Bernoulli Equation Calculator
Apply Bernoulli's equation to find unknown pressure, velocity, or elevation in an ideal fluid flow system between two points.
Results
What is it?
Bernoulli's equation describes conservation of energy in an ideal, incompressible, inviscid fluid along a streamline: P + ½ρv² + ρgz = constant. P is static pressure (Pa), ρ is fluid density (kg/m³), v is flow velocity (m/s), g is gravitational acceleration (9.81 m/s²), and z is elevation (m). It explains why aircraft wings generate lift and why water jets faster through narrow pipes.
How to use
Select which variable you want to solve for at Point 2. Enter all known values at both points. Leave the "solve for" variable's input at any value — the calculator will compute it from the Bernoulli equation.
Example scenario
Water pipe narrows: P1=200 kPa, V1=2 m/s, z1=0 m. At the narrow section: V2=4 m/s, z2=0 m. Solve P2: P2 = 200,000 + ½×1000×(4−16) = 200,000 − 6,000 = 194,000 Pa (194 kPa). Velocity increase causes pressure drop.
Pro tip
Bernoulli's equation assumes ideal flow — no viscosity, no energy losses. For real piping systems, add head loss terms (Darcy-Weisbach equation for friction losses, minor loss coefficients for fittings). The equation is most accurate for low-viscosity fluids (water, air at low Mach) along short flow paths.