Pressure Calculator
Calculate pressure using the pressure formula P=F/A (force per unit area), hydrostatic pressure P=ρgh at any fluid depth, convert between absolute and gauge pressure, find pressure at altitude using the ISA formula, and convert all pressure units (Pa, psi, bar, atm, mmHg, inHg). This pressure calculator covers every pressure formula in physics and engineering.
The hydrostatic pressure formula P = ρgh gives pressure due to a fluid column. Every 10 m of water adds ≈ 98,070 Pa ≈ 1 atm of pressure.
| Depth (m) | Depth (ft) | Gauge P (kPa) | Gauge P (psi) | Total P (atm) |
|---|
Absolute pressure is measured from perfect vacuum. Gauge pressure is relative to atmospheric pressure. P_absolute = P_gauge + P_atmospheric (101,325 Pa standard).
Uses the International Standard Atmosphere (ISA) formula: P(h) = 101325 × (1 − 0.0000225577h)^5.25588 for the troposphere (0–11,000m).
| Altitude | Pressure (Pa) | Pressure (mb) | Pressure (inHg) | Temp (°C) |
|---|---|---|---|---|
| 0 m (sea level) | 101,325 | 1013.25 | 29.92 | 15.0 |
| 1,000 m | 89,875 | 898.75 | 26.55 | 8.5 |
| 2,000 m | 79,495 | 794.95 | 23.48 | 2.0 |
| 3,000 m | 70,109 | 701.09 | 20.72 | −4.5 |
| 5,000 m | 54,048 | 540.48 | 15.96 | −17.5 |
| 10,000 m | 26,500 | 265.00 | 7.83 | −50.0 |
| 11,000 m | 22,632 | 226.32 | 6.68 | −56.5 |
Pressure head h = P/(ρg) converts pressure to the equivalent column height of fluid. Used in hydraulics, pump engineering, and HVAC. Inverse: P = ρgh.
Enter any pressure value in any unit — instantly converts to all pressure units (Pa, kPa, MPa, bar, psi, atm, mmHg, inHg, and more).
Table A — Pressure Formulas Quick Reference
| Formula | Equation | Variables | Notes |
|---|---|---|---|
| Basic pressure | P = F/A | Force F (N), Area A (m²) | SI unit: Pascal (Pa = N/m²) |
| Hydrostatic pressure | P = ρgh | Density ρ, depth h, gravity g | Gives gauge pressure |
| Absolute pressure | P_abs = P_gauge + P_atm | P_atm = 101,325 Pa | From perfect vacuum |
| Pressure head | h = P/(ρg) | Fluid density ρ | Equivalent column height |
| Pressure altitude | P = 101325(1−0.0000225577h)^5.25588 | h in meters (troposphere) | ISA formula |
| Fluid pressure diff | ΔP = ρgΔh | Height difference Δh | Between two points |
Table B — Standard Atmospheric Pressure in All Pressure Units
| Unit | Value | Notes |
|---|---|---|
| Pascal (Pa) | 101,325 | SI base unit of pressure — exact definition |
| kilopascal (kPa) | 101.325 | |
| megapascal (MPa) | 0.101325 | |
| bar | 1.01325 | 1 bar = 100,000 Pa ≠ 1 atm |
| millibar (mbar) | 1013.25 | = hPa, used in meteorology |
| psi | 14.6959 | Pounds per square inch |
| atm | 1.000 (definition) | Standard atmosphere = exact 101,325 Pa |
| mmHg (torr) | 760.000 | Exact by definition of 1 atm |
| inHg | 29.9213 | Used in aviation, weather |
| kgf/cm² | 1.03323 | Kilogram-force per cm² |
Table C — Water Pressure at Common Depths
| Depth | Gauge P (kPa) | Gauge P (psi) | Total P (atm) | Notes |
|---|---|---|---|---|
| 1 m (3.28 ft) | 9.81 | 1.42 | 1.10 | Just below surface |
| 5 m (16.4 ft) | 49.0 | 7.11 | 1.48 | Snorkeling depth |
| 10 m (32.8 ft) | 98.1 | 14.2 | 1.97 | ≈ 1 extra atm per 10m |
| 30 m (98 ft) | 294 | 42.6 | 3.90 | Recreational dive limit |
| 100 m (328 ft) | 981 | 142 | 10.7 | Technical diving |
| 300 m (984 ft) | 2,943 | 427 | 30.0 | Submarine depth |
| 11,000 m | 107,930 | 15,655 | 1,076 | Mariana Trench |
Pressure Calculator — P=F/A, P=ρgh, Absolute, Gauge & Altitude
This pressure calculator computes pressure using the pressure formula P=F/A (force divided by area), hydrostatic pressure P=ρgh for any fluid at depth, converts between absolute and gauge pressure, finds pressure at altitude using the ISA formula, and converts between all pressure units including Pa, psi, bar, atm, and mmHg.
