Pressure Calculator

Key conversion factors: 1 atm = 101,325 Pa = 101.325 kPa = 14.696 psi = 1.01325 bar = 760 mmHg = 29.92 inHg = 407.2 inWC = 33.9 ftH₂O.

Quick approximations: 1 bar ≈ 14.5 psi ≈ 100 kPa (exact: 14.504 psi, 100 kPa). 1 psi ≈ 6.895 kPa ≈ 51.72 mmHg ≈ 27.68 inWC.

In practice:

• car tires use psi (32-44 psi)
• bicycle tires use psi or bar (road bikes 80-130 psi / 5.5-9 bar)
• scuba tanks use psi or bar (3,000 psi / 207 bar full)
• blood pressure uses mmHg (normal 120/80)
• weather reports use mbar or inHg
• HVAC systems use inWC (0.5-2.0 inWC typical duct pressure)
• industrial hydraulics use psi or MPa (hydraulic presses operate at 3,000-10,000 psi / 20-70 MPa)

Hydrostatic pressure increases linearly with depth: P = ρgh + P_atmospheric, where ρ is fluid density (1,000 kg/m³ for freshwater, 1,025 kg/m³ for seawater), g is gravity (9.81 m/s²), and h is depth.

Every 10 meters of water depth adds approximately 1 atmosphere (14.7 psi) of pressure. At 100 meters depth, pressure is approximately 11 atm (161.7 psi).

The Mariana Trench at 10,994 meters experiences approximately 1,099 atm (16,149 psi) — enough to crush most structures.

For practical applications: a residential water tower 50 meters tall provides 50 × 1,000 × 9.81 = 490,500 Pa ≈ 71 psi of water pressure at ground level — more than adequate for the 40-60 psi typical for household plumbing.

The ideal gas law PV = nRT relates pressure (P), volume (V), amount of gas (n in moles), the gas constant (R = 8.314 J/mol·K), and absolute temperature (T in Kelvin).

At constant temperature, halving the volume doubles the pressure (Boyle's law). At constant volume, temperature and pressure are proportional (Gay-Lussac's law).

Practical applications:

• a scuba tank filled to 3,000 psi at room temperature (293K) will reach 3,275 psi if left in a hot car (320K) — a 9.2% increase that could approach the tank's burst rating.
• Tire pressure changes by approximately 1 psi per 10°F of temperature change, which is why tire pressure monitoring systems (TPMS) alert during cold weather even without leaks.
• Industrial compressed air systems typically operate at 90-150 psi, with compressors sized based on cubic feet per minute (CFM) at the required pressure.

To calculate pressure, divide the applied force by the area it acts on: P = F/A. In SI units, force is in newtons (N) and area is in square meters (m²), giving pressure in pascals (Pa), where 1 Pa = 1 N/m².

For example, a 5,000 N force pressing on 0.002 m² produces P = 5,000 ÷ 0.002 = 2,500,000 Pa, which equals 25 bar or about 362.6 psi.

Because force and area are inversely related in this formula, concentrating the same force onto a smaller area sharply raises pressure — the principle behind knife edges and stiletto heels.

NIST defines the pascal as the coherent SI unit for pressure.

The SI unit of pressure is the pascal (Pa), defined by NIST and the BIPM as one newton per square meter (1 Pa = 1 N/m²).

Because the pascal is small, engineers use multiples:

• 1 kilopascal (kPa) = 1,000 Pa
• 1 megapascal (MPa) = 1,000,000 Pa

The bar (100,000 Pa) is a widely used non-SI metric unit, while the pound per square inch (psi) dominates US engineering. Standard atmospheric pressure is 101,325 Pa = 101.325 kPa = 1.01325 bar = 14.696 psi = 760 mmHg.

Encyclopaedia Britannica notes the unit honors Blaise Pascal, whose experiments established that fluid pressure acts equally in all directions.

Convert pressure units by multiplying by a fixed factor, since all pressure units measure the same quantity — force per area.

