Hydrostatic Pressure Calculator
Calculate fluid pressure at depth using P = ρgh plus atmospheric pressure.
ρ: Fresh water=1000, Sea water=1025, Mercury=13,534, Blood=1060 kg/m³
What Is Hydrostatic Pressure Calculator?
Calculate fluid pressure at depth using P = ρgh plus atmospheric pressure. is a fundamental physics relationship with wide applications in science and engineering.
The formula arises from first principles and has been verified experimentally across many scales and conditions. Understanding the underlying derivation helps avoid common errors.
Engineers and scientists use this relationship daily in design, analysis, and problem-solving. The calculator handles the arithmetic so you can focus on the physics.
Pay careful attention to units — all formulas require SI units (meters, kilograms, seconds, Newtons, Pascals) unless a specific unit is built into the constant.
Formula Reference Table
| Solve For | Formula | Notes |
|---|---|---|
| Gauge pressure | P_gauge = ρgh | Above atmospheric |
| Absolute pressure | P_abs = P_atm + ρgh | P_atm = 101,325 Pa |
| Depth | h = P_gauge/(ρg) | From gauge pressure |
| Density | ρ = P_gauge/(gh) | From measured P and h |
| Atmospheric equivalent | 10.3 m of water = 1 atm | Sea water: 10.05 m |
| Pressure in bar | 1 bar = 10⁵ Pa; 1 atm = 1.01325 bar |
3 Worked Examples
Diver at 30 m in sea water (ρ=1025).
- P_gauge = 1025×9.81×30 = 301,657 Pa = 3.01 bar
- P_abs = 101,325 + 301,657 = 402,982 Pa ≈ 4 atm
- Air in lungs compresses to 1/4 of surface volume
Systolic BP = 120 mmHg. Pressure in Pa?
- P = ρgh = 13,534×9.81×0.120 = 15,932 Pa
- 1 mmHg = 133.3 Pa; 120×133.3 = 15,996 Pa ✓
Water tower: h = 30 m. Gauge pressure at base?
- P = 1000×9.81×30 = 294,300 Pa = 2.94 bar = 42.7 psi
- This provides adequate household water pressure
Real-World Applications
Common Mistakes to Avoid
Use SI units throughout.
Check the specific geometry or conditions.
Formula assumes ideal conditions.
Check positive directions.
Keep full precision until final answer.