A manometer is the most transparent pressure instrument ever built. There is no diaphragm to drift, no amplifier to zero and no calibration certificate hiding inside a housing — the reading is a height of liquid, and the pressure follows from that height, the density of the liquid and the strength of gravity. This calculator does that arithmetic for a vertical U-tube or an inclined-tube gauge, and reports the answer in the five units engineers actually use.
It also handles the correction almost every quick calculation skips: the fluid sitting above the manometer liquid has weight of its own, and it pushes back. Arb Digital built this page because the version of the formula that circulates online, Δp = ρgh, silently assumes that fluid is a vacuum. For mercury against air the error is one part in eleven thousand and nobody cares. For an oil gauge with water above it, the same shortcut overstates the pressure by more than 20%.
What This Manometer Calculator Does
Enter the reading, tell the calculator what liquid is in the tube and what is sitting on top of it, and you get the pressure difference between the two legs. The headline figure is in pascals, the SI unit; the supporting grid gives the same pressure in kilopascals, in pounds per square inch and in inches of water column, which is still the working unit for ventilation, filter monitoring and gas-appliance commissioning across much of the world.
The grid also reports the vertical height the calculation actually used: for an inclined gauge that is the reading multiplied by the sine of the tube angle, so a 300 mm sweep along a 15° tube is only a 78 mm change in true height. The tool is a conversion from a measured column to a pressure. It is not a fluid-flow calculation, and it does not know what your manometer is connected to. If you want the pressure at a given depth in a still tank rather than across two tappings, the hydrostatic pressure calculator is the single-column version of the same physics. If you already have a differential pressure and want the flow it implies through an orifice or a filter, that is the job of the differential pressure calculator.
How to Use It
- Pick the manometer type. A vertical U-tube is read as the height difference between the two liquid surfaces. An inclined gauge is read as a length measured along the sloping tube, and the angle field appears when you select it.
- Enter the reading and its unit. Millimetres, centimetres, metres or inches — use whatever the scale on the instrument is graduated in rather than converting by hand first.
- Choose the manometer liquid. Mercury, water and coloured gauge oil are pre-loaded at their densities near 20 °C. Select the custom option to type in a density from the fluid's own data sheet.
- Enter the density of the fluid above the column. Air at about 1.2 kg/m³ is the usual case. If both legs are flooded with process liquid down to the seal, enter that liquid's density instead — the correction is large.
- Adjust gravity if you need laboratory accuracy, then read the pressure difference and its equivalents in the grid.
The Formula: How It's Calculated
A manometer balances a pressure difference against the weight of a liquid column. Working down one leg and back up the other, every segment of stationary fluid contributes ρgh to the pressure, and at the balance point the two sides are equal. Rearranged, that gives the relation this calculator uses:
Δp = (ρm − ρf) × g × h
where ρm is the density of the manometer liquid, ρf is the density of the fluid filling the tube above that liquid, g is local gravitational acceleration and h is the vertical height difference between the two liquid surfaces. For an inclined gauge, h is not what you read: h = L × sin θ, where L is the length along the tube and θ is the angle from horizontal. The underlying derivation, along with the barometer and the open-tube manometer as worked cases, is set out in OpenStax University Physics Volume 1, section 14.2 “Measuring Pressure”.
A worked example, reproducible with the default values on this page: a mercury U-tube reads a 250 mm difference between the legs, with air at 1.2 kg/m³ above the mercury. The effective density is 13,534 − 1.2 = 13,532.8 kg/m³. Multiply by 9.80665 m/s² and by 0.250 m and you get 33,177.9 Pa — 33.18 kPa, 331.8 mbar, or 4.812 psi.
Why the Fluid Above the Column Is Not Optional
Textbook manometer problems almost always put air above the liquid, and air is so light that dropping it out of the formula changes nothing. That habit becomes a real error the moment the manometer is used the way industry actually uses it: with process liquid filling both impulse lines down to the seal.
Take a gauge-oil manometer at 826 kg/m³ measuring the differential across a filter in a water line. If the impulse lines are full of water at 998.2 kg/m³, the effective density driving the column is 826 − 998.2 = −172.2 kg/m³. That is negative, which is the calculator's way of telling you the instrument is upside down for this job — a liquid lighter than the process fluid will float, not sit in the bottom of a U-tube. Swap in mercury and the effective density is 13,534 − 998.2 = 12,535.8 kg/m³, about 7.4% lower than the raw mercury figure. Ignore that and every reading is 7.4% too high, systematically, in the same direction, which is exactly the kind of error that survives a whole commissioning campaign without anyone noticing.
Inclined Tubes: Where the Extra Resolution Comes From
An inclined manometer is a U-tube with one leg laid over at a shallow angle. The pressure still balances against vertical height, but you read the liquid position along the tube, and the ratio between the two is 1 ÷ sin θ. At 30° the scale is stretched by a factor of two. At 15° it is stretched by 3.86. At 5° the magnification is 11.5, and a pressure change that would move a vertical column one millimetre moves the inclined meniscus nearly twelve.
That magnification is free resolution, and it is why inclined gauges dominate low-pressure air work — duct static pressure, filter loading, burner draught. It is not free accuracy: the angle enters the answer directly, so a gauge knocked out of level introduces a proportional error in every reading. It also costs range, because stretching the scale divides the full-scale pressure by the same factor.
Gauge, Absolute and Differential: Three Readings, One Instrument
What a manometer reports depends entirely on what its two legs are connected to, and the same glass tube produces three different quantities. With one leg vented to atmosphere, the reading is a gauge pressure — the amount by which the process exceeds the air around it. With one leg evacuated and sealed, it is an absolute pressure, which is what a mercury barometer is. With both legs connected to two points in a process, it is a true differential, and atmospheric pressure cancels out of the answer entirely.
