How to Calculate Pressure

In this lesson, you will learn

  • How to use the pressure formula, Pressure = F / A.
  • How to find a weight in newtons from a mass in kilograms.
  • How to convert an area between cm2 and m2.
  • How to find the area when you know the force and the pressure.

The Pressure Formula

You will learn how to calculate pressure when a force is applied to an area with some word problems.

The formula we are going to use is:

Pressure = FA
  • F = forcein newtons (N)
  • A = areain square meters (m2)
  • Pressurein pascals (Pa): 1 Pa = 1 N per m2
Remember

When an object rests on the ground, the force is its weight. To find the weight in newtons, multiply the mass in kilograms by 9.8.

A force of 600 N pushes on an area of 2 m2. What is the pressure?

Show answer

300 Pa. Pressure = 600 ÷ 2 = 300 N per m2, which is 300 pascals.

Word Problem #1: Pressure of an Elephant on the Ground

Word problem #1:

A human may apply around 18000 pascals of pressure on the ground.

The mass of an adult elephant can be around 5000 kg. Calculate the pressure applied by this elephant on the ground. How does the pressure compare with that of humans?

Solution:

We need to do a couple of things here to find the pressure.

First, we need to find the weight in newtons.

A mass of 1 kg weighs 9.8 newtons, so 5000 kg weighs 5000 × 9.8 newtons.

Weight = 49000 newtons

Now we need to get the area of the feet of the elephant. An elephant foot is usually 40 to 50 cm in length and width.

Pick 45 cm, the area is approximately equal to 2025 cm2

For 4 feet, the area is 8100 cm2

Convert the area to m2 using the following:

1 cm2 = 0.0001 m2

8100 cm2 = 8100 × 0.0001 m2 = 0.81 m2

Pressure = 49000 / 0.81

The pressure exerted on the ground by the elephant is about 60494 pascals.

To compare the pressure, just do a ratio of the elephant's pressure to a human's pressure.

60494 divided by 18000 equals 3.36, so the pressure is about 3 times bigger.

This is not huge compared to humans. Keep in mind that the elephant has 4 feet, which helps increase the area, which in turn decreases the pressure.

Common mistake

Dividing by the area in cm2. 49000 ÷ 8100 gives about 6, which is far too small. Convert the area to m2 first, so the answer is in pascals.

An elephant with a mass of 5000 kg stands on 4 feet, each 50 cm by 50 cm. What is the pressure on the ground?

Show answer

49000 Pa. The weight is 49000 N. The area is 4 × 2500 = 10000 cm2 = 1 m2, so the pressure is 49000 ÷ 1 = 49000 Pa.

Word Problem #2: Area of a Pencil on a Table

Problem #2:

The mass of a pencil is 0.01 kg and the pressure the pencil applies to a table is 108.88 newtons per square meter. Calculate the area of the pencil in contact with the table.

The weight of the pencil is 0.01 × 9.8 = 0.098 newtons.

If 4 = 24 / 6

Then, 6 = 24 / 4

By the same token,

If P = F / A

Then, A = F / P

Then, A = 0.098 / 108.88

Area ≈ 0.0009 m2.

0.0009 m2 = 0.0009 × 10000 cm2 = 9 cm2.

The 9 cm2 makes sense since a pencil can be 18 cm long and 0.5 centimeter wide.

A pencil 18 cm long and 0.5 cm wide
Worked example: A box with a mass of 20 kg presses on the floor with a pressure of 1960 Pa. What area of the box touches the floor?
  1. Find the weight: 20 × 9.8 = 196 N.
  2. If P = F / A, then A = F / P.
  3. A = 196 / 1960 = 0.1 m2.
  4. Convert to cm2: 0.1 × 10000 = 1000 cm2. That could be a box bottom 40 cm by 25 cm.

The box touches the floor on an area of 1000 cm2 (0.1 m2).

You know the pressure P and the area A. Which formula gives the force F?

Show answer

F = P × A. If P = F / A, multiply both sides by A.

How to Calculate Pressure of a Car on the Ground

The idea here is to get the weight of your car. I will let you do this one with some guidelines.

Some cars have a mass of 1500 kg, so their weight is 1500 × 9.8 = 14700 newtons. Then, get the area of the 4 tires in contact with the floor in square meters. Finally, divide the weight by the area you found. Something similar is done if you wanted to know how to calculate pressure of a book on a table, pressure of your television on a stand, etc.

Each tire of a 1500 kg car touches the road on 150 cm2. What pressure does the car apply on the road?

Show answer

245000 Pa. The area is 4 × 150 = 600 cm2 = 0.06 m2, so the pressure is 14700 ÷ 0.06 = 245000 Pa.

Summary

  • Pressure = F / A, with the force in newtons, the area in m2 and the pressure in pascals.
  • The weight in newtons is the mass in kg times 9.8.
  • 1 cm2 = 0.0001 m2, and 1 m2 = 10000 cm2.
  • To find the area, use A = F / P.
  • The same force on a bigger area gives a smaller pressure.

Interactive Practice: Solve 5 Pressure Problems

Problems 1 and 2 guide you through every step. Problem 3 has fewer steps, with a hint for each one. In problems 4 and 5, you do only the key steps, and the answer is never shown, so keep trying. You can skip a problem at any time, and each time you play you get new problems.

Problem 1 of 5Score: 0

Keep learning