Hong Life CalculatorsUnderstanding the manometer calculator — concept and principle
This calculator turns a manometer reading into a pressure difference for a vertical U-tube or an inclined-tube manometer. It accounts for the density of the manometer liquid and of the fluid above it, and gives the result in Pa, kPa, hPa, psi, mmH₂O and mmHg. It is used for HVAC duct pressure, filter checks, gas lines and lab measurements.
How it is calculated
Δp = (ρ_m − ρ_f) × g × h
Inclined tube: h = L × sin θ
- ρ_m is the manometer liquid density, ρ_f the density of the fluid above it, g gravity, h the vertical height difference (L is the length read along an inclined tube).
- Conventional units: 1 mmH₂O = 9.80665 Pa; 1 mmHg = 133.322 Pa; 1 psi = 6,894.757 Pa.
The principle
In a fluid at rest, pressure increases with depth by ρ g per metre. Walking down one leg of the U-tube and up the other, the only unbalanced part is the extra column of manometer liquid on one side, replaced on the other side by the lighter fluid above. That difference in weight per area equals the pressure difference. An inclined tube spreads the same height over a longer length, making small pressures easier to read.
Worked example
Default inputs: vertical U-tube, reading 150 mm, ρ_m = 998 kg/m³ (water), ρ_f = 1.2 kg/m³ (air), g = 9.80665 m/s².
- h = 150 mm = 0.15 m (vertical tube).
- Δp = (998 − 1.2) × 9.80665 × 0.15 = 1,466.3 Pa = 1.4663 kPa = 14.663 hPa.
- In psi: 1,466.3 ÷ 6,894.757 = 0.2127 psi.
- Conventional columns: 149.52 mmH₂O and 10.998 mmHg.
| Manometer liquid density ρₘ (kg/m³) | Pressure difference Δp (Pa) |
|---|---|
| 250 | 365.2 |
| 499 | 732.3 |
| 748 | 1,099.3 |
| 998 | 1,466.3 |
| 1,248 | 1,833.3 |
| 1,497 | 2,200.3 |
| 1,996 | 2,934.3 |
How to read the result
The conventional mmH₂O figure is slightly less than the 150 mm reading because the water is at 998 kg/m³, not the conventional 1,000 kg/m³, and air sits above it. For small pressures, such as duct static pressure of a few hundred pascals, an inclined manometer improves resolution.
Common mistakes
- Reading the height on one leg only instead of the difference between the two surfaces.
- Forgetting sin θ for an inclined tube.
- Ignoring the fluid above when it is a liquid; it can change the answer a lot.
- Mixing mm readings with m in the formula.
Frequently asked questions
Why use an inclined manometer?
It spreads a small vertical height over a longer scale, making low pressures easier to read.
What liquid is used in manometers?
Water, coloured oils and, historically, mercury for larger pressures.
Does the fluid above the liquid matter?
For gases it is a small correction; for liquids above it, it matters a lot.
How many pascals is 1 mmH₂O?
9.80665 Pa by convention.
Sources: Hydrostatic balance Δp = (ρ_m − ρ_f) g h; conventional units from standard gravity 9.80665 m/s² (NIST Special Publication 811)