What is hydrostatic pressure?
Hydrostatic pressure is the pressure increase inside a stationary fluid as depth rises. The pressure difference is found from the product of density, gravitational acceleration and vertical depth difference.
This calculator is suitable for quick engineering checks in tanks, dams, diving, piezometers and manometer readings.
The ΔP = ρgh formula
- ΔP = ρ × g × h
- ρ = ΔP / (g × h)
- g = ΔP / (ρ × h)
- h = ΔP / (ρ × g)
Variables and SI units
- ΔP
- Hydrostatic pressure difference, expressed in pascal (Pa) in SI.
- ρ
- Fluid density. The SI base unit used here is kilogram per cubic meter (kg/m³).
- g
- Gravitational acceleration. The SI base unit is meter per second squared (m/s²).
- h
- Vertical depth or liquid-column height. The SI base unit is meter (m).
Difference between pressure rise and absolute pressure
The direct output of the formula is the hydrostatic pressure difference between the reference surface and the point of interest.
If you need absolute pressure, add the surface pressure separately: P_absolute = P_surface + ρgh.
How temperature affects density
Density changes with temperature, pressure, salinity and fluid composition. For more precise water or seawater calculations, use a density that matches the actual conditions.
For gases over large height changes, the constant-density assumption can become weak and a layered or integral approach may be more appropriate.
Technical reference
Density of water as a function of temperature
This technical sheet summarizes liquid-water density near atmospheric pressure as a table and graph.
Definition
Density is mass per unit volume and is a core input in hydrostatic pressure, level and fluid-property calculations.
For liquid water, density changes with temperature, so a fixed value of 1000 kg/m³ is not always adequate for precise work.
Formula
- ΔP = ρ g h
- ρ = m / V
Variables
- ρ
- Density, kg/m³
- m
- Mass, kg
- V
- Volume, m³
- ΔP
- Pressure difference, Pa
Short engineering example
Using a water density of about 998.20509 kg/m³ near 20 °C, the hydrostatic pressure rise at 10 m depth is ΔP ≈ 998.20509 × 9.80665 × 10 = 97.89 kPa.
Validity conditions and assumptions
- The data are selected at a constant pressure of 0.101325 MPa on the liquid-water branch.
- The temperature range is approximately 0.01 °C to 99.97 °C.
- The values come from an NIST output based on the IAPWS-95 formulation and serve as approximate engineering reference data.
| Temperature (°C) | Density (kg/m³) |
|---|---|
| 0.01 | 999.84376 |
| 10.01 | 999.70159 |
| 20.01 | 998.20509 |
| 30.01 | 995.64643 |
| 40.01 | 992.21253 |
| 50.01 | 988.03052 |
| 60.01 | 983.19068 |
| 70.01 | 977.75892 |
| 80.01 | 971.78417 |
| 90.01 | 965.30286 |
| 99.97 | 958.3675 |
Use cases
- Selecting a temperature-appropriate water density for hydrostatic-pressure work.
- Reducing error in tank, vessel and level calculations.
- Providing technical reference data for lab reports or coursework.
Common mistake
- Using 1000 kg/m³ at every temperature and ignoring the temperature effect.