Confusing the first two is the classic error, because a gauge reading and an absolute reading of the same system differ by about 101 kPa and both look perfectly plausible on a data sheet. Adding or removing the local barometric pressure is the whole of the conversion, and the gauge to absolute pressure converter handles it directly. If you just need the same number expressed in a different unit — bar, torr, mmHg, atmospheres — the pressure converter does the rescaling without the physics. The definitions of the pascal and the conversion factors between it and the older pressure units are published by NIST in its pressure and gas flow unit conversions tables.
Where a Manometer Still Beats an Electronic Transmitter
Differential-pressure transmitters are more convenient than manometers in every way except one: they drift, and you cannot see them drifting. A manometer's reading is a length of liquid against a scale, traceable to a ruler and a density, with no span, no zero offset and no electronics in between. That is why manometers survive as the reference used to verify transmitters.
The trade-offs are equally real. A liquid column has no electrical output, responds too slowly to follow a pulsating pressure, must be mounted level, and is range-limited by the physical length of the tube. Mercury, still the densest practical fill, is a toxic material subject to handling and disposal controls in most jurisdictions. In practice the modern division of labour is that a transmitter takes the continuous reading and a manometer — or a deadweight tester — checks the transmitter. If your interest is what the differential implies about flow through a restriction rather than the differential itself, that calculation depends on the geometry of the element and belongs to the differential pressure calculator or, for full pipe-run losses, the pipe flow calculator.
Temperature, Meniscus and the Errors That Actually Matter
Liquid density is a function of temperature. Mercury expands by roughly 0.018% per kelvin, so a manometer filled at 20 °C and read at 35 °C carries a density error of about 0.27% if you keep using the 20 °C figure. That is small, but it is a bias rather than noise, so it does not average away. The water density calculator will give you a temperature-corrected figure to paste into the custom density field.
Meniscus reading is the next largest source of error and the least discussed. Mercury forms a convex meniscus and is read at the crown; water and oil form a concave one and are read at the trough. Reading one leg at the top and the other at the bottom puts a fixed offset into every measurement, and parallax adds to it, which is why laboratory manometers have mirrored scales. Capillary rise then matters in narrow bores: surface tension can lift a wetting liquid by a millimetre or more, and the two legs will not do it identically unless their bores match closely. Finally, the impulse lines must be genuinely free of trapped gas, because a bubble is a compressible spring that both offsets and slows the reading. The energy balance behind why a stationary column reads static pressure while a moving one does not is covered by Bernoulli's equation.
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Browse All Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Using ρgh with the process fluid flooding the lines — if both legs are full of liquid down to the seal, the effective density is the difference between the two fluids, not the manometer fluid alone.
- Reading an inclined gauge as if it were a height — the length along the tube must be multiplied by sin θ, and forgetting that overstates the pressure by the full magnification factor.
- Mixing meniscus conventions between the legs — read mercury at the crown on both sides, water or oil at the trough on both sides.
- Treating a vented-leg reading as an absolute pressure — it is a gauge pressure, and the two differ by roughly one atmosphere.
- Leaving air trapped in a liquid-filled impulse line — a bubble acts as a compressible spring and makes the reading both offset and sluggish.
Related Free Tools From Arb Digital
For the single-column case — pressure at a depth in a still tank — use the hydrostatic pressure calculator. To convert a reading between bar, psi, torr and pascals, use the pressure converter, and to shift between gauge and absolute reference use the gauge to absolute pressure converter. The differential pressure calculator takes a DP and turns it into the flow a metering element would report, while the pipe flow calculator handles losses along a whole run. Temperature-corrected fill densities come from the water density calculator, and the wider physics sits in Bernoulli's equation. Everything else is in the free online tools hub.
Frequently Asked Questions
It measures the difference in pressure between whatever is connected to its two legs, expressed as the height of liquid that difference can support. Vent one leg to atmosphere and the reading is a gauge pressure; connect both legs to a process and it is a true differential pressure with atmospheric pressure cancelled out.
Because it has weight and pushes down on the column too. The pressure difference is driven by the density difference between the two fluids, not by the manometer liquid alone. With air above mercury the correction is under 0.01%, but with water flooding the lines above a mercury column it is about 7.4%, which is far too large to ignore.
Read the length of liquid along the sloping tube, then multiply by the sine of the angle from horizontal to get the vertical height the pressure is balancing. A 300 mm reading on a tube at 15 degrees corresponds to a vertical height of only 77.6 mm, which is why the scale appears so much finer.
Because the magnification that stretches the scale also divides the full-scale pressure by the same factor. A tube at 15 degrees gives 3.86 times the resolution of a vertical column of the same length, and 3.86 times less range. Choosing the angle is a direct trade between the two.
It is more traceable rather than automatically more accurate. Its reading depends only on a length, a density and gravity, with no electronics to drift, which is why manometers are used to verify transmitters. Transmitters win on speed, range, logging and safety, and a liquid column cannot follow a fast or pulsating pressure at all.
Through the fill density. Mercury expands by roughly 0.018% per kelvin, so reading a gauge 15 kelvin above its fill temperature while still using the original density introduces a bias of about 0.27%. It is a systematic offset rather than random noise, so it does not average away over repeated readings.
One inch of water at 4 degrees Celsius is 249.0889 pascals, which is where the conventional conversion factor used by this calculator comes from. Inches of water remain the working unit for ventilation, filter differential pressure and gas-appliance commissioning because the numbers land in a convenient range.
This tool is provided for educational and engineering-estimate use. It applies the ideal static-column relation and does not account for capillary rise, meniscus reading error, tube tilt, thermal expansion of the scale or trapped gas in the impulse lines. Instrument calibration, mercury handling and any pressurised system work should be carried out by a qualified person against the applicable standard.
