What is the formula for the distance between two points in 2D?

The 2D distance formula is `d = √[(x₂ - x₁)² + (y₂ - y₁)²]`, derived directly from the Pythagorean theorem.

How do you find the midpoint between two points?

The midpoint formula averages coordinates: `Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)`.

What is Manhattan distance versus Euclidean distance?

Euclidean distance is the straight-line ('as the crow flies') diagonal distance. Manhattan distance measures grid-based distance along axes (`|x₂ - x₁| + |y₂ - y₁|`).

Can distance between points ever be negative?

No. Geometric distance is always a non-negative real number ($d \ge 0$). Distance equals zero only if both points are identical.

How does the distance formula work in 3D space?

It extends the 2D formula by adding the squared difference of z-coordinates: `d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]`.

Math & Statistics Cluster

Distance Between Two Points Calculator (2D & 3D Coordinates)

Calculate straight-line Euclidean distance, midpoint, and slope between two coordinate points.

TL;DR: Distance Between Two Points Calculator computes straight-line distance in 2D space using $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ and in 3D space.

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What Is the 2D and 3D Distance Formula Between Two Coordinates?

The 2D Euclidean distance formula between points (x₁, y₁) and (x₂, y₂) is: d = √[(x₂ - x₁)² + (y₂ - y₁)²]. In 3D space between (x₁, y₁, z₁) and (x₂, y₂, z₂), the formula is: d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²].

How to Use the Distance Between Two Points Calculator

Our Distance Between Two Points Calculator performs high-precision mathematical operations directly in your browser with zero latency and complete client-side privacy.

Select dimension mode: 2D Plane $(x, y)$ OR 3D Space $(x, y, z)$.
Enter coordinates for Point 1 $(x_1, y_1)$ and Point 2 $(x_2, y_2)$.
Click 'Calculate Distance' to solve for the Euclidean distance.
Review the step-by-step coordinate delta squaring and square root.
View additional metrics: Midpoint coordinates $M$ and line slope $m$.

Mathematical Formula & Equations

Computes Euclidean distance, midpoint, and directional slope between Cartesian coordinate points in 2D and 3D space.

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

Calculation Example

Distance between points $(2, 3)$ and $(7, 15)$: $$d = \sqrt{(7-2)^2 + (15-3)^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13$$

100% Client-Side Privacy & Data Security

All calculations, amortization schedules, variables, and sensitive numerical datasets execute 100% locally in your web browser memory. Your financial, medical, and personal values are never transmitted, logged, or uploaded to any external server.

Frequently Asked Questions

: The 2D distance formula is `d = √[(x₂ - x₁)² + (y₂ - y₁)²]`, derived directly from the Pythagorean theorem.
: The midpoint formula averages coordinates: `Midpoint M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)`.
: Euclidean distance is the straight-line ('as the crow flies') diagonal distance. Manhattan distance measures grid-based distance along axes (`|x₂ - x₁| + |y₂ - y₁|`).
: No. Geometric distance is always a non-negative real number ($d \ge 0$). Distance equals zero only if both points are identical.
: It extends the 2D formula by adding the squared difference of z-coordinates: `d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]`.
: The Euclidean distance formula between points (x₁, y₁) and (x₂, y₂) is: `d = sqrt[(x₂ - x₁)² + (y₂ - y₁)²]`.

Cite This Calculator

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NexLove.org. (2026). Distance Between Two Points Calculator [Online Calculation Tool]. https://nexlove.org/tools/distance-between-points-calculator

“Distance Between Two Points Calculator.” NexLove.org, 2026, nexlove.org/tools/distance-between-points-calculator.

NexLove.org (2026) Distance Between Two Points Calculator. Available at: https://nexlove.org/tools/distance-between-points-calculator (Accessed: 2026).

@misc{nexlove_distance_between_points_calculator,
  title = {Distance Between Two Points Calculator},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/distance-between-points-calculator}
}

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