Bernoulli Equation Calculator

Solve for a missing pressure, velocity, or elevation between two points in steady incompressible flow using the Bernoulli equation with optional head loss.

How It Works

Formula

P_1 + \frac{1}{2} \rho v_1^2 + \rho g z_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g z_2 + \rho g h_{loss}

\frac{P_1}{\rho g} + \frac{v_1^2}{2g} + z_1 = \frac{P_2}{\rho g} + \frac{v_2^2}{2g} + z_2 + h_{loss}

Variables, symbols and units

$P$: Pressure(Pa, kPa, bar, psi)
$v$: Velocity(m/s, km/h, ft/s, mph)
$z$: Elevation(m, cm, ft)
$\rho$: Fluid density(kg/m^3, g/cm^3, lb/ft^3)
$g$: Gravity(m/s^2, ft/s^2)
$h_{loss}$: User-entered head loss(m, cm, ft)

Calculation method explained

Bernoulli balances pressure energy, velocity energy, and elevation energy between Point 1 and Point 2. Choose one unknown, enter the other terms, and the calculator rearranges the equation for that target. If you include head loss, the tool treats it as energy removed from the streamline.

The calculator evaluates the Bernoulli equation in two equivalent views. In pressure form it sums static pressure, dynamic pressure $\left(\frac{1}{2}\rho v^2\right)$ , and elevation pressure $\left(\rho g z\right)$ . In head form it shows pressure head $\left(\frac{P}{\rho g}\right)$ , velocity head $\left(\frac{v^2}{2g}\right)$ , elevation head, and optional loss head on one comparable scale. Velocity targets are solved from a square root, so a negative radicand is surfaced as an impossible state rather than hidden.

Frequently Asked Questions

What does this calculator assume?

It assumes steady, incompressible flow between two points on the same streamline. It uses only the values you enter plus an optional head-loss term.

Can I use gauge pressure or absolute pressure?

Yes, but be consistent. Use the same reference on both points. Mixing gauge on one side with absolute on the other breaks the balance.

What should I enter for head loss?

Enter any loss you already know as a head term, such as a measured or separately estimated total loss. This calculator does not estimate friction factors or loss coefficients for you.

Why can a velocity solve become impossible?

If the known pressure, elevation, and loss terms already consume more energy than the streamline has available, the velocity term would need a negative square root. The tool shows that explicitly instead of returning NaN.

What does this tool not do?

It is not CFD, not a pump-curve selector, and not a full pipe-design workflow. It does not infer roughness, turbulence losses, cavitation limits, compressibility, or fitting data.