What is a manometer?
A manometer is a scientific instrument used to measure fluid pressure, such as in gases and liquids. A manometer is a simple tool made of a uniform-diameter glass tube attached to a reservoir or a pipe. A manometer could also be just a tube used to measure atmospheric pressure and the pressure difference caused by fluids interacting with each other. A manometer usually contains a high-density liquid like mercury, but it can also be filled with water, oil, or any liquid, as long as we know its density or specific gravity. In certain applications, manometers may contain multiple liquids.
How does a manometer work?
Manometers work by following Pascal's Principle, which states that:
"Pressure applied to any part of an enclosed incompressible liquid will be transmitted equally in all directions through the fluid."
To understand Pascal's Principle, think of toothpaste in a tube. Squeezing the tube's body transmits pressure throughout the toothpaste until it oozes out of the nozzle. The amount of toothpaste squeezed out is the result of the amount of pressure applied to the tube. If we attach a U-tube manometer at the nozzle and squeeze again, the toothpaste rises in the manometer to a certain height, h.
We can calculate the pressure using the hydrostatic pressure equation, which is also the manometer equation:
P = ρ × g × h
Where:
- P — the pressure the liquid experiences at height h (Pa or psi);
- ρ (rho) — the liquid's density (kg/m³ or lb/ft³);
- g — the gravitational acceleration, 9.806 m/s² (or approximately 32.174 ft/s²); and
- h — the height of the fluid column (m or ft).
Pascal's Principle tells us that the pressure around the tube equals the fluid pressure at the given height, so the hydrostatic pressure equation is also the manometer equation.
How to use a manometer?
- Connect one end of the tube to the source whose pressure you want to measure.
- Let the fluid settle until the liquid column stops moving.
- Read the height difference h between the two liquid levels in the tube.
- Apply the equation P = ρ × g × h using the density of the manometer fluid.
How to use this manometer calculator?
- Choose your unit system — metric (SI) or American (imperial).
- Pick the manometer fluid from the presets (mercury, water, oil, glycerin, ethanol) or enter a custom density.
- Enter the column height h read from the manometer.
- Select the gravitational acceleration (Earth by default, or Moon, Mars, or custom).
- Click "Calculate" to get the hydrostatic pressure in Pa, kPa, bar, atm, psi, mmHg, and inHg.
Worked example
Let's say the manometer fluid (toothpaste) has a density of 1.3 g/cm³ (equivalent to 1,300 kg/m³), and h is 5.0 cm (or 0.05 m) from the nozzle. Substituting into the manometer equation:
P = 1,300 kg/m³ × 9.806 m/s² × 0.05 m = 637.4 Pa
Common manometer fluid densities
| Fluid | Metric (kg/m³) | Imperial (lb/ft³) |
|---|---|---|
| Mercury | 13534 | 845.0 |
| Water | 1000 | 62.43 |
| Seawater | 1025 | 64.0 |
| Engine Oil | 870 | 54.31 |
| Glycerin | 1260 | 78.66 |
| Ethanol | 789 | 49.26 |
Frequently Asked Questions
What is a U-tube manometer?
A U-tube manometer is a U-shaped tube partially filled with a liquid (often mercury or water). When different pressures act on the two open ends, the liquid levels become uneven. The height difference h between the two columns, together with the fluid density, gives the pressure difference via P = ρ × g × h.
Why is mercury used in manometers?
Mercury has a very high density (13,534 kg/m³), about 13.6 times denser than water. This means a tall pressure can be measured with a short, compact column, which keeps the instrument small. Mercury also does not stick to glass and has very low vapor pressure.
What units does a manometer measure pressure in?
The SI unit of pressure is the pascal (Pa). Manometer readings are also commonly given in millimeters of mercury (mmHg), inches of mercury (inHg), kilopascals (kPa), bar, atmospheres (atm), and pounds per square inch (psi). This calculator reports all of them at once.
Does the tube diameter affect the reading?
No. The hydrostatic pressure depends only on the fluid density, gravity, and the height of the column — not on the cross-sectional area or shape of the tube. This is known as the hydrostatic paradox.