Bernoulli Equation Calculator

About this calculator

This calculator applies Bernoulli's equation, P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂, which expresses conservation of energy for an ideal (incompressible, non-viscous) fluid in steady flow — the sum of static pressure, dynamic pressure (½ρv²) and hydrostatic pressure (ρgh) stays constant along a streamline. Solving for downstream pressure shows why fluid speeding up (e.g., through a narrowing pipe) causes its pressure to drop, and vice versa.

Mechanical and civil engineers use it to size pipes, ducts and venturi meters; aerospace engineers invoke a version of it to explain lift over an airfoil; and physics students use it to solve classic flow problems. Enter the upstream pressure, fluid density, and the two flow speeds (plus any elevation change) to find the downstream pressure.