Pressure Calculator - Comprehensive Pressure Calculation Tool
A pressure calculator is an essential physics and engineering tool that computes pressure values based on force, area, fluid properties, and depth parameters using fundamental pressure equations. Pressure is defined as force per unit area and represents how concentrated a force is when applied to a surface. Understanding pressure calculations is critical across numerous fields including fluid mechanics, hydraulics, pneumatics, meteorology, diving, engineering design, and industrial applications where accurate pressure determination affects safety, performance, and efficiency. Whether calculating atmospheric pressure, hydrostatic pressure in fluids, gas pressure in containers, or force-based pressure on surfaces, this calculator provides precise results with multiple unit options.
The fundamental pressure formula is \(P = \frac{F}{A}\), where P represents pressure (measured in Pascals, psi, bar, or atmospheres), F is the applied force (Newtons or pounds-force), and A is the area over which the force acts (square meters or square inches). For fluids at rest, hydrostatic pressure increases with depth according to \(P = \rho g h\), where ρ is fluid density (kg/m³), g is gravitational acceleration (9.81 m/s²), and h is depth below the surface (meters). Total pressure at a depth combines atmospheric pressure at the surface with hydrostatic pressure: \(P_{total} = P_{atm} + \rho g h\). Standard atmospheric pressure at sea level equals 101,325 Pa (101.325 kPa), 1 atm, 14.696 psi, or 1.01325 bar, serving as the reference for many pressure measurements.
Our comprehensive pressure calculator offers six specialized calculation modes to address diverse scientific and engineering needs. You can calculate basic pressure from force and area using the fundamental formula, determine hydrostatic pressure at various depths in fluids considering density and gravity, convert between multiple pressure units including Pa, kPa, bar, psi, atm, mmHg, and torr, calculate atmospheric pressure at different altitudes above sea level, determine gas pressure using the ideal gas law (PV = nRT), and analyze pressure differences and gauge pressure relative to atmospheric pressure. Each calculation mode provides detailed step-by-step solutions showing formulas, unit conversions, and intermediate calculations, making this tool invaluable for physicists, engineers, divers, meteorologists, students, HVAC technicians, and anyone working with pressure measurements in scientific, industrial, or practical applications.
Interactive Pressure Calculator
Calculate Pressure from Force and Area
Calculate Hydrostatic Pressure at Depth
Pressure Unit Converter
Calculate Atmospheric Pressure at Altitude
Calculate Gas Pressure (Ideal Gas Law)
Calculate Gauge and Absolute Pressure
Essential Pressure Formulas
Basic Pressure Formula
Pressure is defined as force per unit area acting perpendicular to a surface.
Where P is pressure (Pa or psi), F is force (N or lbf), and A is area (m² or in²). One Pascal (Pa) equals one Newton per square meter (N/m²).
Hydrostatic Pressure Formula
Hydrostatic pressure increases linearly with depth in a fluid due to the weight of fluid above.
Where ρ (rho) is fluid density (kg/m³), g is gravitational acceleration (9.81 m/s²), and h is depth (m). For water: P ≈ 9,810 Pa per meter depth.
Total Pressure at Depth
Absolute pressure at depth equals atmospheric pressure plus hydrostatic pressure.
Where P_atm is atmospheric pressure at surface (101.325 kPa at sea level). Gauge pressure is P_gauge = ρgh (excluding atmospheric).
Ideal Gas Law (Pressure Form)
For ideal gases, pressure relates to moles, temperature, and volume through the gas constant.
Where n is moles, R is gas constant (8.314 J/(mol·K)), T is temperature (K), and V is volume (m³). P increases with temperature and moles, decreases with volume.
Atmospheric Pressure with Altitude
Atmospheric pressure decreases exponentially with altitude above sea level.
Simplified approximation: P ≈ P₀(1 - 0.0000226h)^5.26, where h is altitude in meters and P₀ = 101.325 kPa. Pressure drops ~12% per 1000m elevation.
Gauge vs Absolute Pressure
Gauge pressure measures relative to atmospheric pressure; absolute pressure relative to perfect vacuum.
Most pressure gauges read gauge pressure (0 at atmospheric). Absolute pressure is always positive; gauge can be negative (vacuum).