• To convert psi to bar, multiply by 0.0689476 (100 psi = 6.895 bar); to go from bar to psi, multiply by 14.5038.
• For kPa to psi, multiply by 0.145038 (100 kPa = 14.50 psi).
• To convert atm to psi, multiply by 14.696
• mmHg (torr) to kPa, multiply by 0.133322.

A reliable anchor point is standard atmosphere: 1 atm = 101.325 kPa = 14.696 psi = 1.01325 bar = 760 mmHg.

Khan Academy recommends checking conversions against this reference to catch order-of-magnitude errors before trusting a result.

Water pressure at depth follows the hydrostatic formula P = ρgh, where ρ is fluid density, g is gravitational acceleration (9.80665 m/s² per NIST), and h is depth in meters.

For freshwater (ρ ≈ 1,000 kg/m³) at 10 m depth: P = 1,000 × 9.80665 × 10 = 98,067 Pa, roughly 1 atmosphere or about 14.2 psi of gauge pressure. Total absolute pressure adds the 1 atm of air above: about 2 atm at 10 m.

Seawater is denser (≈1,025 kg/m³), so pressure rises slightly faster.

HyperPhysics (Georgia State University) emphasizes that hydrostatic pressure depends only on depth and density, not on the container's shape or the volume of water above.

Absolute pressure is measured from a perfect vacuum (0 Pa), while gauge pressure is measured relative to the surrounding atmosphere, so P_absolute = P_gauge + P_atmospheric. At sea level, P_atmospheric ≈ 101.325 kPa (14.696 psi).

A tire reading 32 psi on a gauge therefore holds about 32 + 14.7 = 46.7 psi absolute. Negative gauge readings indicate a partial vacuum: −50 kPa gauge equals roughly 51.3 kPa absolute.

Most everyday instruments — tire gauges, blood-pressure cuffs, and hydraulic gauges — report gauge pressure, whereas thermodynamic calculations and the ideal gas law require absolute pressure. Confusing the two is a leading cause of error in HVAC, diving, and process-engineering work.

Pressure calculations underpin engineering, medicine, and everyday life.

• Automotive engineers set tire pressures (typically 32–35 psi) to balance grip, wear, and fuel economy.
• Divers use hydrostatic pressure (P = ρgh) to plan decompression, since pressure roughly doubles by 10 m depth.
• Plumbers rely on P = ρgh to size water towers — a 50 m column yields about 71 psi at ground level, comfortably within the 40–60 psi household range.
• HVAC technicians measure duct static pressure in inches of water column, while hydraulic presses convert modest pump pressures into large forces via F = P × A.
• In medicine, blood pressure (normal 120/80 mmHg) is a gauge measurement clinicians monitor daily, as noted by Khan Academy's physiology resources.

A hydraulic press multiplies force using Pascal's principle: pressure applied to a confined fluid is transmitted undiminished throughout the fluid. Because P = F/A is equal on both pistons, F₁/A₁ = F₂/A₂, so a small input force on a small piston produces a large output force on a large piston.

For example, applying 100 N to a piston of area 0.001 m² creates P = 100 ÷ 0.001 = 100,000 Pa; that same pressure acting on a 0.05 m² piston yields F = P × A = 100,000 × 0.05 = 5,000 N — a 50-fold force gain matching the 50:1 area ratio.

HyperPhysics explains this force multiplication conserves energy: the larger piston moves proportionally less distance.

The most frequent pressure errors come from mismatched units and reference frames.

• Mixing units — using force in newtons but area in cm² instead of m² — produces results off by factors of 10,000, so always convert to SI before applying P = F/A.
• Confusing gauge and absolute pressure breaks any calculation that needs absolute values, such as the ideal gas law PV = nRT, which requires pressure in absolute units.
• Forgetting to add atmospheric pressure when computing total pressure at depth understates the true load on submerged equipment.
• Others reverse conversion factors (dividing instead of multiplying by 0.0689476 for psi to bar) or drop the 9.80665 m/s² gravity term in P = ρgh.

Cross-check against the 1 atm ≈ 14.7 psi anchor to catch these.