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Distance Calculator

Calculate the distance between two points using the distance formula.

Point 1 Coordinates

Point 2 Coordinates

0
units
Distance
d = √[(x₂-x₁)² + (y₂-y₁)²]
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Reviewed by Dr. Alex M., Ph.D.
Last updated: November 2025

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💡 Expert Tips

It's Just Pythagoras!

The distance formula is really just the Pythagorean theorem (a² + b² = c²) in disguise. The horizontal distance is 'a', the vertical distance is 'b', and the straight-line distance is the hypotenuse 'c'.

Order Doesn't Matter

Don't worry about which point is (x₁, y₁) and which is (x₂, y₂). Since you square the difference, (5-2)² is the same as (2-5)². You'll get the same answer.

Manhattan Distance

This calculator finds the "crow flies" distance (Euclidean). If you can only move along a grid (like city blocks), you need Manhattan distance: |x₂ - x₁| + |y₂ - y₁|.

⚠️ Common Mistakes

Subtracting Wrong Coordinates

Make sure you subtract x from x, and y from y. A common error is subtracting y₁ from x₁.

Forgetting to Square Root

After adding the squared differences, you must take the square root. If your answer seems huge, you probably forgot this last step.

Sign Errors

Be careful with negative coordinates. Subtracting a negative is adding a positive (e.g., 5 - (-3) = 5 + 3 = 8).

❓ Frequently Asked Questions

What is the distance formula? +

The distance formula is derived from the Pythagorean theorem: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. It calculates the straight-line distance between two points in a 2D plane.

How do I calculate distance between two points? +

1. Subtract the x-coordinates of the two points (x₂ - x₁). 2. Subtract the y-coordinates (y₂ - y₁). 3. Square both results. 4. Add the squared values. 5. Take the square root of the sum.

Can distance be negative? +

No, distance is a scalar quantity representing length, so it is always non-negative. The result of the square root function in the distance formula is always positive or zero.

Does the order of points matter? +

No, the order doesn't matter. Because you square the differences (x₂ - x₁)² and (x₁ - x₂)², the result is the same regardless of which point is first.

What is Euclidean distance? +

Euclidean distance is the straight-line distance between two points in Euclidean space. This calculator computes the 2D Euclidean distance.

📚 References