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Physics

Manometer Calculator

Enter the manometer type, fluid densities, and column heights to get the gauge pressure and absolute pressure at the measurement point instantly. Supports single-column, U-tube single-fluid, U-tube two-fluid, and differential U-tube configurations, with common preset fluids (water, mercury, oil, seawater) and full unit switching.

Your details

Single-column: one open tube dipped into the fluid. U-tube single: one manometer fluid. U-tube two: one process fluid below the manometer fluid. Differential: pressure difference between two pipe points.
The fluid inside the manometer tube. Mercury is most common for high-pressure systems; water for low-pressure.
Vertical height of the manometer-fluid column above the datum. For single-column this is the full reading.
Standard Earth gravity is 9.80665 m/s². Adjust for other locations or planets.
m/s²
Standard atmosphere is 101,325 Pa. Used only to compute absolute pressure. Gauge pressure is independent of this value.
Pa
Unit for the gauge and absolute pressure outputs.
Gauge pressure (Pₘₐᵤᵧᵉ)Medium pressure
19,908.4802

Pressure at the measurement point relative to atmospheric pressure.

Absolute pressure (Pₐᵇˢ)121,233.4802
Gauge pressure in Pa19,908.48
Pressure unit selectedPa
19,908.48 Pa
Vacuum<-1Low-1-10000Medium-low10000-100000Medium-high100000+
033k66k02550
Column height (cm)
Gauge pressure (Pa)
Column height (cm)Gauge pressure vs. column height
00
2.53k
57k
7.510k
1013k
12.517k
1520k
17.523k
2027k
22.530k
2533k
27.536k
3040k
32.543k
3546k
37.550k
4053k
42.556k
4560k
47.563k
5066k

Gauge pressure: 19908.4802 Pa

  • Your U-tube single-fluid manometer reads a gauge pressure of 19908.4802 Pa, which is the pressure relative to the local atmosphere.
  • Absolute pressure (gauge + atmospheric) is 121233.4802 Pa, which is the total pressure regardless of reference.
  • For reference: 19908.5 Pa = 149.3 mmHg = 2.8875 psi.

Next stepUse this gauge pressure in Bernoulli or pipe-flow equations, or compare against the rated pressure of your equipment.

Formula

Singlecolumn/Utube(onefluid):Pgauge=rhoghUtube(twofluids):Pgauge=rho2gh2rho1gh1Differential:dP=rho2g(h2h3)Absolutepressure:Pabs=Pgauge+PatmSingle-column / U-tube (one fluid): P_gauge = rho * g * h U-tube (two fluids): P_gauge = rho2 * g * h2 - rho1 * g * h1 Differential: dP = rho2 * g * (h2 - h3) Absolute pressure: P_abs = P_gauge + P_atm

Worked example

A U-tube manometer filled with mercury (rho = 13,534 kg/m^3) shows a column height of 150 mm = 0.150 m. With standard gravity g = 9.80665 m/s^2: P_gauge = 13534 * 9.80665 * 0.150 = 19,913 Pa = 19.9 kPa. Adding atmospheric pressure (101,325 Pa): P_abs = 19,913 + 101,325 = 121,238 Pa = 121.2 kPa.

What is a manometer?

A manometer is a simple instrument that measures fluid pressure by balancing it against a column of liquid whose weight is known. The most common form is the U-tube: a transparent tube bent into a U shape and partially filled with a dense liquid such as mercury or water. One arm is open to the atmosphere (or to a reference pressure), and the other is connected to the system being measured. The height difference between the two liquid surfaces is directly proportional to the pressure difference across the two arms. Because the instrument relies only on the density of the liquid and the height of the column - two quantities that are easy to measure accurately - manometers are among the oldest and most reliable pressure gauges in engineering and medicine.

Types of manometer and when to use each

A single-column manometer has one arm open to atmosphere and the other immersed in the tank or vessel whose pressure you want. It gives gauge pressure directly: P = rho * g * h. A U-tube single-fluid manometer uses the same principle but the process connection is at one end of the U rather than inside the tank. A U-tube two-fluid manometer has the process fluid occupying the lower part of the measuring arm and the denser manometer fluid (e.g. mercury) above a clear boundary; the formula subtracts the weight of the process-fluid column from the weight of the manometer-fluid column. A differential manometer connects both arms to different points in the same system - for example, upstream and downstream of a valve - and reads the pressure difference directly without needing the absolute atmospheric reference. Each type is included in this calculator.

