Flow Rate Calculator: Q = A x v

Volume flow from the area of a pipe or channel and the fluid velocity.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • Q = A\,v
  • A = \frac{Q}{v}
  • v = \frac{Q}{A}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the volume flow rate: volume flow rate = cross-section area of the flow x mean velocity
  2. Put the values in (every value in its SI unit): volume flow rate = 0.01 x 2
  3. The answer: volume flow rate: 0.02 m3/s
  4. The same answer in other units: 20 L/s; 1200 L/min; 72 m3/h; 317.006 US gal/min; 0.706293 ft3/s

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Mean velocity; Volume flow rate (leave it as it is if this is what you are finding) 0.02 m3/s; Cross-section area of the flow (leave it as it is if this is what you are finding) 0.01 m2.

  1. The formula, arranged to find the mean velocity: mean velocity = (volume flow rate) / (cross-section area of the flow)
  2. Put the values in (every value in its SI unit): mean velocity = (0.02) / (0.01)
  3. The answer: mean velocity: 2 m/s
  4. The same answer in other units: 7.2 km/h; 6.56168 ft/s

Common questions

What is the flow rate formula?

Volume flow equals the area times the velocity. Water at 2 m/s in a pipe of 0.01 m2 flows at 0.02 m3/s, which is 20 L/s.

How do I convert m3/s to L/min?

Multiply by 60 000.

What is the continuity equation?

For an incompressible fluid the flow rate is the same at every section, so a narrower pipe has a higher velocity.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any fluid mechanics text (continuity and flow rate).

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