Bernoulli Equation Pressure Calculator
Bernoulli's equation links a flowing fluid's pressure, speed and height along a streamline: where it speeds up or rises, its pressure falls, and where it slows or drops, its pressure rises. This calculator solves for the pressure at a second point from the pressure at the first, the two flow speeds and the two heights, for an ideal incompressible flow. It breaks out the dynamic and elevation contributions so you can see what drives the change. Fluid density and gravity are user-editable inputs so you can match water, air or another fluid.
Bernoulli formula
Dynamic term = 0.5 * rho * (v1^2 - v2^2)
Elevation term = rho * g * (h1 - h2)
P2 = P1 + dynamic term + elevation term
kPa = P2 / 1,000
A positive dynamic term means the fluid slowed (pressure recovered); a negative one means it sped up (pressure dropped). The elevation term behaves the same way for changes in height. P2 sums these onto the upstream pressure.
Applying the result
- Use consistent SI units: pressures in pascals, speeds in m/s, heights in metres, density in kg/m3.
- Use about 998 kg/m3 for water and about 1.225 kg/m3 for sea-level air.
- Bernoulli ignores friction; real pipes lose pressure to viscosity and fittings.
- The equation holds along one streamline for steady, incompressible flow.
Bernoulli equation: frequently asked questions
What is Bernoulli's equation?
Bernoulli's equation states that for an ideal (inviscid, incompressible, steady) flow, the sum of static pressure, dynamic pressure and gravitational pressure is constant along a streamline: P + half * rho * v^2 + rho * g * h is the same at every point. This calculator rearranges it to solve for the pressure at a second point given the first.
How is the downstream pressure found?
P2 = P1 + half * rho * (v1^2 - v2^2) + rho * g * (h1 - h2). Where the fluid speeds up (v2 greater than v1), pressure drops; where it rises in height (h2 greater than h1), pressure also drops. The calculator computes each term so you can see the contributions.
What assumptions does Bernoulli's equation make?
It assumes steady, incompressible, inviscid (frictionless) flow along a single streamline. Real flows with viscosity, turbulence, heat transfer or compressibility deviate from it. It is nonetheless an excellent first approximation for many liquid and low-speed gas flows.
What density and gravity should I use?
Use the fluid's density (about 998 kg/m3 for water near room temperature, about 1.225 kg/m3 for air at sea level) and the local gravitational acceleration (about 9.80665 m/s2). Both are user-editable inputs so you can match your fluid and location.
Official sources
- NASA Glenn Research Center: Bernoulli's Equation.
- U.S. National Institute of Standards and Technology: SI units reference.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.