Pressure Calculator

General Physics

Select the calculation method and enter the required values to find the pressure.

Practical Examples

See how the Pressure Calculator is used in different scenarios.

Calculating Tire Pressure

force

A car weighing 15000 N rests on four tires, each with a contact area of 0.02 m². Calculate the pressure exerted by one tire on the ground.

Force: 3750 N, Area: 0.02 m²

Stiletto Heel Pressure

force

A person weighing 600 N puts all their weight on a stiletto heel with an area of 0.0001 m². Find the pressure exerted on the floor.

Force: 600 N, Area: 0.0001 m²

Pressure at the Bottom of a Pool

fluid

Calculate the water pressure at the bottom of a 3-meter deep swimming pool. The density of water is 1000 kg/m³.

Density: 1000 kg/m³, Height: 3 m

Atmospheric Pressure Analogy

fluid

Estimate the pressure exerted by a 1-meter column of mercury, which has a density of 13593 kg/m³.

Density: 13593 kg/m³, Height: 1 m

Other Titles
Understanding the Pressure Calculator: A Comprehensive Guide
This guide covers everything you need to know about pressure, its calculation, and practical applications, helping you use our tool effectively.

What is Pressure?

  • The Fundamental Definition of Pressure
  • Units of Pressure: Pascals, PSI, Bar, and More
  • The Difference Between Gauge and Absolute Pressure
In physics, pressure (symbol: P or p) is defined as the amount of force exerted perpendicular to a surface, per unit of area. It quantifies how concentrated a force is. A large force on a small area creates high pressure, while the same force on a larger area creates lower pressure. This concept is fundamental in many areas of science and engineering, from fluid mechanics to materials science.
Key Formulas
1. P = F / A: Used for solid surfaces, where P is pressure, F is the normal force, and A is the area.
2. P = ρgh: Used for fluids, where P is the gauge pressure, ρ (rho) is the fluid density, g is the acceleration due to gravity, and h is the fluid depth or height.

Conceptual Examples

  • A knife cuts because the small area of the blade concentrates the force, creating high pressure.
  • Snowshoes work by distributing a person's weight over a large area, reducing the pressure on the snow.
  • Dams are built much thicker at the bottom because the water pressure increases with depth.

Step-by-Step Guide to Using the Pressure Calculator

  • Selecting the Correct Calculation Type
  • Inputting Your Values and Units
  • Interpreting the Multi-Unit Results
Our calculator is designed for ease of use. Here's how to get your results in a few simple steps:
Method 1: Calculating Pressure from Force and Area
1. Select 'Force and Area' from the 'Calculation Type' dropdown.
2. Enter the total force applied in the 'Force (F)' field.
3. Enter the surface area in the 'Area (A)' field.
4. Click 'Calculate' to see the pressure displayed in multiple units like Pascals, PSI, and Bar.
Method 2: Calculating Fluid Pressure
1. Select 'Fluid Pressure' from the 'Calculation Type' dropdown.
2. Input the density of the fluid in the 'Fluid Density (ρ)' field.
3. Enter the height or depth of the fluid in the 'Fluid Height (h)' field.
4. Optionally, adjust the 'Gravity (g)' value if you are not on Earth or require higher precision. The default is 9.81 m/s².
5. Click 'Calculate' to view the resulting gauge pressure.

Real-World Applications of Pressure

  • Automotive Systems: Tire and Brake Pressure
  • Meteorology: Atmospheric Pressure and Weather Forecasting
  • Medicine: Blood Pressure and Syringes
The concept of pressure is not just academic; it's integral to countless real-world technologies and natural phenomena.
Hydraulic Systems
Hydraulic systems, such as car brakes and construction equipment, use Pascal's principle. A small force applied to a small area in an enclosed fluid creates pressure that is transmitted to a larger area, generating a much larger force.
Diving and Submarines
As a diver descends, the water pressure increases significantly. Understanding this relationship is crucial for safety and for designing submersibles that can withstand the immense forces at great depths.

Common Misconceptions and Correct Methods

  • Confusing Pressure with Force
  • Ignoring the Role of Area
  • Forgetting that Fluid Pressure is Independent of a Container's Shape
Pressure vs. Force
A common mistake is to use 'pressure' and 'force' interchangeably. Force is a push or a pull (a vector quantity), while pressure is the amount of that force applied per unit of area (a scalar quantity). A strong force doesn't necessarily mean high pressure if it's spread over a large area.
The Hydrostatic Paradox
It might seem counterintuitive, but the pressure at a certain depth in a fluid is the same regardless of the total volume or shape of the container. A tall, thin tube of water can exert the same pressure at its base as a wide lake of the same depth. This is because fluid pressure depends on depth (h) and density (ρ), not the total weight of the fluid.

Mathematical Derivation and Examples

  • Derivation of the P = F/A Formula
  • Derivation of the P = ρgh Formula
  • Worked-Out Numerical Examples
Derivation of P = ρgh

The pressure exerted by a fluid column comes from its weight. Consider a cylindrical column of fluid with height 'h' and area 'A'.

  1. The volume of the fluid is V = A * h.
  2. The mass of the fluid is m = Density Volume = ρ A * h.
  3. The weight of the fluid is the force it exerts, F = mass gravity = (ρ A h) g.
  4. Pressure is Force / Area, so P = (ρ A h * g) / A.
  5. The 'A' terms cancel out, leaving P = ρgh.

Worked Example

  • Calculate the pressure on a submarine window with an area of 0.5 m² at a depth of 200 meters in seawater (density ≈ 1025 kg/m³). Force = P * A = (ρgh) * A P = 1025 kg/m³ * 9.81 m/s² * 200 m = 2,010,050 Pa or 2.01 MPa. Total Force on window = 2,010,050 Pa * 0.5 m² = 1,005,025 Newtons.