How this instrument works
A manometer measures pressure by balancing it against the weight of a fluid column. At the base of a U-tube, the pressure pushing down on one side equals the weight per unit area of the fluid column standing higher on the other side. Cancel the shared cross-section and what remains is ΔP = ρgh — density times gravitational acceleration times the height difference between the two legs, a force balance rather than an empirical fit.
Mercury became the classical manometer fluid because of that density term: at 13,600 kg/m³, a mercury column needs only millimetres of height to register everyday pressures, which is also why blood pressure and barometric pressure are still quoted in mmHg. A water manometer measuring the same pressure would need a column about 13.6 times taller, which is impractical past a few kPa — a reason low-pressure duct gauges use water and higher-pressure gauges use mercury or oil.
The formula assumes the fluid is incompressible, at rest, and sitting in a gravity field that does not change along the column — true for a lab bench, not for a mercury barometer carried up a mountain without correction. The common mistake is reading the height of one leg instead of the difference between the two; a manometer's zero sits where the two menisci line up level, and only the gap that opens between them once pressure is applied belongs in h.
- Enter the Manometer fluid density — 13,600 kg/m³ for mercury, 1,000 kg/m³ for water, or your working fluid's own value.
- Enter the Column height difference: the vertical gap between the two menisci, not the tube length on either leg.
- The instrument multiplies by standard gravity, 9.80665 m/s², automatically — no separate gravity entry is needed.
- Read the Pressure difference field; switch its unit to kPa, psi, or mmHg as the job requires.
Worked example — a 50 mm mercury column
A mercury manometer reads a 50 mm gap between its two legs. Set Manometer fluid density to 13,600 kg/m³ for mercury and Column height difference to 0.05 m. The formula gives ΔP = 13,600 × 9.80665 × 0.05 = 6,668.522 Pa — about 6.67 kPa.
That is roughly 6.6% of standard atmospheric pressure, 101,325 Pa: small enough to matter on a gas-line pressure check, far too small to register on a car tyre gauge. It is also why mercury manometers remain a calibration reference — a height read off a steel rule converts straight to a pressure figure with no sensor to drift or need recalibrating.
Questions
Why does mercury work better than water for a manometer?
Because mercury is far denser — 13,600 kg/m³ against water's 1,000 kg/m³ — the same pressure produces a column about 13.6 times shorter. A pressure that needs a 68 cm water column collapses to about 5 cm of mercury, which kept mercury gauges compact enough for a bench while an equivalent water column would need a tube roughly two metres tall for the same range.
What is the difference between gauge and absolute pressure here?
A basic open U-tube manometer reads gauge pressure: the difference between the measured pressure and whatever pushes on the open leg, usually the atmosphere. To get absolute pressure, add the current atmospheric pressure, about 101,325 Pa at sea level, to the ΔP this calculator returns. A closed, evacuated reference leg gives absolute pressure directly, with no addition needed.
Does temperature change the reading?
Yes, because density shifts with temperature. Mercury's density falls by roughly 0.018% per °C, which is negligible for a shop-floor pressure check but matters for calibration-grade barometers, which apply a published temperature correction table rather than trust the density value entered here to hold exactly at every temperature the instrument sees.
Can I use ΔP = ρgh when the leg above the fluid is filled with gas?
Only approximately, and usually safely so. The formula ignores the weight of whatever sits above the measuring fluid, treating it as negligible next to the fluid's own weight. Air is roughly 1,000 times less dense than water and over 10,000 times less dense than mercury, so for either fluid the omitted term is normally smaller than the error in reading the meniscus by eye.
What height should I actually measure on the tube?
The vertical distance between the two fluid menisci, not the length of tubing on either side. Tilt in the mounting, extra coiled tubing, or an uneven bench do not change the reading — only the straight vertical gap between where each surface sits matters, because that vertical gap is the column of fluid whose weight is doing the balancing.
Does the formula still hold if the tube is angled instead of vertical?
Only after you convert. Angling a leg to stretch a small reading along a longer, easier-to-read tube is a genuine technique for measuring tiny pressures, but the h in ΔP = ρgh is always the vertical height difference. Multiply the length read along a tilted tube by the sine of its angle from horizontal to recover the true vertical h before using this formula.