Easily calculate the distance between two points on 2 dimensional plane with our free tool. Just enter the coordinates, and get accurate results instantly.
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What Is the Distance Between Two Points?
Have you ever thought about the shortest path between your home and the local market or the straight-line distance between two cities on a map? The distance between two points is exactly that—it’s the straight-line measurement connecting them, whether on a flat plane (2D) or in space (3D). This concept is fundamental in geometry and is essential for various real-world applications like navigation, engineering, and even in computer graphics.
How to Calculate the Distance Between 2 Points?
Calculating this distance between 2 points is simple when you have the coordinates of the 2 points. By applying below distance formula derived from the Pythagorean theorem, you can find the shortest distance between any two points on a coordinate plane. This method involves basic arithmetic and square roots, making it accessible and easy to use in different scenarios.
Distance Formula to Find Distance Between Two Points on 2D Coordinate Plane
The formula for calculating the distance between 2 points is:
How to Use
- The use of this distance between 2 points calculator is very simple.
- To find the distance between 2 points, you need to input the x-coordinates and y-coordinates of both points in their respective fields.
- Once you provide these coordinates, the tool will calculate and display the straight-line distance between the two points.
Step-by-Step Examples: Calculating Distance Between 2 Points
Example :
1. Find the distance between Point A (3, 4) and Point B (7, 8).
Solution :
Step 1: Identify the coordinates.
- x1 = 3, y1 = 4
- x2 = 7, y2 = 8
Step 2: Subtract the x-coordinates and y-coordinates.
- x2 − x1 = 7 − 3 = 4
- y2 − y1= 8 − 4 = 4
Step 3: Square the differences.
- (x2 − x1)2 = (4)2 = 16
- (y2 − y1)2 = (4)2 = 16
Step 4: Add the squared differences.
- 16+16 = 32
Step 5: Take the square root of the sum to find the distance.
d = √32
d = 5.66
Result:
The distance between Point A and Point B is approximately 5.66 units.
Example :
2. Find the distance between Point C (−3, 7) and Point D (2, −1).
Solution :
Step 1: Identify the coordinates.
- x1 = -3, y1 = 7
- x2 = 2, y2 = -1
Step 2: Subtract the x-coordinates and y-coordinates.
- x2 − x1 = 2 − (-3) = 5
- y2 − y1= (-1) − 7 = -8
Step 3: Square the differences.
- (x2 − x1)2 = (5)2 = 25
- (y2 − y1)2 = (-8)2 = 64
Step 4: Add the squared differences.
- 25 +64 = 89
Step 5: Take the square root of the sum to find the distance.
d = √89
d = 9.43
Result:
The distance between Point C and Point D is approximately 9.43 units.
Does the Distance Formula Work with Negative Coordinates?
Absolutely! The distance formula works flawlessly with both positive and negative coordinates.
When calculating the distance between two points (x1, y1) and (x2, y2), you subtract the coordinates, which might yield negative values.
However, since these differences are squared in the formula, any negative signs disappear.
This ensures that the distance is always a positive value, accurately representing the straight-line separation between two points, regardless of their positions on the coordinate plane.
How Can I Calculate the Distance Between 2 Points in 3D Space?
For points in three-dimensional space with coordinates (x1, y1, z1) and (x2, y2, z2) the distance formula extends to:
d = (x2 − x1)2 + (y2 − y1)2 + (z2 − z1)2
This formula accounts for the additional depth (z-coordinate), allowing you to calculate the straight-line distance between two points in space.
Why is the Distance Always a Positive Value?
Distance represents the magnitude of separation between two points and is always a non-negative value by definition. In the distance formula, even if the differences (x2 − x1) or (y2 − y1) are negative, squaring them results in positive values.
This means the sum under the square root is always positive or zero, ensuring that the calculated distance ‘d’ is always a positive value or zero (when both points are the same). This reflects the fact that distance, as a scalar quantity, has magnitude but no direction.
Understanding that distance is always positive is important when you’re calculating midpoints or endpoints. If you’re looking to find the exact middle point between two locations, our Midpoint Calculator is a handy tool. And if you have a midpoint and one endpoint and need to find the other endpoint, our End Point Calculator can assist you in determining the missing coordinate naturally.