Related calculator
Sources
- NIST Chemistry WebBook - Thermophysical Properties of Fluid Systems (water query)
- IAPWS-95 release page
Unit reference tables
Pressure units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Nanopascal | nPa | 1.0000000000e-9 Pa | Extremely small differential pressures and experimental measurements |
| Micropascal | µPa | 0.000001 Pa | Acoustics and precision sensor applications |
| Millipascal | mPa | 0.001 Pa | Very small pressure differences and laboratory instruments |
| Pascal | Pa | 1 Pa | Base SI pressure unit and scientific calculations |
| Hectopascal | hPa | 100 Pa | Meteorology and atmospheric pressure reporting |
| Kilopascal | kPa | 1,000 Pa | Building, HVAC and general engineering measurements |
| Megapascal | MPa | 1,000,000 Pa | Material strength and higher-pressure systems |
| Gigapascal | GPa | 1,000,000,000 Pa | Elastic modulus and advanced materials engineering |
| Terapascal | TPa | 1.0000000000e+12 Pa | Theoretical material models and extreme stiffness calculations |
| Millibar | mbar | 100 Pa | Legacy meteorology and process gauges |
| Bar | bar | 100,000 Pa | Compressors, hydraulics, pneumatics and industry |
| Standard atmosphere | atm | 101,325 Pa | Reference atmospheric pressure and laboratory work |
| Technical atmosphere | at | 98,066.5 Pa | Legacy technical documents and some mechanical tables |
| Kilogram-force per square centimeter | kgf/cm² | 98,066.5 Pa | Legacy pump, boiler and analog gauge usage |
| Torr | Torr | 133.322368421 Pa | Vacuum technology and laboratory pressures |
| Millimeter of mercury | mmHg | 133.322387415 Pa | Medical measurements and manometer readings |
| Millimeter of water column | mmH₂O | 9.80665 Pa | Low differential pressure and ventilation systems |
| Centimeter of water column | cmH₂O | 98.0665 Pa | Respiratory devices and low-pressure applications |
| Pound-force per square inch | psi | 6,894.75729317 Pa | Tires, hydraulics and Anglo-American equipment |
| Kilopound-force per square inch | ksi | 6,894,757.29317 Pa | Material strength and structural engineering |
| Pound-force per square foot | psf | 47.8802589803 Pa | Building loads and HVAC differential pressures |
| Inch of mercury | inHg | 3,386.389 Pa | Barometers, aviation and engine vacuum |
| Inch of water column | inH₂O | 249.08891 Pa | Gas lines and low-pressure air systems |
Density units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Kilogram per cubic meter | kg/m³ | 1 kg/m³ | Base SI density unit and engineering calculations |
| Gram per cubic meter | g/m³ | 0.001 kg/m³ | Very low-density gas or aerosol comparisons |
| Gram per liter | g/L | 1 kg/m³ | Solutions and fluid-mixture descriptions |
| Kilogram per liter | kg/L | 1,000 kg/m³ | Practical expression of liquid densities |
| Gram per milliliter | g/mL | 1,000 kg/m³ | Chemistry and laboratory density reporting |
| Gram per cubic centimeter | g/cm³ | 1,000 kg/m³ | Common engineering expression for liquids and solids |
| Pound per cubic foot | lb/ft³ | 16.018463374 kg/m³ | Imperial/US fluid and construction applications |
| Pound per cubic inch | lb/in³ | 27,679.9047102 kg/m³ | Imperial/US expression for high-density materials |
Depth units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Micrometer | µm | 0.000001 m | Microchannels and precision liquid-column differences |
| Millimeter | mm | 0.001 m | Small manometer heights and laboratory measurements |
| Centimeter | cm | 0.01 m | Bench experiments and short liquid columns |
| Meter | m | 1 m | Tank, well and general engineering depths |
| Kilometer | km | 1,000 m | Very large geophysical depth differences |
| Inch | in | 0.0254 m | Small column heights and device dimensions |
| Foot | ft | 0.3048 m | Diving, storage and field measurements |
| Yard | yd | 0.9144 m | Short field distances and open-area measurements |
Gravitational acceleration units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Meter per second squared | m/s² | 1 m/s² | Base SI acceleration unit |
| Centimeter per second squared | cm/s² | 0.01 m/s² | CGS-based acceleration reporting |
| Foot per second squared | ft/s² | 0.3048 m/s² | Imperial/US engineering calculations |
| Gal | Gal | 0.01 m/s² | Geophysics and gravimetry work |
| Standard gravity | g₀ | 9.80665 m/s² | Standard Earth gravity reference |
Worked examples
1000 kg/m³ × 9.80665 m/s² × 10 m = 98.0665 kPa
Using rounded engineering water, the hydrostatic pressure rise at 10 meters of depth is 98066.5 Pa, or 98.0665 kPa.
1 g/cm³ × 9.80665 m/s² × 100 cm = 9.80665 kPa
A density of 1 g/cm³ equals 1000 kg/m³. A depth of 100 cm equals 1 m, so the result is 9806.65 Pa, or 9.80665 kPa.
98.0665 kPa / (1000 kg/m³ × 9.80665 m/s²) = 10 m
For the given pressure difference in water, the vertical liquid height back-calculates to 10 meters.
Typical applications
- Bottom pressure estimates in water tanks and reservoirs
- First-pass pressure checks for dams and gate systems
- Pressure rise with depth in diving contexts
- Manometers and other liquid-column measurement setups
Assumptions and limitations
- The formula is intended for a stationary fluid with approximately constant density.
- h is the vertical depth difference, not the length of an inclined path.
- If density changes significantly with depth, an integral approach is required.
- For gases across large altitude changes, the constant-density assumption may not be suitable.
- The base result is a pressure difference; add surface pressure if absolute pressure is required.