.3048, mph ×0.44704 |
| Area | m² ×1, cm² ×0.0001, in² ×0.00064516, ft² ×0.092903 |
| Diameter | m ×1, cm ×0.01, in ×0.0254 |
| Volumetric flow | m³/s ×1, L/s ×0.001, gal/min ×0.0000630902 |
The lb/ft³ factor is stored as 16.0185 rather than the fuller 16.0184634, and the lb/s output line multiplies by 2.20462 rather than 2.2046226218. Both roundings sit far below the precision of any density you will type in, but they are why the lb/s line for the worked example reads 220.46 instead of 220.4623. The SI outputs (kg/s, kg/h, g/s, tonnes/h) carry no such rounding. Standard factors of this kind are tabulated in the NIST guidance on metric unit conversion if you want to check any row by hand.
Mass flow vs volumetric flow: why density is the whole game
Volumetric flow tells you how much space the fluid occupies per second; mass flow tells you how much stuff arrives per second. Processes consume mass, so the second number is usually the one that matters.
For a liquid at near-constant temperature the distinction is mostly bookkeeping, because the density barely moves. For a gas it is decisive: heat the air in a duct or drop its pressure and the same volumetric flow carries noticeably less mass, which is why HVAC and compressor work is specified in mass flow. Where a pressure drop is what you actually know, the flow rate and pressure calculator approaches the problem from that side, and where the run is a long straight channel with a steady speed, the linear flow rate calculator covers the simpler one-dimensional case. Two practical cautions belong here. First, velocity in a real pipe is not uniform: it peaks at the center and falls to zero at the wall, so the v in the formula is the cross-section average, and a centerline probe reading will overstate the flow. Second, density must be the density at the section where you measured v and A. Use a value from a different pressure or temperature and the answer inherits that error undiluted, one for one.
What competing calculators miss
The ranking pages for this keyword split into SI-only tools, formula essays with a token calculator, and guides with no calculator at all:
- Sage Calculator’s mass flow rate tool: clean and correct on its own worked example (the same 100 kg/s water run pre-filled here), but SI-only: density in kg/m³, velocity in m/s, area in m², or you convert by hand first. No diameter helper either.
- TrueGeometry’s flow pages: the formula material is extensive, but the calculators are parameter dumps aimed at other engineers’ problem statements, not a usable two-mode tool.
- Firgell’s continuity equation calculator: genuinely good on two-section continuity (A₁v₁ = A₂v₂), which is a different job: it assumes you already accept the mass flow and want the second section’s velocity.
- NumberAnalytics guides: solid explanations of ṁ = ρQ with worked examples, and no working calculator attached, so the reader still does the unit conversions alone.
- The gap this page fills: per-input unit selectors so mixed metric and imperial entries just work, a diameter helper because engineers know diameters rather than areas, both input forms in one tool, five output units from one run, and the conversion factors printed on the page so the arithmetic can be audited.
Frequently asked questions
The mass of fluid passing through a cross-section per unit of time, usually in kg/s. It is the quantity that matters for pump sizing, heat transfer, and chemical dosing, because processes consume mass, not volume.
Volumetric flow (Q = v × A, in m³/s) measures volume per time; mass flow (ṁ = ρ × Q) multiplies by density. For gases, density changes with pressure and temperature, so mass flow is the more reliable quantity.
Yes. Each input has its own unit selector and everything is converted to SI before the calculation, so 10 ft/s with 2 in² and 62.4 lb/ft³ works directly.
Enter the diameter in the optional field and the tool uses A = πd²/4. For example, a 0.1 m diameter pipe has an area of 0.007854 m².
The diameter wins. If the diameter field holds a valid positive number, the tool computes the area as πd²/4 and ignores the area field, and the result line notes that the area came from the pipe diameter. An invalid or non-positive diameter is ignored instead, and the area field is used.
Liquid density is nearly constant, but gas density depends strongly on pressure and temperature. Use the density at the point where you measure velocity and area, or the result inherits the density error one to one.
kg/s, kg/h, g/s, lb/s, and tonnes/h, all from the same calculation.
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References
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure), 9th edition. Accessed October 22, 2026.
- National Institute of Standards and Technology, Office of Weights and Measures. Metric (SI) Unit Conversion. Accessed October 22, 2026.
- Kytola Oy. How Do You Calculate Flow Rates? Accessed October 22, 2026.
- Engineering ToolBox. Water Flow: Recommended Velocity in Water Pipes. Accessed October 22, 2026.
- Engineering ToolBox. Densities of Common Materials. Accessed October 22, 2026.