What is the distance formula? The distance formula is a mathematical formula used to calculate the distance between two points in a two- or three-dimensional space. It is derived from the Pythagorean theorem and states that the distance between two points with coordinates (x1, y1) and (x2, y2) in a two-dimensional space is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

In a three-dimensional space, the distance between two points with coordinates (x1, y1, z1) and (x2, y2, z2) is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

The distance formula is a fundamental concept in mathematics and is used in many fields, including physics, engineering, and computer science. It is important to understand and apply the distance formula to solve problems related to distances between two points in space.

## Distance Formula Calculator

These **Distance Formula Calculators** can be used to find the distance between two points on a 2D plane or 3D space. They can also be used to find the distance between two pairs of latitude and longitude, or two chosen points on a map: https://www.calculator.net/distance-calculator.html

Here’s a step-by-step guide on how to use the Distance Formula Calculator:

- Identify the two points in the two- or three-dimensional space that you want to calculate the distance between. Let’s call these points Point 1 and Point 2.
- Write down the coordinates of each point. For example, if Point 1 has coordinates (x1, y1) and Point 2 has coordinates (x2, y2) in a two-dimensional space, or if Point 1 has coordinates (x1, y1, z1) and Point 2 has coordinates (x2, y2, z2) in a three-dimensional space.
- Open the Distance Formula Calculator in your web browser.
- Enter the values of the coordinates of Point 1 and Point 2 into the corresponding fields.
- Click the “Calculate” button.
- The calculator will show the result, which is the distance between Point 1 and Point 2.
- You can also use the “Reset” button to clear the fields and start a new calculation.

### Example Using the Distance Formula Between Two Points

### Examples Using the Stopping Distance Formula

### Examples of Euclidean Distance and Manhattan Distance

## What is the Distance Formula?

The Distance Formula is a mathematical formula that is used to calculate the distance between two points in a two-dimensional or three-dimensional space. It is an important concept in mathematics that is widely used in many fields, including engineering, physics, and computer science.

The Distance Formula is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In the case of two points in a two-dimensional space, the hypotenuse is the distance between the two points.

The Distance Formula can be expressed in terms of the coordinates of the two points. If the two points have coordinates (x1, y1) and (x2, y2), then the distance between them is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

In a three-dimensional space, the formula is slightly different. If the two points have coordinates (x1, y1, z1) and (x2, y2, z2), then the distance between them is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2 + (z2 – z1)^2)

The Distance Formula is a fundamental concept in mathematics that is used in many applications. For example, it can be used to calculate the distance between two cities on a map, or the distance between two points in a three-dimensional space in a physics problem.

The Distance Formula is an essential tool in mathematics that allows us to calculate the distance between two points in a two- or three-dimensional space. It is a fundamental concept that is used in various fields and has a wide range of applications. By understanding and applying the Distance Formula, we can solve problems related to distances in space and improve our mathematical skills.

## How is the Pythagorean Theorem Related to the Distance Formula?

The distance formula is derived from the Pythagorean theorem. The Pythagorean Theorem and the Distance Formula are two fundamental concepts in mathematics that are closely related. In fact, the Distance Formula is derived from the Pythagorean Theorem.

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

The Distance Formula is used to calculate the distance between two points in a two- or three-dimensional space. It is derived from the Pythagorean Theorem by treating the distance between the two points as the hypotenuse of a right-angled triangle. If the two points have coordinates (x1, y1) and (x2, y2), then the distance between them is given by:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

This formula can be derived by considering the distance between the two points as the hypotenuse of a right-angled triangle, with the horizontal and vertical differences between the points as the other two sides.

In a three-dimensional space, the Distance Formula is derived in a similar way, by treating the distance between the two points as the hypotenuse of a right-angled triangle with three sides.

In conclusion, the Pythagorean Theorem and the Distance Formula are related in that the Distance Formula is derived from the Pythagorean Theorem by treating the distance between two points as the hypotenuse of a right-angled triangle. By understanding the relationship between these two concepts, we can better understand how to apply them in various mathematical problems and improve our overall mathematical skills.