Gauge pressure versus absolute pressure

Gauge pressure is measured relative to the local atmospheric pressure, so atmospheric conditions read zero. Absolute pressure is measured relative to a perfect vacuum and equals gauge pressure plus atmospheric pressure. For most engineering flow calculations - pipe losses, pump heads, Bernoulli - gauge pressure is the most convenient form. For thermodynamic calculations involving compressible fluids or phase changes, absolute pressure is required. Standard atmospheric pressure at sea level is 101,325 Pa (1 atm, 14.696 psi, 760 mmHg). This calculator outputs both values; adjust the atmospheric pressure input if you are at elevation or in a non-standard environment.

Pressure unit conversions

Pressure appears in many units across different industries. Pascal (Pa) is the SI base unit and equals one newton per square metre. A kilopascal (kPa) is 1,000 Pa. One bar equals 100,000 Pa, and one standard atmosphere (atm) is 101,325 Pa. Pounds per square inch (psi) is common in US engineering: 1 psi = 6,894.757 Pa. A millimetre of mercury (mmHg) - also called a Torr in vacuum work - is 133.322 Pa, and an inch of mercury (inHg) is 3,386.389 Pa. This calculator accepts column heights in metres, centimetres, millimetres, feet, or inches, and outputs pressure in any of those seven units.

Common manometer fluid densities

FluidDensity (kg/m³)Typical use
Mercury (Hg)13,534High-pressure measurement (blood pressure, barometers)
Glycerin1,261Low-pressure, non-toxic applications
Seawater1,025Marine and offshore systems
Water998.2General low-pressure measurement
Ethanol789Low-density, low-freeze-point applications
Oil (light)870Hydraulic and HVAC systems
Gasoline750Fuel system testing

Densities at approximately 20 C (68 F) and 1 atm. Exact values vary with temperature.

Frequently asked questions

What is the manometer formula?

For a single-fluid manometer: gauge pressure P = rho * g * h, where rho is the fluid density in kg/m^3, g is gravitational acceleration (9.80665 m/s^2), and h is the column height in metres. For a two-fluid U-tube: P = rho2 * g * h2 - rho1 * g * h1, where rho1 and h1 are the density and column height of the process (lower) fluid. For a differential manometer connected at two points: dP = rho * g * (h2 - h3).

What is the difference between gauge pressure and absolute pressure?

Gauge pressure is measured relative to atmospheric pressure, so atmosphere reads zero. Absolute pressure adds the local atmospheric pressure to the gauge reading and is referenced to a perfect vacuum. The relationship is: P_absolute = P_gauge + P_atmospheric. Standard atmospheric pressure is 101,325 Pa at sea level.

Why is mercury used in manometers?

Mercury has a very high density (about 13,534 kg/m^3 at 20 C), which is roughly 13.5 times denser than water. This means a mercury column only needs to be about 1/13.5 the height of a water column to balance the same pressure, making the instrument much more compact for high-pressure readings. Standard atmospheric pressure corresponds to a mercury column height of exactly 760 mm (29.92 inches). Mercury is also a liquid metal with negligible vapor pressure and does not dissolve in the process fluid in most cases, making it a stable reference medium. However, its toxicity means water-based and oil-based manometers are increasingly preferred where the pressures are low enough to allow the taller columns.

How do I read a U-tube manometer?

Connect one arm to the pressure source and leave the other open to atmosphere (or to the second pressure source for a differential reading). Wait for the liquid to stop moving, then measure the vertical height difference between the two liquid surfaces. Multiply that height by the fluid density and by g (9.80665 m/s^2) to get gauge pressure in pascals. If the connected arm is lower than the open arm, pressure is above atmospheric; if higher, pressure is below atmospheric (a partial vacuum).

Can this calculator handle negative gauge pressure (vacuum)?

Yes. If the column on the measurement side is higher than the reference side, the gauge pressure is negative, indicating the system is at below-atmospheric pressure. Enter the column height as measured and the calculator will return a negative gauge pressure value. Absolute pressure will still be positive as long as the vacuum is not perfect.

What column height do I enter for a two-fluid U-tube?

In a two-fluid setup, h2 is the height of the dense manometer fluid (e.g. mercury) above the lower meniscus (the fluid boundary inside the manometer tube). h1 is the height of the process fluid above that same datum on the other side. The gauge pressure at point A is rho2 * g * h2 minus rho1 * g * h1. If the process fluid is a gas, its density is negligible and you can set h1 to zero or use the single-fluid mode.

Sources

Written by Dr. Tomás Okafor, PhD Physicist · Lagos, Nigeria

Physicist specializing in classical mechanics, bringing 17 years of research and applied dynamics expertise to every calculator he reviews.

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