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Distance Formula Calculator

Enter the coordinates of the points, and the calculator will compute the distance between them in one to four-dimensional space, including calculations using latitude and longitude.

Type:

Dimensions :

First Point:

Second Point:

First Point:

Second Point:

Third Point:

First Point:

Line [y = mx + b]:

Second Line [y = m₂x + b₂]:

First Point:

Second Point:

Third Point:

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This distance formula calculator helps you determine the distance between points, lines, or parallel lines in 1D to 4D space. It works with positive and negative numbers, decimals, and fractions for accurate results.

Understanding Distance

Distance represents the length of the straight line connecting two points or the separation between two lines. In everyday terms, it could measure the space between your home and a parking spot or between two locations on a map.

Key Points About Distance Calculations:

You need at least two points to calculate distance.
Points are described by their coordinates in 1D, 2D, 3D, or 4D space.
Each point has unique coordinates that identify its exact position.
The distance formula accurately accounts for all coordinates of each point.

For midpoint calculations, try our endpoint calculator.

Finding Distance Between Points

Here are examples of distance calculations for two and three points.

Example 1: Distance Between Two Points

Points:

Point A: (-3, 2)
Point B: (3, 5)

Assign coordinates:

X1 = -3, Y1 = 2
X2 = 3, Y2 = 5

Distance formula:

\(D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

Substitute the values:

\(D = \sqrt{(3 - (-3))^2 + (5 - 2)^2} = \sqrt{6^2 + 3^2} = \sqrt{36 + 9} = \sqrt{45} \approx 6.708\)

Example 2: Distance Among Three Points

Coordinates:

Point 1: (4, 1)
Point 2: (-2, 10)
Point 3: (7, 2)

Step 1: Distance between points 1 and 2:

\(D_1 = \sqrt{(-2 - 4)^2 + (10 - 1)^2} = \sqrt{(-6)^2 + 9^2} = \sqrt{36 + 81} = \sqrt{117} \approx 10.816\)

Step 2: Distance between points 2 and 3:

\(D_2 = \sqrt{(7 - (-2))^2 + (2 - 10)^2} = \sqrt{9^2 + (-8)^2} = \sqrt{81 + 64} = \sqrt{145} \approx 12.042\)

Step 3: Distance between points 3 and 1:

\(D_3 = \sqrt{(7 - 4)^2 + (2 - 1)^2} = \sqrt{3^2 + 1^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.162\)

Step 4: Average distance:

\(D_{avg} = \frac{D_1 + D_2 + D_3}{3} = \frac{10.816 + 12.042 + 3.162}{3} \approx 8.673\)

Using the Distance Formula Calculator

Steps to calculate distance in 1D to 4D:

Input:

Select the type (2 points, 3 points, or lines).
Select the dimension (1D, 2D, 3D, or 4D).
Enter the coordinates:
- 1D: X1, X2
- 2D: X1, Y1, X2, Y2
- 3D: X1, Y1, Z1, X2, Y2, Z2
- 4D: X1, Y1, Z1, K1, X2, Y2, Z2, K2
Click "Calculate."

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