Pressure Calculator

For Solid Surfaces (P = F/A)

This is the most direct calculation.

• Input Force (F): Enter the total force being applied perpendicular to the surface. Ensure your units are in Newtons (N) for standard calculations.
• Input Area (A): Enter the total area over which the force is distributed, in square meters (m²).
• Calculate: The tool will provide the pressure in Pascals (Pa).

For Fluid Pressure at Depth (P = ρgh)

This mode is for calculating the pressure exerted by a column of fluid (a liquid or gas).

• Input Fluid Density (ρ): Enter the density of the fluid in kilograms per cubic meter (kg/m³). For fresh water, this is about 1000 kg/m³.
• Input Gravitational Acceleration (g): This is typically a constant, ~9.81 m/s² on Earth.
• Input Height/Depth (h): Enter the depth from the surface of the fluid in meters (m).
• Calculate: The calculator will determine the gauge pressure at that depth.

The Standard Unit: The Pascal (Pa)

The SI (International System) unit for pressure is the **Pascal**, named after the French physicist Blaise Pascal. One Pascal is defined as one Newton of force applied over an area of one square meter (1 Pa = 1 N/m²). A single Pascal is a very small amount of pressure, so we often use kilopascals (1 kPa = 1,000 Pa) or megapascals (1 MPa = 1,000,000 Pa).

Other Common Pressure Units

You'll encounter many other units in various fields, and understanding them is crucial for real-world application.

• Pounds per Square Inch (PSI): The standard in the US. Used for everything from tire pressure to industrial systems. 1 PSI ≈ 6,895 Pa.
• Bar: Roughly equal to atmospheric pressure at sea level. 1 bar = 100,000 Pa. Millibars (mb) are commonly used in meteorology.
• Standard Atmosphere (atm): Defined as the average atmospheric pressure at sea level. 1 atm = 101,325 Pa ≈ 14.7 PSI.
• Torr: Named after Torricelli, an early pioneer in pressure measurement. Often used for measuring vacuums. 1 atm ≈ 760 Torr.

Absolute Pressure (P_abs)

This is the "true" pressure, measured relative to a perfect vacuum (zero pressure). An absolute pressure of zero can only exist in empty space. This is the value used in most scientific formulas like the Ideal Gas Law.

Gauge Pressure (P_gauge)

This is the pressure measured relative to the local atmospheric pressure. It is the pressure difference between the system and its surroundings. The reading on a tire pressure gauge is a gauge pressure. If your gauge reads 32 PSI, it means the pressure inside the tire is 32 PSI *higher* than the atmospheric pressure outside. A gauge pressure of zero means the pressure is equal to the surrounding atmospheric pressure.

Q: If atmospheric pressure is so high (~14.7 PSI), why doesn't it crush us?

The fluids inside our bodies (our blood, the fluid in our cells) exert an outward pressure that perfectly balances the inward pressure from the atmosphere. We are essentially "pressurized" from the inside out. We only notice changes in external pressure, which is why our ears "pop" when we change altitude quickly.

Q: Does the shape of a container affect the pressure at the bottom?

Surprisingly, no. For a fluid of a certain depth, the pressure at the bottom depends only on the depth (h) and the fluid's density (ρ), not on the width or shape of the container. This is known as the hydrostatic paradox.

Q: What is Boyle's Law?

Boyle's Law describes the relationship between pressure and volume for a gas at a constant temperature. It states that pressure and volume are inversely proportional (`P₁V₁ = P₂V₂`). If you decrease the volume of a container of gas (like pushing a piston in), its pressure increases.