Pressure Formula — P = F/A
The pressure formula P = F/A defines pressure as force per unit area. P is pressure in Pascals (Pa = N/m²), F is the perpendicular force in Newtons, and A is the contact area in square meters. The pressure equation P = F/A shows why sharp knives cut easily — the same force applied over a tiny area creates enormous pressure — and why snowshoes prevent sinking (large area = low pressure).
The pressure calculation formula can be rearranged: F = P × A (force from pressure and area) and A = F/P (area from force and pressure). All three forms are the same equation.
Example: Elephant on one foot (5,000 kg, foot area 0.05 m²)
- Force: F = m × g = 5000 × 9.807 = 49,033 N
- Area: A = 0.05 m²
- Pressure formula: P = F/A = 49,033 / 0.05 = 980,665 Pa = 980.7 kPa = 142.3 psi
Hydrostatic Pressure — P = ρgh (Pressure at Depth)
The hydrostatic pressure formula P = ρgh gives pressure in any static fluid at depth h. ρ (rho) is the fluid density in kg/m³, g = 9.807 m/s², and h is depth below the surface in meters. Hydrostatic pressure is why deep-sea submarines need thick hulls — every 10 meters of water adds approximately 98,070 Pa ≈ 1 atmosphere of pressure.
The fluid pressure equation P = ρgh gives gauge pressure only (pressure above atmospheric). For total absolute pressure underwater: P_total = P_atm + ρgh. The static pressure formula P = ρgh applies equally to water, mercury, oil, or any fluid — including air (where it gives the variation of atmospheric pressure with altitude).
Rule of thumb (static water pressure): Every 10 m of fresh water ≈ 0.970 atm additional pressure. Every 10 m of seawater ≈ 0.994 atm. At 30 m (recreational dive limit): total pressure ≈ 4 atm = 58.8 psi — four times the surface pressure. This is why scuba divers decompress when ascending.
Absolute vs Gauge Pressure — What's the Difference?
Absolute pressure is measured from absolute zero pressure (perfect vacuum). Gauge pressure is measured relative to atmospheric pressure (101,325 Pa). The absolute pressure formula is: P_absolute = P_gauge + P_atmospheric. The gauge pressure formula is: P_gauge = P_absolute − P_atmospheric.
- Car tire at "35 psi" → 35 psig (gauge) = 35 + 14.696 = 49.7 psia (absolute)
- Blood pressure "120/80 mmHg" → gauge pressure relative to atmosphere
- A perfect vacuum → absolute pressure = 0 Pa, gauge pressure = −101,325 Pa
- Standard atmosphere → absolute = 101,325 Pa, gauge = 0 Pa (by definition)
PSIA vs PSIG: PSIA = pounds per square inch absolute. PSIG = pounds per square inch gauge. They always differ by 14.696 psi (= 1 atm) at sea level. Never confuse them — a tire at 0 psig is flat (absolute pressure = 14.696 psia = 1 atm), not a vacuum.
Pressure Altitude — The ISA Formula
The pressure altitude formula from the International Standard Atmosphere (ISA) predicts how atmospheric pressure decreases with altitude. The pressure altitude calculator uses:
At 10,000 m (typical cruise altitude), pressure altitude gives only 26,500 Pa — just 26% of sea level pressure. This is why aircraft cabins are pressurized. The inverse formula — altitude from pressure — is: h = 44330.77 × (1 − (P/101325)^0.190263). Pilots use pressure altitude to calibrate altimeters using exactly this ISA formula.
Pressure Head — Converting Pressure to Fluid Column Height
Pressure head (h = P/ρg) expresses any pressure as the equivalent height of a specific fluid column. "50 feet of head" means pressure equivalent to a 50-foot water column = 21.7 psi = 149.5 kPa. The pressure head formula h = P/(ρg) is used in hydraulics, pump engineering, and HVAC because pump performance is described in "head" independently of fluid density.
