Flow Rate Calculator
Pipe flow in one card: the bore's area times the speed, with the unit conversions computed and a continuity card showing what a constriction does to velocity.
Flow Rate Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Circular bore, average speed; no velocity profile
- No friction losses — flow bookkeeping, not pump sizing
In short: A 5 cm bore carrying water at 2 m/s: the section is π·d²/4 = 0.001963 m², so Q = A·v = 0.003927 m³/s — 3.926991 L/s, 14.137167 m³/h, 235.619449 L/min, or 62.244073 US gal/min. The gallon is exact (3.785411784 L by definition), so the conversion is arithmetic, not folklore. The constriction card is the one to remember: narrow the bore to half the diameter and the SAME flow rate pushes 8.000000 m/s — quarter the area, four times the speed. That is continuity, and it is why a nozzle and a thumb over the hose do the same trick.
Formula
Q = A·v = π·d²/4 · v · continuity: A₁·v₁ = A₂·v₂ · 1 US gal = 3.785411784 L (exact)
Flow rate is a geometry times a speed: the circular section grows with the SQUARE of the bore, so a pipe twice as wide carries four times as much at the same speed. Continuity is bookkeeping, not physics — what goes in must come out — which is why the constriction card computes a speed rather than a new flow.
Worked Example
- Enter the bore diameter and the average flow speed.
- Read Q in SI, then in the trade units on the conversion card.
- Use the constriction card before buying fittings: it prices the speed you buy with area.
- Halving the diameter quadruples the velocity at the same Q — check the Reynolds page for what that does.
Defaults: 0.003927 m³/s — 62.244073 US gal/min. Half the bore: the same Q at 8.000000 m/s.
Strengths & Limits Of This Model
Where this engine is strong
- Continuity constriction card computed from your bore
- Exact US gallon conversion, full precision
Where it stops
- No pressure-loss or friction-factor pricing
- Circular sections only — no rectangular ducts
Practical Use Cases
Plumbing
size a pump or check a tap's delivery
Irrigation
litres per minute against emitter budgets
Teaching
continuity, made live on your own pipe
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Flow Rate Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does area use the square of the diameter?
Because the section is a circle: A = π·d²/4. The square is why pipe sizes jump in effect — a 100 mm main carries four times a 50 mm pipe at the same speed, sixteen times a 25 mm line. The card computes the section from your bore so the scaling is visible, not remembered.
Is average speed the same as the speed at the wall?
No — viscosity drags the water at the wall to a standstill, so the profile is peaked in the middle. The v you enter is the average that carries the volume; the profile shape belongs to the Reynolds page. For most sizing work the average is the honest number.
How exact is the US gallon conversion?
Exact by definition: 1 US gallon = 3.785411784 L, a defined number, so gallons per minute here is arithmetic carried out at full precision, never a rounded factor quoted from a table. The imperial gallon is a different animal (about 4.546 L) and the card does not mix them.
What does the constriction card actually assume?
Continuity only: the same volume per second must pass through a smaller section, so the speed rises by the ratio of areas. It does not price the pressure cost of that speed — that bill is the Bernoulli page's to collect.
Why is zero speed an answer and not an error?
A closed valve is a real state of a real pipe: the bore is real, the flow rate is honestly zero. The page prints the zero rather than refusing, because 'nothing is moving' is a measurement, not a failure to measure.
Can I enter a negative speed?
Not as a speed — a negative sign is direction, and the card asks for a magnitude. Reverse the flow by reading the pipe backwards; the rate is the same number either way.
Where do the losses go — bends, friction, fittings?
Out of this page. Q = A·v is pure bookkeeping and holds at every section regardless of losses; the losses price PRESSURE, not flow. Sizing the pump that pays those losses is a different calculation with friction factors on it.
How does this connect to the Reynolds page?
Directly: this page's speed and bore are that page's inputs. Halve the bore at constant Q and the speed quadruples — and so does the Reynolds number, moving the flow toward turbulence. The two pages are one decision read twice.