Pressure Unit Conversion Table
| Unit | Symbol | Equivalent to 1 Pascal (Pa) | Common Uses |
|---|---|---|---|
| Pascal | Pa | 1 Pa = 1 N/m² | SI unit, scientific calculations |
| Kilopascal | kPa | 1 kPa = 1,000 Pa | Engineering, weather (1 atm ≈ 101.3 kPa) |
| Bar | bar | 1 bar = 100,000 Pa | Meteorology, industrial (≈ 1 atm) |
| Atmosphere | atm | 1 atm = 101,325 Pa | Standard pressure reference |
| Pound per Square Inch | psi | 1 psi = 6,894.76 Pa | US engineering, tire pressure |
| Millimeter of Mercury | mmHg (torr) | 1 mmHg = 133.322 Pa | Blood pressure, vacuum (760 mmHg = 1 atm) |
| Inch of Mercury | inHg | 1 inHg = 3,386.39 Pa | Barometric pressure, aviation |
| Millibar | mbar | 1 mbar = 100 Pa | Meteorology (1 atm = 1013.25 mbar) |
Hydrostatic Pressure vs Depth Reference
| Depth | Hydrostatic Pressure (Water) | Total Pressure (+ 1 atm) | Common Examples |
|---|---|---|---|
| 1 m | 9.81 kPa (1.42 psi) | 111.1 kPa (16.1 psi) | Shallow pool |
| 10 m (33 ft) | 98.1 kPa (14.2 psi) | 199.4 kPa (28.9 psi) | Recreational diving limit |
| 30 m (98 ft) | 294.3 kPa (42.7 psi) | 395.6 kPa (57.4 psi) | Advanced diving |
| 100 m (328 ft) | 981 kPa (142 psi) | 1,082 kPa (157 psi) | Technical diving |
| 1,000 m | 9.81 MPa (1,422 psi) | 9.91 MPa (1,437 psi) | Deep sea exploration |
| 4,000 m | 39.2 MPa (5,690 psi) | 39.3 MPa (5,705 psi) | Titanic depth |
| 10,994 m | 107.6 MPa (15,600 psi) | 107.7 MPa (15,615 psi) | Mariana Trench (deepest) |
Atmospheric Pressure vs Altitude
| Altitude | Atmospheric Pressure | % of Sea Level | Location Examples |
|---|---|---|---|
| Sea Level (0 m) | 101.325 kPa (14.7 psi) | 100% | Coast, oceans |
| 500 m (1,640 ft) | 95.5 kPa (13.8 psi) | 94.3% | Low elevation cities |
| 1,000 m (3,281 ft) | 89.9 kPa (13.0 psi) | 88.7% | Many inland cities |
| 1,500 m (4,921 ft) | 84.6 kPa (12.3 psi) | 83.5% | Denver, CO elevation |
| 3,000 m (9,843 ft) | 70.1 kPa (10.2 psi) | 69.2% | High altitude cities |
| 5,500 m (18,045 ft) | 50.5 kPa (7.3 psi) | 49.8% | Everest Base Camp |
| 8,848 m (29,029 ft) | 33.7 kPa (4.9 psi) | 33.3% | Mt. Everest summit |
Key Takeaways
- Basic pressure formula: P = F/A (force per unit area), measured in Pascals (Pa) or psi
- Hydrostatic pressure: P = ρgh - increases linearly with depth in fluids
- Standard atmospheric pressure: 101.325 kPa = 1 atm = 14.696 psi = 1.01325 bar at sea level
- Absolute pressure = gauge pressure + atmospheric pressure (gauge reads 0 at atmospheric)
- Water pressure increases ~9.81 kPa (1.42 psi) per meter of depth
- Ideal gas law: PV = nRT relates pressure to moles, temperature, and volume
- Atmospheric pressure decreases ~12% per 1,000 meters altitude gain
- 1 Pascal = 1 N/m² (SI unit); 1 bar ≈ 1 atm; 1 psi = 6,894.76 Pa
- Pressure acts equally in all directions at a point in a fluid (Pascal's principle)
- Convert gauge to absolute by adding 101.325 kPa; absolute to gauge by subtracting 101.325 kPa