Distance Formula Calculator

What is an Online Distance Formula Calculator?

An Online Distance Formula Calculator is a tool that calculates the distance between two points in a coordinate plane. It uses the distance formula, which is derived from the Pythagorean theorem, to determine the straight-line (or Euclidean) distance between two points. The distance formula is often used in geometry and trigonometry and applies to two-dimensional and three-dimensional space.

The distance formula for two points $(x_1, y_1)$ and $(x_2, y_2)$ in a 2D plane is:

In three-dimensional space, the formula is extended as:

Where:

• $d$ is the distance between the two points,
• $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points (in 2D),
• $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are the coordinates of the points in 3D space.

How to Use an Online Distance Formula Calculator?

1. Access the Tool: Open a web browser and go to an online distance formula calculator.
2. Input the Coordinates: Enter the coordinates of the two points for which you want to calculate the distance. For example, in 2D space, you will input the values for $x_1, y_1$ and $x_2, y_2$.
3. Choose the Dimension (if needed): Some calculators offer the option to select 2D or 3D space for the distance calculation.
4. Click "Calculate" or "Solve": Press the button to compute the distance between the points.
5. View the Result: The calculator will display the distance between the two points, either as an exact value or a decimal approximation.
6. Repeat or Adjust (if needed): You can input new coordinates to calculate the distance for different points.

Frequently Asked Questions-

1. What is the distance formula?
   The distance formula calculates the straight-line distance between two points in a coordinate plane. For 2D space, the formula is:

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

   In 3D space, it is extended to:

   $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$$

   The formula is derived from the Pythagorean theorem.

2. Can I calculate the distance between two points in 3D space?
   Yes, the distance formula calculator can be used to calculate the distance between two points in 3D space. You just need to enter the coordinates for the third dimension ($z_1$ and $z_2$) along with the 2D coordinates.

3. How do I use the calculator if the coordinates are in negative values?
   The calculator can handle negative values for coordinates. Simply enter the negative values as needed. The formula will correctly handle the signs during calculation. For example, if the points are $(-3, -2)$ and $(4, 1)$, the calculator will compute the correct distance.

4. What happens if the two points have the same coordinates?
   If the two points have the same coordinates (i.e., $(x_1, y_1) = (x_2, y_2)$), the distance between them is zero, as there is no separation between the points. The calculator will show the result as $0$.

5. Can the calculator provide the distance as a fraction or decimal?
   Yes, the calculator typically provides the distance in decimal form for non-perfect distances. However, if the result is a perfect square, it may provide the distance as an integer or fraction. You can usually adjust the precision (number of decimal places) based on your needs.