Hydrostatic Pressure Calculator (P = ρ·g·h)
Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight: P = ρ · g · h, where ρ is the fluid density, g is gravitational acceleration, and h is the depth. Greater depth means greater pressure. It's essential in hydraulics, scuba diving, civil engineering, and meteorology.
When to use this calculator
- Calculate water pressure at different depths.
- Solve hydrostatics problems in physics.
- Determine pressure in pipes and tanks.
- Understand depth limits for scuba diving.
- Calculate force on dams and retaining walls.
Real-world example: Pressure at the bottom of a 3 m swimming pool
- Given: depth = 3 m, fresh water density = 1,000 kg/m³, g = 9.81 m/s².
- Formula: P = ρ · g · h = 1,000 × 9.81 × 3.
- Result: P = 29,430 Pa = 0.29 bar ≈ 0.29 atm.
- Absolute pressure with atmosphere: 29,430 + 101,325 = 130,755 Pa ≈ 1.29 atm.
How it works
1 min readWhat Is Hydrostatic Pressure
Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight: P = ρ · g · h, where ρ is the fluid density (kg/m³), g is gravitational acceleration (9.81 m/s²), and h is the depth (m). Important: it does not depend on the shape of the container—only on depth.
Typical Fluid Densities
| Fluid | ρ (kg/m³) |
|---|---|
| Air | 1,225 |
| Vegetable Oil | 920 |
| Fresh Water | 1,000 |
| Seawater | 1,025 |
| Milk | 1,030 |
| Blood | 1,060 |
| Honey | 1,420 |
| Mercury | 13,600 |
Pressure vs. Depth Table (Fresh Water)
| Depth | Pressure (Pa) | Bar | Atm |
|---|---|---|---|
| 1 m | 9,810 | 0.098 | 0.097 |
| 10 m | 98,100 | 0.98 | 0.97 |
| 100 m | 981,000 | 9.81 | 9.68 |
| 1,000 m | 9,810,000 | 98.1 | 96.8 |
When to Use It and Common Mistakes
Frequently asked questions
What is hydrostatic pressure?
Hydrostatic pressure is the pressure exerted by a fluid at rest due to its weight. It increases linearly with depth: approximately every 10 meters of water adds 1 atmosphere of pressure.
How deep can a diver safely go?
Recreational scuba divers are typically limited to 40 meters (130 feet). At 30 meters (~4 atm), nitrogen narcosis becomes a serious concern, and decompression sickness becomes more likely.
Why does pressure increase with depth in water?
Water above you exerts weight, and that weight is distributed across the area below. The deeper you go, the more water is above you, creating greater cumulative pressure.
Does the shape of a container affect water pressure at the bottom?
No—this is the hydrostatic paradox. Pressure at the bottom depends only on depth and fluid density, not on the container's shape or total volume.
What is 1 atmosphere in pascals?
1 atm = 101,325 Pa = 1.01325 bar. This is standard air pressure at sea level.
How much pressure is at 100 meters deep?
At 100 meters in fresh water, the pressure is about 981,000 Pa or 9.68 atmospheres—far beyond safe recreational diving limits.
What's the difference between gauge and absolute pressure?
Gauge pressure is the pressure from the fluid alone (P = ρgh). Absolute pressure adds atmospheric pressure: P_absolute = P_gauge + 101,325 Pa.
Can this formula work for gases?
For short gas columns (like mercury in a barometer), yes. For tall columns, gas density changes with pressure, making calculations more complex.
How much pressure is in the Mariana Trench?
At about 11,000 meters deep, the Mariana Trench experiences roughly 1,100 atmospheres (~111 MPa)—more than 1,000 kg/cm².