Bernoulli Equation Calculator

It states that P plus half rho v squared plus rho g h stays constant along a streamline. This tool rearranges it to P2 = P1 + half rho times (v1 squared minus v2 squared) plus rho g times (h1 minus h2).

It assumes steady, incompressible, frictionless flow along a single streamline, with no energy added or removed by a pump, fan or turbine between the two points. Real pipes lose some pressure to friction, so treat the answer as an ideal upper bound.

The three energy terms must sum to the same total, so a larger velocity term forces a smaller pressure term. That is why the air over a wing or through a narrowing nozzle has lower static pressure than the slower air around it.

Heights are elevations measured on any consistent vertical axis you choose. If point 2 sits below point 1, give it a smaller or negative height, as in the 2 m drop example above.

It uses standard gravity, g = 9.80665 m/s squared, inside the elevation term rho g times the change in height. The height term only matters when the two points are at different elevations.

The tool works in SI units: density in kg/m3, pressures in pascals, velocities in m/s and heights in metres. Convert other units first, for example multiply bar by 100000 to get pascals, or km/h by 0.2778 to get m/s.

Not directly. This calculator only outputs the static pressure at point 2. To find an unknown velocity you would rearrange the equation by hand, or vary the input velocity until the resulting pressure matches your target.

No. The incompressible form used here is accurate for liquids and for gases well below roughly Mach 0.3. Near or above that speed density changes matter and you need the compressible energy equation instead.

No. The equation is solved in your browser as you type, so none of the numbers you enter leave your device.