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This hydrostatic pressure calculator works in three directions. Give it a gauge pressure and a fluid, and it returns the liquid level or depth that produced it. Give it a level and a fluid, and it returns the pressure a transmitter at the bottom will see. Give it a 4-20 mA reading and the calibrated range, and it returns the level right off the loop. All three rest on one equation, P = ρ × g × h: pressure equals density times gravity times the height of the liquid column.
The one input that decides whether the answer is right is the density, entered here as specific gravity (SG). Water is 1.0; seawater is about 1.025; diesel is about 0.85. Read the same 49 kPa on water and on diesel and the levels differ by 18 percent. Presets are built in, and the worked examples below show the math.
Calculator
Hydrostatic pressure, level and 4-20 mA
mA (level units above)
Grayed fields are not used by the selected mode. Pressures are gauge, relative to the liquid surface; results assume a vented or surface-referenced measurement.
The formula
Hydrostatic pressure is the weight of the liquid column above the measuring point: P = ρgh, where ρ is the density, g is 9.80665 m/s², and h is the vertical depth below the surface. In practical units, P in kPa = SG × 9.807 × h in meters, and the reverse, h = P / (SG × 9.807), turns a pressure reading back into a level. The size and shape of the tank play no part; a thin standpipe and a wide tank with the same liquid height read the same pressure at the bottom. The same equation gives the water pressure at any depth: at 10 m down, plain water adds about 98 kPa on top of whatever sits at the surface.
Both directions here use gauge pressure, measured relative to the surface. A vented hydrostatic level transmitter handles that reference automatically through its breather cable; in a closed, pressurized tank the vapor-space pressure sits on top of the liquid and a differential measurement is needed instead. For the unit conversions themselves, see the pressure units guide.
Worked examples
- 2 m of water: P = 1.0 × 9.807 × 2 = 19.61 kPa, which is 196 mbar or 2.85 psi. That is why a 2 m chilled-water sump is a natural fit for a 0-20 kPa or 0-200 mbar span.
- 35 kPa on water, read backward: h = 35 / (1.0 × 9.807) = 3.57 m (11.7 ft). If the tank is only 3 m tall, the reading, not the tank, is telling you something is wrong: check the SG setting or the zero.
- 5 m of diesel (SG 0.85): P = 0.85 × 9.807 × 5 = 41.7 kPa, against 49.0 kPa for the same 5 m of water. Convert a diesel tank reading with SG 1.0 and you overstate the level by 18 percent.
Density decides the level
The pressure-to-level conversion is only as good as the density you feed it. The table gives per-meter values for common liquids; for anything blended or temperature-sensitive, use the measured SG of the actual batch.
| Liquid | Typical SG | kPa per meter | psi per meter |
|---|---|---|---|
| Fresh water | 1.0 | 9.81 | 1.42 |
| Seawater | 1.025 | 10.05 | 1.46 |
| Diesel | 0.85 | 8.34 | 1.21 |
| Drilling mud (varies) | 1.2 to 2.0+ | 11.8 to 19.6 | 1.71 to 2.84 |
A useful cross-check in US units: 1 psi corresponds to 0.703 m (2.31 ft) of fresh water. Values are typical at ambient temperature; density moves with temperature and composition, so treat SG as a process variable, not a constant, on anything other than clean water.
Level from a 4-20 mA reading
On a calibrated loop you do not need the density at all: the transmitter already did the conversion. Level = level at 4 mA + (reading − 4) / 16 × span. A 12 mA reading on a 0-5 m range is 50 percent, so 2.5 m. The third calculator mode does this directly, and our 4-20 mA calculator covers the general current-to-units case. The assumption is a linear, correctly zeroed instrument; if the reading parks below 4 mA or above 20 mA, check the loop against the wiring guide before trusting any level number.
Sizing a new point instead? Compute the full-tank pressure with mode two and pick a submersible pressure transducer or one of the hydrostatic level sensors with a span at or just above it.
Application example
Oil and gas, mud logging unit. A drilling services contractor needed a 5 m range level transmitter, 24 VDC with a 4-20 mA output, for tanks in a mud logging unit. Drilling mud is exactly the case where the density term cannot be ignored: at SG 1.44 a full 5 m tank puts 70.6 kPa on the sensor, versus 49.0 kPa if it held water, and the mud weight changes from batch to batch. Scaling the level from pressure with the actual mud density, rather than assuming water, is what keeps the tank inventory numbers honest.
Related tools
The 4-20 mA calculator converts loop current to any engineering range and back. The absolute and gauge pressure calculator handles the reference conversion when a spec mixes PSIA and PSIG. All calculators live on the tools page.
FAQ
What is the formula for hydrostatic pressure?
P = ρgh: pressure equals fluid density times gravitational acceleration (9.80665 m/s²) times the depth below the surface. In everyday units, pressure in kPa = specific gravity × 9.807 × depth in meters. For gauge pressure that is the whole formula; for absolute pressure, add the pressure sitting on the surface.
What is hydrostatic pressure for dummies?
It is the squeeze from the weight of liquid above you. Go deeper and there is more liquid overhead, so the pressure rises; a denser liquid weighs more, so it rises faster. Nothing else matters, not the tank shape and not the total volume, which is why a narrow pipe and a wide tank filled to the same height press equally hard at the bottom.
How do you calculate hydrostatic pressure load?
Pressure on a wall grows linearly with depth, from zero at the surface to ρgH at the bottom. For a vertical wall of height H, the resultant force per meter of width is ρgH²/2, acting at H/3 above the base. For example, a 3 m water wall carries 1000 × 9.807 × 9 / 2, about 44.1 kN per meter of width.
How to calculate hydrostatic pressure in a tank?
Multiply the depth below the liquid surface by the density and by g, exactly as in an open pool; the tank walls do not change it. In a vented tank that is the pressure a bottom-mounted sensor reads. In a closed, pressurized tank, the gas pressure above the liquid adds on top, which is why closed tanks are measured with a differential pressure transmitter instead of a single gauge sensor.
Size the level measurement, not just the math
Tell us the tank height, the liquid and its SG, and whether the tank is vented or pressurized, and we will confirm the span and quote a hydrostatic level transmitter that fits. Tell us the application and we configure one unit, not a shelf part.
Written and technically reviewed by Wu Peng and the Instranova engineering team. Based on the hydrostatic equation P = ρgh with g = 9.80665 m/s², and field experience sizing submersible and hydrostatic level transmitters. Questions? Reach our application engineers.