Bernoulli Equation Solver Calculator

Solver Inputs

Select the unknown variable, enter known values, and submit. Units can be changed anytime.

Solve for (unknown)

The selected field is treated as unknown.

Pressure unit

Velocity unit

Elevation and head unit

Density unit

Gravity unit

Point 1

Pressure P1

Static pressure at point 1.

Velocity v1

Average speed at point 1.

Elevation z1

Height relative to a reference datum.

Point 2

Pressure P2

Static pressure at point 2.

Velocity v2

Average speed at point 2.

Elevation z2

Height relative to the same datum.

Fluid and system terms

Density ρ

Typical water: 1000 kg/m^3.

Gravity g

Standard: 9.80665 m/s^2.

Pump head h_p

Added energy per weight (head units).

Turbine head h_t

Extracted energy per weight (head units).

Head loss h_L

Friction and minor losses (head units).

Formula Used

This solver uses the extended Bernoulli equation between point 1 and point 2:

P1/(ρg) + v1²/(2g) + z1 + h_p − h_t − h_L = P2/(ρg) + v2²/(2g) + z2

P/(ρg) is pressure head.
v²/(2g) is velocity head.
z is elevation head.
h_p, h_t, h_L are pump, turbine, and loss heads.

How to Use This Calculator

Select the variable you want to solve for.
Choose consistent units for pressure, velocity, and elevation.
Enter the known values at point 1 and point 2.
Provide density and gravity, then optional heads and losses.
Press Calculate to view results above the form.
Use the CSV or PDF buttons to export your result.

Example Data Table

Example values (solve for P2):

Unknown	P1 (kPa)	v1 (m/s)	z1 (m)	v2 (m/s)	z2 (m)	ρ (kg/m^3)	g (m/s^2)	hL (m)	Estimated P2 (kPa)
P2	200	2.0	1.0	3.0	0.0	1000	9.80665	0.2	~189.0

Your result may differ slightly due to rounding and unit choices.

Solver Inputs

Formula Used

How to Use This Calculator

Example Data Table

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