Bernoulli's Equation Calculator
Enter 6 of 7 variables — the calculator solves for the missing one
Leave exactly one field blank — it will be solved automatically.
Result is negative — this may represent suction or an unphysical absolute pressure.
| Unit | Value |
|---|
Bernoulli Components (Pa)
| Component | Point 1 | Point 2 |
|---|
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Bernoulli's Equation Calculator Formula
Bernoulli's equation expresses conservation of mechanical energy along a streamline in steady, incompressible, inviscid flow.
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
P = static pressure, ρ = fluid density, v = fluid velocity, g = 9.80665 m/s² (standard gravity), h = elevation above datum. Subscripts 1 and 2 denote the two points along the streamline.
How to Use This Calculator
- Leave exactly one of the seven fields blank — that is the variable to solve for.
- Enter values for the remaining six fields. Use the unit dropdown beside each field to choose your preferred unit — you can mix and match freely (e.g., pressure in psi, velocity in ft/s, height in m).
- Common fluid densities: water ≈ 998 kg/m³ (0.998 g/cm³ or 1.937 slug/ft³); air at sea level ≈ 1.225 kg/m³.
- Click Calculate to solve for the missing variable.
- The result is shown in multiple unit equivalents. The Bernoulli Component Breakdown table (always in Pa) confirms energy conservation — the total at Point 1 and Point 2 must be equal.
Frequently Asked Questions
What is Bernoulli's equation?
Bernoulli's equation states that along a streamline in steady, incompressible, inviscid flow the sum of static pressure, dynamic pressure (½ρv²), and elevation pressure (ρgh) is constant. Where fluid speeds up, pressure drops — and vice versa. This principle explains how airplane wings generate lift, how venturi meters measure flow rate, and how a garden hose nozzle increases water speed.
Which variable should I leave blank?
Leave blank the variable you want to find. For example, to find the fluid speed at a downstream nozzle exit, leave v₂ blank and fill in P₁, v₁, h₁, P₂, h₂, and ρ.
Can I mix metric and imperial units?
Yes. Each field has its own unit dropdown. You can enter pressure in psi, velocity in ft/s, and height in metres all at the same time. The calculator converts every input to SI internally before solving, then converts the result back to all equivalent units. For another physics calculator that solves for a missing variable, see our Ohm's law calculator.
What are the assumptions behind Bernoulli's equation?
The equation applies to steady (time-invariant), incompressible (constant density), inviscid (frictionless) flow along a single streamline. It does not account for viscous losses, turbulence, heat transfer, or compressibility at high Mach numbers.
What density should I use for common fluids?
Water at 20 °C: approximately 998 kg/m³ (0.998 g/cm³, 1.937 slug/ft³). Air at sea level and 15 °C: approximately 1.225 kg/m³ (0.001225 g/cm³, 0.00237 slug/ft³). For other fluids, consult an engineering reference or fluid properties table.
What is the venturi effect?
The venturi effect is a direct application of Bernoulli's principle: when fluid flows through a constricted section of pipe, its velocity increases and its pressure decreases. This is used in carburetors, atomizers, and flow measurement devices like venturi meters.