Manometer Calculator

Enter the manometer fluid's density and the height difference between its two liquid columns to calculate the pressure difference (ΔP = ρ × g × h), plus absolute pressure and the mmHg equivalent.

Quick Facts

Manometer equation
ΔP = ρ × g × h
Pressure difference equals fluid density times gravity times the height difference between the two liquid columns.
Standard gravity
g = 9.80665 m/s²
The internationally accepted standard value used in most pressure calculations.
Common fluid densities
Mercury ≈ 13,590 kg/m³ · Water ≈ 1,000 kg/m³
Denser fluids (like mercury) give a smaller, more manageable column height for a given pressure.
Pressure unit reference
1 atm = 101.325 kPa = 760 mmHg
Useful for converting a manometer reading into standard atmosphere units.

Your Results

Calculated
Differential Pressure
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ΔP = ρ × g × h, in pascals
Differential Pressure
-
Same result in kilopascals
Equivalent Mercury Column
-
Pressure expressed as mmHg (1 mmHg = 133.322 Pa)
Absolute Pressure
-
Atmospheric pressure + differential pressure

Ready

Enter the fluid density and height difference, then press Calculate.

How a Manometer Calculates Pressure

A manometer is a simple, direct pressure-measuring instrument: typically a U-shaped tube partially filled with a liquid (commonly mercury, water, or a light oil). When one leg of the tube is connected to a pressure source and the other is left open to the atmosphere (or connected to a second pressure source), the liquid settles at a height difference that is directly proportional to the pressure difference between the two connection points. This calculator converts that height difference into pressure using the standard manometer equation, ΔP = ρ × g × h.

Deriving ΔP = ρ × g × h

The manometer equation comes straight from hydrostatic equilibrium. At the bottom of the U-tube, the pressure contributed by each fluid column must balance. Moving up from that common point, the pressure at the higher liquid surface is lower than at the lower surface by exactly the weight of the fluid column between them, per unit area: density (ρ) × gravitational acceleration (g) × height difference (h). Rearranging that balance gives the pressure difference between the two ends of the tube directly from a height difference you can measure with a ruler — no moving parts or electronics required.

Gauge pressure vs. absolute pressure

A manometer open to the atmosphere on one leg reads gauge pressure — the pressure above or below atmospheric. To get absolute pressure (the pressure relative to a perfect vacuum, which is what the ideal gas law and most thermodynamic equations require), add the local atmospheric pressure to the gauge reading: Pabsolute = Patmospheric + ΔP. Enter your local atmospheric pressure (101.325 kPa at sea level under standard conditions) to see both values side by side.

Choosing the right manometer fluid — and common mistakes

The fluid's density sets the scale of the instrument. Dense fluids like mercury (≈13,590 kg/m³) produce small, easy-to-read column heights even at high pressures, which is why barometric and vacuum pressures are still often quoted in millimeters of mercury (mmHg). Lighter fluids like water or light oils (used in inclined and micromanometers) stretch small pressure differences into larger, more readable heights, which is useful for measuring low-pressure HVAC duct pressures or furnace draft.

  • Mixing up height and pressure: the height difference h is not the pressure itself — always multiply by ρ and g to convert it to pascals.
  • Inconsistent units: keep density, gravity, and height in matching SI units (kg/m³, m/s², m) before multiplying, or use this calculator's unit selectors to convert automatically.
  • Forgetting atmospheric pressure: a manometer reading is gauge pressure by default; add atmospheric pressure only when you specifically need absolute pressure.
  • Wrong fluid for the range: mercury suits high pressures in a compact tube, while water or light oil suits small pressure differences, where a denser fluid would barely move.

Frequently Asked Questions

What is the formula for calculating pressure with a manometer?
A manometer measures pressure using the hydrostatic equation ΔP = ρ × g × h, where ρ is the density of the manometer fluid, g is gravitational acceleration (9.80665 m/s² standard), and h is the height difference between the two fluid columns. This gives the pressure difference between the two points connected to the manometer.
What's the difference between gauge pressure and absolute pressure?
Gauge pressure (what a manometer reads directly, ΔP = ρgh) is measured relative to the surrounding atmosphere. Absolute pressure adds the atmospheric pressure to the gauge reading: P_absolute = P_atmospheric + ΔP. Use absolute pressure for gas-law calculations and gauge pressure for comparing to ambient conditions.
Why is mercury commonly used as a manometer fluid?
Mercury's high density (about 13,590 kg/m³) means a given pressure produces a much shorter column height than lighter fluids like water, keeping the instrument compact. This is also why atmospheric pressure is traditionally reported in millimeters of mercury (mmHg), with standard atmospheric pressure equal to 760 mmHg.
How do I convert a manometer reading into other pressure units?
Once you have the pressure in pascals (ΔP = ρgh), divide by 1,000 for kilopascals, by 133.322 for mmHg, by 6,894.76 for psi, or by 101,325 for atmospheres. This calculator performs the pascal, kilopascal, and mmHg conversions automatically.

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