Fluid Pressure Calculator

Engineer‑grade hydrostatic pressure calculations: P = ρ·g·h. Real‑time multi‑unit display and reverse depth.

Fundamental equation: P = ρ·g·h (gauge pressure). Absolute pressure = P0 + ρgh, where P0 is surface pressure.

kg/m³
Water (4°C) Seawater Gasoline Mercury Air (20°C)
m/s²
Add 101325 Pa for atmospheric pressure at sea level.
Hydrostatic Pressure (gauge)   ISO 80000‑4
49050 Pa
49.05 kPa
0.4905 bar
7.11 psi
0.484 atm
Pressure vs Depth
Current Depth
Reverse: Pressure → Depth
Depth: 5.00 m
Reverse: Pressure → Depth
Depth: 5.00 m

In‑depth: Hydrostatic Pressure Fundamentals

Derivation from Fluid Statics

Consider a column of fluid of density ρ, height h, and cross‑sectional area A. The weight of the fluid is W = ρ·g·h·A. This weight is supported by the pressure difference between bottom and top: (Pbottom – Ptop)·A = ρ·g·h·A. Hence Pbottom – Ptop = ρgh. If the top is open to atmosphere, Ptop = Patm, then absolute pressure at depth h is Pabs = Patm + ρgh.

Gauge vs. Absolute Pressure

Gauge pressure is the pressure relative to atmospheric pressure: Pgauge = ρgh. Most engineering sensors (e.g., tire pressure gauges) measure gauge pressure. Absolute pressure includes atmospheric pressure and is used in thermodynamics and deep‑sea applications.

Engineering Verification & Accuracy

This calculator implements the exact formula P = ρgh with unit conversions traceable to SI standards:

  • 1 m = 100 cm = 3.28084 ft = 39.3701 in (NIST SP 811).
  • 1 bar ≡ 100 000 Pa (IUPAC).
  • 1 atm = 101 325 Pa (standard atmosphere).
  • 1 psi = 6894.757 29 Pa (exact by definition).

For water at 4 °C (ρ = 1000 kg/m³, g = 9.80665 m/s²), pressure at 10 m depth is 98 066.5 Pa ≈ 0.9807 bar, matching oceanographic reference tables.

Practical Engineering Examples

Dam design
A 30 m high dam wall experiences maximum pressure at the base: P = 1000 kg/m³ × 9.81 m/s² × 30 m = 294 300 Pa (2.94 bar). The force on the wall is calculated by integrating pressure.
Submarine hull
At 300 m depth in seawater (ρ = 1025 kg/m³), pressure = 1025 × 9.81 × 300 ≈ 3.02 MPa (30.2 bar). Hulls are designed for this extreme pressure.

Compressibility Considerations

For liquids, density is nearly constant, so the linear formula holds up to thousands of meters (water compresses only ~1.8% at 4000 m). For gases, ρ varies with pressure; use the ideal gas law for accurate pressure‑depth profiles in air.

Key takeaway: Hydrostatic pressure increases by about 9.81 kPa per meter of freshwater column (or 1 atm per 10.3 m of water). This calculator provides fast, trustworthy results for engineering, education, and design.

Frequently Asked Questions

Pressure depends only on depth, density, and gravity – not on the amount of fluid or container shape (hydrostatic paradox). The weight is supported by vertical walls, but pressure at a given depth is uniform.

1 psi ≡ 6894.757 293 168 37 Pa (exact from the international inch and pound definitions). We use 6894.76 for readability.