Free Flow Rate Calculator
Calculate volumetric flow rate from cross-sectional area and fluid velocity using Q = A·v, with instant results in both m³/s and L/s.
Volumetric flow rate Q = A · v. Enter cross-sectional area and average velocity.
For a round pipe, first convert diameter to area with A = π·(d/2)². The velocity v is the average across the cross-section, not the peak centreline value.
Quick answer
Volumetric flow rate is found with Q = A·v, where A is the cross-sectional area the fluid passes through (in m²) and v is the average flow velocity (in m/s). For example, a duct of area A = 0.05 m² carrying air at v = 2 m/s gives Q = 0.05 × 2 = 0.1 m³/s, which equals 100 L/s. The result is always in cubic metres per second; multiply by 1000 to convert to litres per second.
Formula & method
Q = A · v
- Q — Volumetric flow rate (m³/s)
- A — Cross-sectional area perpendicular to flow (m²)
- v — Average fluid velocity (m/s)
Volumetric flow rate equals cross-sectional area times the average velocity of the fluid through that area. The area must be measured perpendicular to the flow direction.
Q (L/s) = Q (m³/s) × 1000
1 cubic metre equals 1000 litres, so multiply the m³/s result by 1000 to express flow in litres per second.
Examples
- Input
- A = 0.05 m², v = 2 m/s
- Result
- Q = 0.1 m³/s = 100 L/s
- Why
- Q = A·v = 0.05 × 2 = 0.1 m³/s. Converting: 0.1 × 1000 = 100 L/s. A square HVAC duct moving air at 2 m/s through a 0.05 m² opening delivers 100 litres of air every second.
- Input
- A = 0.00785398 m² (Ø100 mm, r = 0.05 m), v = 1.5 m/s
- Result
- Q = 0.0117810 m³/s = 11.781 L/s
- Why
- First find the area: A = π·r² = π × 0.05² = 0.00785398 m². Then Q = A·v = 0.00785398 × 1.5 = 0.0117810 m³/s, which is 0.0117810 × 1000 = 11.781 L/s.
- Input
- A = 2 m², v = 1.2 m/s
- Result
- Q = 2.4 m³/s = 2400 L/s
- Why
- Q = A·v = 2 × 1.2 = 2.4 m³/s. Multiplying by 1000 gives 2400 L/s. A stream with a 2 m² wetted cross-section flowing at 1.2 m/s discharges 2.4 cubic metres of water per second.
- Input
- A = 0.000314159 m² (Ø20 mm, r = 0.01 m), v = 0.8 m/s
- Result
- Q = 0.000251327 m³/s = 0.251327 L/s
- Why
- Area A = π × 0.01² = 0.000314159 m². Then Q = 0.000314159 × 0.8 = 0.000251327 m³/s = 0.251327 L/s (about 0.25 litres per second, or roughly 15 L/min).
When to use this tool
- Sizing pipes, ducts, or channels — checking whether a given diameter and velocity deliver the required discharge.
- HVAC and ventilation design, where airflow in L/s or m³/s must meet a room's air-change requirement.
- Estimating river, stream, or open-channel discharge from a measured cross-section and surface velocity.
- Quick fluid-mechanics homework or lab checks that pair with Reynolds number and dynamic pressure calculations.
Common mistakes
- Using the pipe diameter instead of the cross-sectional area. You must convert diameter to area first with A = π·(d/2)², not plug the diameter straight into Q = A·v.
- Mixing units — entering area in cm² or mm² while velocity is in m/s. Keep everything in SI base units (m² and m/s) so the result is in m³/s, then convert if needed.
- Confusing volumetric flow rate (Q in m³/s) with mass flow rate (ṁ in kg/s). To get mass flow, multiply Q by the fluid density: ṁ = ρ·Q.
- Measuring area in the wrong plane. The area A must be taken perpendicular to the flow direction; an angled or slanted cross-section overstates the true flow area.
Frequently asked questions
What is the formula for volumetric flow rate?
Volumetric flow rate is Q = A·v, the product of the cross-sectional area A (m²) the fluid passes through and its average velocity v (m/s). The result Q is in cubic metres per second (m³/s).
How do I convert m³/s to litres per second?
Multiply by 1000, because one cubic metre is exactly 1000 litres. So 0.1 m³/s = 100 L/s. To get litres per minute instead, multiply the m³/s value by 60,000.
How do I find the area of a round pipe for this calculator?
Use A = π·r², where r is the inner radius. For a pipe with a 100 mm inside diameter, the radius is 0.05 m, so A = π × 0.05² = 0.00785398 m². Always use the inside diameter, not the outside.
What is the difference between volumetric and mass flow rate?
Volumetric flow rate Q measures volume per time (m³/s) and ignores how heavy the fluid is. Mass flow rate ṁ measures mass per time (kg/s) and is found from ṁ = ρ·Q, where ρ is the fluid density. For water (ρ ≈ 1000 kg/m³), a flow of 0.1 m³/s carries about 100 kg/s.
Does this formula assume the velocity is the same everywhere in the pipe?
Q = A·v uses the average velocity across the cross-section. Real flows have a velocity profile (slower at the walls, faster in the centre), so v here is the mean velocity, not the peak centreline velocity. Using the centreline value would overestimate the flow.
Can I rearrange Q = A·v to find velocity or area?
Yes. The same relationship gives v = Q / A to find the velocity needed for a target flow, and A = Q / v to find the area needed. This is how engineers size a pipe diameter for a required discharge and acceptable velocity.
Sources & references
- Wikipedia — Volumetric flow rate
- NIST — SI units and unit conversions
- HyperPhysics — Fluid flow and continuity
External references open in a new tab. We are independent and not affiliated with these organizations.
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