Pascal
Symbol: PaWorldwide
What is a Pascal (Pa)?
Formal Definition
The pascal (symbol: Pa) is the SI derived unit of pressure, stress, and elastic modulus. It is defined as one newton per square meter (1 Pa = 1 N/m²). In SI base units, the pascal is expressed as kg·m⁻¹·s⁻² (kilogram per meter per second squared). The pascal quantifies the force applied perpendicular to a surface per unit area of that surface.
The pascal is a relatively small unit in everyday terms. Standard atmospheric pressure at sea level is 101,325 Pa (approximately 101.3 kPa). Because of this, pressure values in many practical applications are large numbers when expressed in pascals, which is why kilopascals (kPa), megapascals (MPa), and gigapascals (GPa) are commonly used. For example, car tire pressure is typically around 220 kPa, and the tensile strength of structural steel is approximately 400 MPa.
Role in the SI System
The pascal is the coherent SI unit for all forms of pressure measurement. It is used for atmospheric pressure, gauge pressure, absolute pressure, differential pressure, stress in materials, sound pressure, and hydraulic pressure. The unit connects directly to fundamental SI quantities: force (newton), length (meter), mass (kilogram), and time (second). This makes it central to physics, engineering, meteorology, and materials science.
Etymology
Named After Blaise Pascal
The pascal is named after Blaise Pascal (1623-1662), the French mathematician, physicist, and philosopher. Pascal made groundbreaking contributions to fluid mechanics, particularly through his work on hydrostatics. In 1648, Pascal directed his brother-in-law Florin Périer to carry a mercury barometer up the Puy de Dôme mountain in central France. The experiment demonstrated that atmospheric pressure decreases with altitude, providing crucial evidence for the existence of atmospheric pressure and the vacuum — concepts that were hotly debated at the time.
Adoption as an SI Unit
The name "pascal" for the unit of pressure was adopted by the 14th General Conference on Weights and Measures (CGPM) in 1971. Before this, pressure in SI was expressed simply as newtons per square meter (N/m²), which remained a valid expression. The naming honored Pascal's experimental work demonstrating atmospheric pressure and his formulation of Pascal's principle — the law that pressure applied to a confined fluid is transmitted equally in all directions. The symbol Pa was chosen as the standard abbreviation.
Precise Definition
SI Definition
The pascal is defined as exactly one newton of force applied over an area of one square meter: 1 Pa = 1 N/m² = 1 kg/(m·s²). Since the newton is itself defined as kg·m/s², the pascal can be fully expressed in SI base units. This definition is exact and does not depend on any physical artifact or environmental conditions.
Derived Units
Several important SI units are defined in terms of the pascal. The bar, while not an SI unit, is defined as exactly 100,000 Pa (100 kPa). Standard atmosphere (atm) is defined as exactly 101,325 Pa. The hectopascal (hPa), equal to 100 Pa, is identical to the millibar and is the standard unit for atmospheric pressure reporting in meteorology worldwide.
Relationship to Other Pressure Units
The pascal relates to other pressure units through exact or approximate conversions: 1 atm = 101,325 Pa exactly; 1 bar = 100,000 Pa exactly; 1 torr = 133.322 Pa approximately; 1 psi = 6,894.76 Pa approximately; 1 mmHg = 133.322 Pa approximately. These relationships allow conversion between the various pressure systems used across different industries and countries.
History
Blaise Pascal's Experiments
Blaise Pascal's interest in pressure began in 1646 when he learned of Evangelista Torricelli's barometric experiments in Italy. Torricelli had demonstrated in 1643 that the atmosphere exerts pressure by inverting a tube of mercury and observing that the mercury column stabilized at approximately 760 mm. Pascal replicated and extended these experiments, notably commissioning the Puy de Dôme experiment in September 1648, which showed that the mercury column was shorter at the summit (about 620 mm) than at the base (about 711 mm), proving that atmospheric pressure decreases with altitude.
Pascal also formulated what is now known as Pascal's principle: a change in pressure at any point in an enclosed incompressible fluid is transmitted equally to all points in the fluid. This principle is the foundation of hydraulic systems, from car brakes to industrial presses.
Evolution of Pressure Measurement
Before the pascal was adopted, pressure was measured in a bewildering variety of units: atmospheres, bars, millimeters of mercury, inches of mercury, torr, pounds per square inch, dynes per square centimeter, and others. The introduction of the SI system in 1960 aimed to standardize measurement, but it was not until 1971 that the pascal was officially named. The transition has been gradual: meteorologists adopted the hectopascal (hPa) as a replacement for the millibar in the 1980s, and many countries still use mmHg for blood pressure measurement.
Modern Usage
Today, the pascal and its multiples are the standard units of pressure in all scientific disciplines, most engineering applications, and many everyday contexts. The International Civil Aviation Organization (ICAO) specifies atmospheric pressure in hectopascals for aviation. The automotive industry uses kilopascals for tire pressure. Materials science uses megapascals and gigapascals for stress and hardness. The pascal's adoption continues to expand, though legacy units persist in specific industries and regions.
Current Use
Meteorology
In meteorology, atmospheric pressure is universally reported in hectopascals (hPa), which are numerically identical to millibars (mbar). Standard atmospheric pressure at sea level is 1013.25 hPa. Weather maps worldwide display isobars labeled in hectopascals. Tropical cyclone intensity is characterized partly by central pressure in hPa — a Category 5 hurricane typically has central pressure below 920 hPa. Barometric pressure readings for weather forecasting range from approximately 870 hPa (extreme low) to 1085 hPa (extreme high).
