Pressure is a fundamental physical quantity describing the force exerted per unit area. The standard international (SI) unit for this measurement is the Pascal, symbolized as Pa. This unit was named after the French polymath Blaise Pascal, who made foundational contributions to hydrodynamics and hydrostatics in the 17th century. The Pascal is a derived unit, meaning its definition is based on a combination of other fundamental SI units.
The Pascal Defined: Force Over Area
The simplest definition of the Pascal relates force to the area over which it is distributed. One Pascal is defined as the pressure exerted by a force of one newton acting perpendicularly upon an area of one square meter. This relationship is expressed concisely as 1 Pa = 1 N/m^2.
Understanding this definition requires looking at the components of the derived unit. The numerator, the newton (N), is the SI unit of force. The denominator, the square meter (m^2), is the SI unit of area, providing the surface over which that force is distributed. Therefore, the Pascal represents the concentration of force on a given surface.
Imagine a single newton of force spread evenly across a square that is one meter on each side. The resulting pressure across that square would be exactly one Pascal. This definition anchors the unit of pressure to tangible units of force and distance. The Pascal is also used to quantify mechanical stress, internal pressure, and Young’s modulus in materials science, as these are concepts based on force per unit area.
Deriving the Pascal from Base SI Units
While the expression N/m^2 defines the Pascal, this uses derived units. To understand the true composition of the Pascal, one must break down the newton into its constituent base units: the kilogram (kg) for mass, the meter (m) for length, and the second (s) for time.
The definition of the newton comes from Newton’s second law of motion, where force equals mass times acceleration (F=ma). Since acceleration is measured in meters per second squared (m/s^2), one newton is equivalent to one kilogram-meter per second squared (1 N = 1 kg⋅m/s^2).
Substituting this fundamental relationship back into the Pascal’s definition (newtons per square meter) reveals its structure in terms of base units. The equation becomes 1 Pa = (1 kg⋅m/s^2) / m^2.
By simplifying this fraction, which involves canceling out one meter unit from the numerator and denominator, the Pascal is shown to be equivalent to one kilogram per meter per second squared. The final, most fundamental expression of the Pascal is 1 Pa = 1 kg/(m⋅s^2). This breakdown confirms the Pascal as a coherent derived SI unit, linking pressure directly back to the basic mechanical units of mass, length, and time.
Practical Context: Multiples and Equivalencies
In practical applications, a single Pascal represents an extremely small amount of pressure, making it inconvenient for many real-world measurements. For example, standard atmospheric pressure at sea level is approximately 101,325 Pa. Due to this small magnitude, the Pascal is most often encountered in the form of its larger multiples.
The kilopascal (kPa), which is 1,000 Pascals, is a common unit; tire pressure gauges often use kPa readings. The megapascal (MPa), equal to one million Pascals, is used in engineering to measure high pressures, such as those in hydraulic systems or for quantifying material strength. Geophysicists use the gigapascal (GPa), one billion Pascals, when measuring stresses within the Earth’s crust.
For comparison, the Bar is a metric unit of pressure defined as exactly 100,000 Pascals, which is close to the standard atmosphere (101,325 Pa). Meteorologists frequently use the hectopascal (hPa), which is 100 Pa, because it is numerically equivalent to the millibar (mbar), a unit historically used in weather reporting. These larger units provide a manageable scale for expressing daily pressures, while still being derived from the fundamental Pascal unit.