Blood Flow Poiseuille Calculator

Enter vessel radius, length, blood viscosity, and pressure difference to calculate volumetric flow rate using the Hagen-Poiseuille equation.

Vessel Parameters

Inner radius of the vessel lumen.

Pressure drop from inlet to outlet.

Pa·s

Whole blood ≈ 0.0027 Pa·s; plasma ≈ 0.0012 Pa·s.

Quick Presets

Enter vessel parameters and click Calculate.

Typical Vessel Parameters

Vessel Radius Typical flow
Aorta 10–15 mm 4–5 L/min
Large artery 1.5–5 mm 50–500 mL/min
Arteriole 5–50 µm < 1 mL/min
Capillary 2–5 µm ~1 µL/min

Educational use only. Poiseuille's law assumes steady laminar Newtonian flow in a rigid straight cylinder. Actual blood flow is pulsatile, non-Newtonian, and occurs in elastic, curved vessels.

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Summary

Enter vessel radius, length, blood viscosity, and pressure difference to calculate volumetric flow rate using the Hagen-Poiseuille equation.

How it works

  1. Enter the vessel inner radius in micrometers (µm) or millimeters (mm) using the unit selector.
  2. Enter the vessel length in millimeters or centimeters.
  3. Set the pressure difference (ΔP) across the vessel in mmHg or Pa.
  4. Set the dynamic viscosity of blood — the default is 0.0027 Pa·s (whole blood at 37°C).
  5. Click Calculate to apply the Hagen-Poiseuille equation: Q = (π × r⁴ × ΔP) / (8 × η × L).
  6. Results are shown in µL/min, mL/min, and mL/s for easy comparison.

Use cases

  • Physiology students studying vascular resistance and flow dynamics.
  • Biomedical engineering coursework on cardiovascular fluid mechanics.
  • Comparing the effect of vessel radius changes (vasoconstriction/dilation) on blood flow.
  • Calculating flow in capillaries, arterioles, or larger conduit vessels.
  • Research and lab exercises estimating flow under known pressure gradients.
  • Exploring how viscosity changes (e.g. anemia, polycythemia) affect perfusion.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu