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.
Formula
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
| Fluid | Density (kg/m³) | Typical use |
|---|---|---|
| Mercury (Hg) | 13,534 | High-pressure measurement (blood pressure, barometers) |
| Glycerin | 1,261 | Low-pressure, non-toxic applications |
| Seawater | 1,025 | Marine and offshore systems |
| Water | 998.2 | General low-pressure measurement |
| Ethanol | 789 | Low-density, low-freeze-point applications |
| Oil (light) | 870 | Hydraulic and HVAC systems |
| Gasoline | 750 | Fuel 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.