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Bernoulli equation calculator

Bernoulli's principle for an ideal fluid: pressure + kinetic + potential head stays constant along a streamline, P + ½ρv² + ρgh = constant. Give the conditions at two points and leave one unknown — pressure, velocity or elevation — and it solves for it, revealing how a pipe that narrows speeds the flow and drops the pressure.

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Need Solved value, Quantity (unit)? The Bernoulli equation calculator derives it from Solve for, Fluid density (kg/m³), Pressure unit, P₁ (pressure), v₁ (m/s), h₁ (m), P₂ (pressure), v₂ (m/s), h₂ (m) in one step. For instance, with Solve for = Pressure P₁, Fluid density (kg/m³) = 998, Pressure unit = Pa, P₁ (pressure) = 200, v₁ (m/s) = 2, h₁ (m) = 0, P₂ (pressure) = 180, v₂ (m/s) = 0 and h₂ (m) = 0 it returns Solved value = -1,816 and Quantity (unit) = P₁ (Pa).

How to use it

  1. Enter your values: Solve for, Fluid density (kg/m³), Pressure unit, P₁ (pressure), v₁ (m/s), h₁ (m), P₂ (pressure), v₂ (m/s), h₂ (m).
  2. Read the result instantly: Solved value, Quantity (unit).

Frequently asked questions

How does the Bernoulli equation calculator work?

It takes Solve for, Fluid density (kg/m³), Pressure unit, P₁ (pressure), v₁ (m/s), h₁ (m), P₂ (pressure), v₂ (m/s) and h₂ (m) and derives Solved value and Quantity (unit) from them. The calculation is live as you type, so the result updates on every change.

Which values does the calculator ask for?

9 values: Solve for, Fluid density (kg/m³), Pressure unit, P₁ (pressure), v₁ (m/s), h₁ (m), P₂ (pressure), v₂ (m/s) and h₂ (m). Nothing else is required — no account, no file upload.

What does a typical calculation look like?

With Solve for = Pressure P₁, Fluid density (kg/m³) = 998, Pressure unit = Pa, P₁ (pressure) = 200, v₁ (m/s) = 2, h₁ (m) = 0, P₂ (pressure) = 180, v₂ (m/s) = 0 and h₂ (m) = 0, the calculator returns Solved value = -1,816 and Quantity (unit) = P₁ (Pa). Those figures come from running this exact tool, so you can reproduce them by entering the same values.

Which “Solve for” option should I choose?

You can pick between « Pressure P₁ », « Velocity v₁ », « Elevation h₁ », « Pressure P₂ », « Velocity v₂ » and « Elevation h₂ ». Each one changes what the calculator works out, so switch and compare — the default is « Pressure P₁ ».

What does it give for smaller values?

Scaled down to Solve for = Pressure P₁, Fluid density (kg/m³) = 499, Pressure unit = Pa, P₁ (pressure) = 100, v₁ (m/s) = 1, h₁ (m) = 1, P₂ (pressure) = 90, v₂ (m/s) = 1 and h₂ (m) = 1, Solved value comes out at 90. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Checking a homework answer, sizing something before building it, and getting an order of magnitude before committing to a design — a torque on a bolt, the force a spring returns, the frequency a circuit resonates at, how long light takes to arrive.

What is the most common mistake?

Feeding in a value in the wrong unit. Physics formulas assume SI throughout, so grams instead of kilograms or centimetres instead of metres shifts the answer by powers of ten without any warning.

How accurate is it, and what are the limits?

Ideal (inviscid, incompressible) flow — no friction or pump losses. Leave the field you're solving for at any value; it is ignored.

What is the difference between the Bernoulli equation calculator and the Lens Equation Calculator (Thin Lens)?

This one returns Solved value and Quantity (unit); the Lens Equation Calculator (Thin Lens) returns Result. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Buoyancy calculator is the closest one after this: Will it float or sink? Archimedes' principle: the buoyant force equals the weight of the displaced fluid, F = ρ·V·g. From the fluid density, the object's volume and mass, it computes the buoyant force, the weight, the net force, the object's density, the float/sink verdict and — if it floats — the fraction that sits below the surface.

Further reading

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ExplainerWhat Is the Reynolds Number? The Formula, the Units That Cancel, and Why 2 300 Is Only for PipesRe = ρvL/μ compares inertia with viscosity, and the units really do cancel. See the number worked out for honey, a household pipe, an artery, a swimmer and a wing — and why the 2 300 threshold belongs to pipe flow alone.ExplainerHow Buoyancy Works: Archimedes' Principle, and Why Ice Floats With 10.5 % Above WaterThe upward force equals the weight of the fluid pushed aside. That one sentence decides whether something floats, and if it floats, exactly how much of it stays under.ExplainerHow the Doppler Effect Works: The Formula, the Sign Convention, and Why Moving the Source Is Not the Same as Moving the ListenerFor sound, f' = f(v + v_o)/(v − v_s) — and getting the signs backwards is the classic error. Here is the convention spelled out, a 440 Hz source computed at four speeds, and why light needs a different equation entirely.ExplainerHooke's Law Explained: F = kx, Real Spring Constants, and Where It Stops HoldingHooke's law says force is proportional to stretch — but only below the elastic limit. Here is F = kx with worked numbers, what a 200 N/m spring actually feels like, and how springs combine.GuideThe Four Kinematics Equations: Which One to Use, and What Each One Leaves OutFive variables, four equations, and each equation is missing exactly one of them. Choose by looking at the variable the question never mentions.ExplainerProjectile Motion Explained: Range, Height, Flight Time — and Why 45° Is Not Always BestThree formulas cover the whole of projectile motion on level ground. The catch is level ground: the moment launch and landing heights differ, the 45° result stops being true.