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Math

Distance Formula Calculator.

Calculates the straight-line distance between two points in a 2D plane using the Euclidean distance formula.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Subtract x₂ - x₁ to find the horizontal difference.

  2. 2

    Subtract y₂ - y₁ to find the vertical difference.

  3. 3

    Square both differences and add them together.

  4. 4

    Take the square root of the sum to get the distance.

sqrt((x2-x1)^2 + (y2-y1)^2)

Frequently asked questions

What is the distance formula?

It calculates the straight-line distance between two points (x₁,y₁) and (x₂,y₂) as √((x₂-x₁)² + (y₂-y₁)²).

Can I use this for 3D points?

No, this calculator is for 2D only. For 3D, you would add the z-difference squared under the square root.

What if the distance is negative?

Distance is always non-negative because it's a square root of a sum of squares. The result will never be negative.

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How it works

Calculates the straight-line distance between two points in a 2D plane using the Euclidean distance formula.

  1. Subtract x₂ - x₁ to find the horizontal difference.
  2. Subtract y₂ - y₁ to find the vertical difference.
  3. Square both differences and add them together.
  4. Take the square root of the sum to get the distance.

Formulas

The math behind this calculator, written out so you can verify the result.

Euclidean Distance

d = √((x₂ - x₁)² + (y₂ - y₁)²)

This formula comes from the Pythagorean theorem, treating the differences as legs of a right triangle.

Example:

Input: Points (0,0) and (3,4)

Calculation: √((3-0)² + (4-0)²) = √(9+16) = √25

Result: 5 units

Real-world use cases

Where this calculation shows up in everyday life.

Navigation

Find the shortest path between two locations on a map, ignoring roads.

Example: Distance from home to work as the crow flies.

Geometry

Determine side lengths in triangles or polygons.

Example: Check if a triangle is right-angled.

Physics

Calculate displacement between two positions.

Example: Distance traveled by an object in a straight line.

Tips and common mistakes

Tips

  • Double-check the order of coordinates: (x₁,y₁) is the first point, (x₂,y₂) is the second.
  • Use negative numbers correctly; the formula handles them automatically.
  • For quick estimates, you can approximate the square root if needed.

Common Mistakes to Avoid

  • Forgetting to square the differences before adding.
  • Subtracting in the wrong order (x₁ - x₂ instead of x₂ - x₁) – it doesn't matter because squaring removes the sign.
  • Using the formula for 3D without adding the z-component.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.