Poiseuille's Law Calculator
The fourth power on radius that dominates everything.
Work out Poiseuille's Law. The fourth power on radius that dominates everything. Free, with no account and nothing to download.
Water 0.001, blood about 0.004, olive oil 0.08.
Laminar flow only. Above a Reynolds number of about 2,300 this overestimates the real flow rate.
Volumetric flow rate
3.927 L/s
12.5 m/s average · narrowing 10% leaves 65.6% of it
Q = πΔPr⁴/8μL. The fourth power on radius is what makes this equation matter: narrowing by 10% cuts flow by a third, and halving the radius drops it to a sixteenth. That sensitivity is why arterial narrowing has such disproportionate clinical effect, and why pipe diameter dominates plumbing design far more than length or pump pressure do. It holds for laminar flow only — check the Reynolds number first, because in turbulent flow this substantially overestimates what you will get.
How the Poiseuille's Law Calculator works
Enter radius, length, pressure drop and viscosity for the laminar flow rate. The r⁴ term is what makes this equation matter — narrowing a pipe by 10% costs a third of the flow.
Also known as: hagen poiseuille equation calculator · laminar flow rate calculator · blood flow resistance calculator · pipe flow resistance calculator
Frequently asked questions
What is Poiseuille's law?
Q = πΔPr⁴ / 8μL for steady laminar flow through a cylindrical pipe. Flow rises with the fourth power of radius and falls with length and viscosity.
Why does the fourth power matter so much?
Because small changes in radius have enormous effects. A 10% narrowing cuts flow by 34%; halving the radius drops it to a sixteenth. Nothing else in the equation comes close to that leverage.
Why does this matter clinically?
Arterial narrowing follows the same r⁴ relationship, so a modest plaque produces a disproportionate drop in blood flow. It is also why vasoconstriction is such an effective way to control circulation.
When does it stop applying?
As soon as the flow turns turbulent, above a Reynolds number of about 2,300. Past that it substantially overestimates the real flow rate, so check Re before trusting it.
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