Article — Flow Rate Calculator
Flow Rate Calculator: Q = V/t and Q = A × v
Flow rate Q is volume per unit time. Two formulas cover almost every case: Q = V/t for filled-container measurements, and Q = A × v for pipe-and-velocity calculations. SI units are m³/s; plumbing uses L/min or GPM, HVAC uses CFM or m³/h.
Whether you are sizing a copper pipe for a kitchen sink, programming an IV infusion pump, or designing the ductwork in an office building, flow rate is the number that ties cross-section, velocity, and elapsed time together. The math is forgiving but the unit conversions are where most engineering mistakes hide.
What flow rate measures
Volumetric flow rate, usually written Q, is the volume of fluid passing through a defined cross-section per unit time. A garden hose running into a bucket that takes 20 seconds to fill its 8-litre capacity has a flow rate of 8 L / 20 s = 0.4 L/s = 24 L/min. The same flow can be expressed as 6.34 US gallons per minute or 0.847 cubic feet per minute.
The defining unit in SI is the cubic metre per second (m³/s), but it is too big for most domestic and industrial applications. Plumbers prefer L/min or GPM, HVAC engineers prefer CFM or m³/h, and chemical engineers like m³/s or kg/s. The calculator above converts between all of them in one step.
The flow rate formula in two forms
Two equivalent forms cover every steady-flow problem. Volume per time: Q = V / t. This is what you measure when you fill a known container and clock the time. Area times velocity: Q = A × v. This is what you compute when you know the pipe inner diameter and the average flow speed. For a circular pipe of diameter d, A = π(d/2)², so Q = π(d/2)² × v.
Q = V / t volume per timeQ = A × v area times velocityA = π d² / 4 round-pipe areaṁ = ρ × Q mass flow rateFlow rate and the continuity equation
For incompressible fluids in steady flow, the same volumetric flow rate passes through every cross-section of the system. This is the continuity equation: A₁ v₁ = A₂ v₂. If the pipe narrows, the velocity must rise. If it widens, the velocity drops. The flow rate Q does not change.
This is why water sprays faster from a partially blocked hose, why blood velocity rises through stenosed arteries, and why a hurricane's wind speeds up as it makes landfall over a narrowing coastal corridor. The simplest demonstration is putting your thumb over a garden hose: same Q, smaller A, much higher v.
In a single human heart, blood passes through the aorta at about 1.4 m/s with a flow rate near 5 L/min at rest. During heavy exercise, cardiac output can rise to 25 L/min — five times normal — without any change in aorta diameter. The velocity has to increase to maintain the higher Q.
Flow rate units: GPM, CFM, L/min, m³/h
The unit zoo is unavoidable. American plumbing uses GPM (US gallons per minute). HVAC uses CFM (cubic feet per minute) for air and GPM for water. European plumbing and most industrial water use L/min or m³/h. Scientific work uses m³/s. Medical infusion pumps use mL/h.
- 1 m³/s = 1000 L/s = 60 000 L/min = 15 850 GPM (US) = 2119 CFM
- 1 GPM (US) = 3.7854 L/min = 0.2271 m³/h = 8.0208 CFH
- 1 CFM = 28.317 L/min = 0.4720 L/s = 1.6990 m³/h
- 1 m³/h = 16.667 L/min = 4.4029 GPM (US) = 0.5886 CFM
- UK gallons differ: 1 UK GPM = 4.546 L/min, ~20 % larger than US
Flow rate and pipe diameter
At a fixed velocity, flow rate scales with the square of pipe diameter. Double the pipe and you quadruple the flow. At a fixed pressure drop in laminar viscous flow, the Hagen–Poiseuille equation says flow scales with the fourth power of radius. Doubling the radius multiplies the flow by 16.
This explains why a partly clogged artery causes so much trouble. A 50 percent narrowing in radius drops the laminar flow rate to (0.5)⁴ = 6.25 percent of normal. The body responds by raising the pressure drop, which raises shear stress on the artery wall, which in turn raises the risk of plaque rupture. Small geometric changes have outsized consequences for pipe flow.
Flow rate in plumbing, HVAC, and medicine
In plumbing, fixture units sum across a building to determine pipe sizing. A typical residential kitchen sink demands 6–8 L/min, a showerhead 9–15 L/min, a toilet 6 L per flush. Whole-house peak demand of 30–60 L/min sizes the service line.
In HVAC, the air change rate is the room volume divided by airflow rate. An office space of 50 m³ supplied with 250 m³/h gets 5 air changes per hour, well above the ASHRAE 62.1 minimum. Diffuser sizing, duct velocity (typically 3–8 m/s in supply ducts), and fan power all depend on the volumetric flow.
In medicine, IV infusion pumps deliver drugs at 1–200 mL/h with high precision. For a patient receiving 50 mL/h of an antibiotic, the pump rotor turns to match Q exactly — overshooting by 10 percent can be clinically significant.
Volumetric vs mass flow rate
Volumetric flow rate (Q, m³/s) and mass flow rate (ṁ, kg/s) are linked by density: ṁ = ρ × Q. For water at room temperature, 1 L/min equals approximately 1 kg/min. For air, the same volumetric flow corresponds to about 1.2 g of mass per litre.
Mass flow matters whenever density changes — gas mixing, combustion, exhaust systems, atmospheric science. For incompressible liquids at constant temperature, volumetric and mass flow rates carry the same information up to a fixed factor.
When dimensioning systems with multiple fluid temperatures, work in mass flow. Volumetric flow shifts with temperature for gases and slightly for liquids, but mass flow is conserved through pumps, heat exchangers, and pipe runs.
Common flow rate mistakes
The US gallon is 3.7854 litres; the UK imperial gallon is 4.546 litres. A pump rated at "10 GPM" in the US is not the same as a UK pump labelled the same. Always state US or imperial. The calculator above uses US gallons throughout, which is the convention in plumbing literature.
Other recurring slips: confusing outer pipe diameter with inner diameter (the flow goes through the inner cross-section), forgetting that average velocity is not the same as peak velocity in laminar flow (peak = 2 × average for parabolic pipe flow), and mixing volumetric and mass flow rates without converting through density. Always carry the units explicitly until the final step.