Engineering
Engineers use kilopascals and megapascals throughout structural, mechanical, and civil engineering. Concrete compressive strength is typically 20-50 MPa. Steel yield strength ranges from 250 to 1,000 MPa. Soil bearing capacity is measured in kPa. Hydraulic systems operate at pressures from 700 kPa to 70 MPa. Tire pressure is specified as 180-350 kPa for passenger cars.
Medicine
In many countries, blood pressure is measured in millimeters of mercury (mmHg) by tradition, but the pascal is the SI-recommended unit. Normal blood pressure is approximately 120/80 mmHg, equivalent to 16.0/10.7 kPa. Respiratory pressure in ventilators is measured in pascals or centimeters of water (cmH₂O). Intracranial pressure monitoring uses mmHg or kPa depending on the institution.
Industry
Industrial pressure measurement spans an enormous range. Vacuum systems operate from 100 kPa down to micropascals. Compressed gas cylinders hold pressure at 15-30 MPa. Water distribution systems operate at 200-700 kPa. Industrial autoclaves and chemical reactors may operate at pressures exceeding 100 MPa.
Everyday Use
Weather Reports
Every time you check the weather, you encounter pascals — even if indirectly. Barometric pressure readings of 1013 hPa (or 1013 mbar) indicate standard conditions. Falling pressure (below 1000 hPa) often indicates approaching storms, while rising pressure (above 1020 hPa) suggests clearing weather. Aviation weather reports (METARs) always include pressure in hectopascals.
Tire Pressure
Car tire pressure is measured in kilopascals in most countries. A typical recommendation is 220-240 kPa (32-35 psi) for passenger cars. The tire pressure monitoring system (TPMS) in modern vehicles alerts drivers when pressure drops below safe levels, typically around 175 kPa. Bicycle tires range from 200 kPa (mountain bikes) to 800 kPa (road racing bikes).
Cooking
Pressure cookers operate at approximately 100 kPa above atmospheric pressure (about 200 kPa absolute), which raises the boiling point of water to approximately 120°C. This higher temperature significantly reduces cooking times. Espresso machines force water through coffee grounds at 900 kPa (9 bar), which extracts flavors differently than gravity brewing.
Scuba Diving
Scuba divers experience pressure changes measured in atmospheres (approximately 101 kPa each). At 10 meters depth, the total pressure is approximately 2 atm (about 202 kPa). At 30 meters — the recreational diving limit — pressure reaches about 4 atm (405 kPa). These pressure differences affect air consumption, decompression requirements, and nitrogen narcosis risk.
In Science & Industry
Fluid Dynamics
In fluid dynamics, pressure is a central variable described in pascals. The Bernoulli equation relates pressure, velocity, and elevation in flowing fluids, with all terms expressible in pascals. Wind tunnel testing measures pressure distributions over aircraft surfaces in pascals to determine lift and drag coefficients. Computational fluid dynamics (CFD) simulations compute pressure fields in pascals across millions of mesh cells.
Materials Science
Materials science uses the pascal extensively in megapascal (MPa) and gigapascal (GPa) ranges. Young's modulus of steel is approximately 200 GPa. Diamond has a Young's modulus of about 1,050 GPa — the highest of any known material. Shear modulus, bulk modulus, and Poisson's ratio are all expressed using pascal-based units. The Mohs hardness scale has been supplemented by the Vickers hardness test, which reports hardness in megapascals.
Acoustics
Sound pressure level is measured in pascals. The threshold of human hearing corresponds to a sound pressure of approximately 20 micropascals (20 μPa), while the threshold of pain is roughly 20 Pa — a range of six orders of magnitude. Sound pressure level in decibels (dB SPL) is defined relative to the 20 μPa reference: dB SPL = 20 × log₁₀(p/20μPa). A normal conversation produces sound pressure of about 0.02 Pa (60 dB SPL).
Geophysics
Geophysicists measure pressure deep within the Earth in gigapascals. At the boundary between the Earth's mantle and core (approximately 2,900 km depth), pressure reaches about 136 GPa. At the center of the Earth, pressure is estimated at 360 GPa. These extreme pressures are replicated in laboratories using diamond anvil cells, which can achieve pressures exceeding 400 GPa — sufficient to study the behavior of matter under conditions found in planetary interiors.
Interesting Facts
The pascal is one of the smallest commonly used SI units — a single pascal is approximately the pressure exerted by a dollar bill resting flat on a table. Standard atmospheric pressure is 101,325 times greater.
Blaise Pascal invented one of the earliest mechanical calculators (the Pascaline) at age 19 to help his father with tax calculations. He later made fundamental contributions to probability theory, projective geometry, and philosophy before dying at age 39.
The deepest point in the ocean — the Challenger Deep in the Mariana Trench at 10,935 meters — has a water pressure of approximately 110 MPa, or about 1,086 atmospheres. This is enough to crush most submarines.
Sound travels as pressure waves. The quietest sound a human ear can detect corresponds to a pressure fluctuation of just 20 micropascals — about 5 billion times less than atmospheric pressure.
Diamond anvil cells can generate pressures exceeding 400 GPa (4 million atmospheres), allowing scientists to recreate conditions found at the center of gas giant planets. Under such pressures, hydrogen becomes a metallic solid.
Atmospheric pressure decreases by roughly 12 Pa for every meter of altitude gained near sea level. At the summit of Mount Everest (8,849 m), atmospheric pressure is only about 33.7 kPa — roughly one-third of sea-level pressure.
The turgor pressure inside a plant cell — which keeps plants rigid and upright — is typically 300-900 kPa, several times atmospheric pressure. When plants wilt, it is because turgor pressure has dropped.