Bernoulli Equation Calculator

The Bernoulli equation is the cornerstone of fluid dynamics, the elegant statement that a flowing liquid or gas trades pressure, speed and height back and forth while keeping their total constant, and this calculator uses it to find the pressure at a second point in a flow from conditions at the first. Enter the fluid density, then the pressure, speed and height at point one, and the speed and height at point two, and it returns the pressure at point two along with the total energy per unit volume that stays constant along the streamline, updating as you type. The equation works because it is really a statement of energy conservation for a fluid: the pressure term, the kinetic energy term that grows with the square of the speed, and the gravitational term that grows with height, must always add to the same total. That single idea explains a remarkable range of everyday phenomena. Where a fluid speeds up, as it does squeezing through a narrow pipe or over a curved wing, its pressure must drop to compensate, which is the venturi effect and a large part of how aircraft generate lift. Where it slows or rises, the pressure climbs. The calculator assumes ideal flow, steady, incompressible and with negligible friction, which is an idealisation real fluids only approach, but a powerful one for understanding pipes, nozzles, venturi meters, atomisers and chimneys. That makes the tool genuinely useful for physics and engineering students learning fluid mechanics and checking homework, and for anyone wanting a quick estimate of how pressure changes as a fluid speeds up or changes height. Using SI units, pascals, metres per second, metres and kilograms per cubic metre, gives a pressure in pascals. The formula and a worked example are explained clearly below.

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Ideal, steady, incompressible flow with negligible friction. g = 9.81 m/s².