Pressure Unit Conversion — Pa, PSI, Bar, ATM, mmHg
All pressure units convert through Pascals (Pa) — the SI unit of pressure = 1 N/m². Key conversion facts: standard atmosphere = 101,325 Pa (exact definition). 1 bar = 100,000 Pa (note: 1 atm ≠ 1 bar — they differ by 1,325 Pa). 1 psi = 6,894.757 Pa. 1 mmHg = 133.322 Pa (used in medicine and meteorology). 1 atm = 760 mmHg = 29.921 inHg = 14.696 psi = 1.01325 bar.
| From → To Pa | Multiply by | Example |
|---|---|---|
| atm → Pa | 101,325 | 1 atm = 101,325 Pa |
| bar → Pa | 100,000 | 1 bar = 100,000 Pa |
| psi → Pa | 6,894.757 | 14.696 psi = 101,325 Pa |
| mmHg → Pa | 133.322 | 760 mmHg = 101,325 Pa |
| inHg → Pa | 3,386.389 | 29.921 inHg = 101,325 Pa |
| kPa → Pa | 1,000 | 101.325 kPa = 101,325 Pa |
Common Mistakes in Pressure Calculations
Mistake 1 — Confusing Gauge and Absolute Pressure
- ❌ Wrong: A tire at "35 psi" has 35 psia absolute pressure
- ✅ Correct: 35 psi gauge (psig) = 35 + 14.696 = 49.696 psia
- A vacuum gauge reads negative gauge pressure but always positive absolute pressure.
Mistake 2 — Using Diameter Instead of Radius for Circular Area
- ❌ Wrong: A = πd² = π × (0.1)² = 0.0314 m² for a 10cm diameter piston
- ✅ Correct: A = πr² = π × (0.05)² = 0.00785 m² — always use radius (d/2)
Mistake 3 — Forgetting Atmospheric Pressure for Total Underwater Pressure
- ❌ Wrong: Total pressure at 10m water = ρgh = 98,070 Pa only
- ✅ Correct: P_total = P_atm + ρgh = 101,325 + 98,070 = 199,395 Pa = 1.97 atm
Mistake 4 — Using Fresh Water Density for Seawater
- Fresh water: ρ = 1,000 kg/m³ → P at 10m = 98,070 Pa
- Seawater: ρ = 1,025 kg/m³ → P at 10m = 100,521 Pa (2.5% more)
- For ocean diving calculations, always use seawater density (1,025 kg/m³).
Mistake 5 — Pressure Altitude Formula Needs Height in Meters
- ❌ Wrong: Using 10,000 (feet) directly in P = 101325×(1−0.0000225577×10000)^5.25588 → gives ~23,000 Pa (wrong)
- ✅ Correct: Convert first — 10,000 ft = 3,048 m → P = 101325×(1−0.0000225577×3048)^5.25588 = 69,682 Pa
Worked Examples — 8 Complete Problems
1. Elephant on one foot (5,000 kg, foot area 0.05 m²)
- F = 5000 × 9.807 = 49,033 N
- Pressure formula P = F/A: P = 49,033 / 0.05 = 980,665 Pa = 980.7 kPa = 142.3 psi
2. Hydrostatic pressure at 20m depth in fresh water
- P = ρgh = 1000 × 9.807 × 20 = 196,140 Pa = 196.1 kPa = 28.4 psi
- Total pressure: P_total = 101,325 + 196,140 = 297,465 Pa = 2.94 atm
3. Submarine at 500m in seawater (ρ = 1,025 kg/m³)
- P_gauge = 1025 × 9.807 × 500 = 5,025,588 Pa = 5.026 MPa
- P_total = 101,325 + 5,025,588 = 5,126,913 Pa = 5.127 MPa = 743 psi
4. Convert 50 psig to absolute pressure (Pa and bar)
- 50 psig = 50 × 6894.757 = 344,738 Pa (gauge)
- P_absolute = 344,738 + 101,325 = 446,063 Pa = 446.1 kPa = 4.461 bar
5. Pressure altitude at 5,000 m
- P = 101325 × (1 − 0.0000225577 × 5000)^5.25588
- = 101325 × (0.887115)^5.25588 = 101325 × 0.5334 = 54,048 Pa = 540.5 mbar = 15.96 inHg
6. Pressure head: 100 kPa in water → equivalent column height
- h = P/(ρg) = 100,000 / (1000 × 9.807) = 100,000 / 9807 = 10.197 m = 33.45 ft
7. Convert 760 mmHg to psi, bar, kPa
- 760 mmHg × 133.322 Pa/mmHg = 101,325 Pa
- = 14.696 psi = 1.01325 bar = 101.325 kPa = 1 atm
8. Force on a 1m² dam wall section at average depth 15m (water)
- P = ρgh = 1000 × 9.807 × 15 = 147,105 Pa
- F = P × A = 147,105 × 1 = 147,105 N = 147.1 kN = 33,076 lbf