Engineering Tools

Bernoulli Equation Calculator

Solve for any unknown in the steady, incompressible Bernoulli equation — pressure, velocity, elevation, or fluid density — and see the full energy balance between two points along a streamline.

P₁+ ½ ρ v₁²+ ρ g h₁ = P₂+ ½ ρ v₂²+ ρ g h₂

Inputs

Pick the variable to solve for, then enter the rest. Results update as you type.

Solve for

Pressure unit

Point 1

Pressure P₁ (kPa)

Velocity v₁ (m/s)

Elevation h₁ (m)

Point 2

Pressure P₂ (kPa)

Velocity v₂ (m/s)

Elevation h₂ (m)

Fluid preset

Density ρ (kg/m³)

Gravity g (m/s²)

Reference

What the equation means

Bernoulli's principle is a statement of energy conservation for a flowing fluid: the sum of pressure, kinetic, and potential energy per unit volume stays constant along a streamline.

Variables & units (SI)

P	Static pressure (Pa). Use gauge or absolute consistently at both points.
v	Flow velocity (m/s).
h	Elevation above a common reference datum (m).
ρ	Fluid density (kg/m³). Assumed constant.
g	Gravitational acceleration, 9.81 m/s².

Assumptions & limits

Steady (time-independent) flow.
Incompressible fluid — constant density.
Negligible viscosity, so no friction or head loss between the points.
Both points lie on the same streamline.
No pump, turbine, or heat added between the two points.