Distance Calculator – 2D & 3D Euclidean Distance Between Two Points

Free Online Tool

Distance Calculator

Q: How do you calculate distance between two points?

Subtract the coordinates, square each difference, sum them, then take the square root: d = √((x2−x1)² + (y2−y1)²).

Q: What is the Euclidean distance formula?

The Euclidean distance formula calculates the straight-line distance between two points using the Pythagorean theorem in n-dimensional space.

Q: How do I calculate 3D distance?

Use d = √((x2−x1)² + (y2−y1)² + (z2−z1)²), adding the z-axis component to the 2D formula.

Q: Can this calculator calculate coordinate distance?

Yes. Enter Cartesian coordinates for two points in 2D or 3D and the calculator returns the exact distance.

Q: What units can I use?

You can display results in meters, kilometers, miles, feet, or yards.

Calculate the distance between two points using the Euclidean Distance Formula in 2D and 3D space.

Inputs

Point A

x₁

y₁

Point B

x₂

y₂

UNIT

Result

10.00

Meters

ΔX6

ΔY8

Formula Used d = √((x₂−x₁)² + (y₂−y₁)²)

Calculation Breakdown √((8−2)² + (11−3)²) = √(36 + 64) = √100 = 10

What Is a Distance Calculator?

A distance calculator is an online tool that computes the straight-line — or Euclidean — distance between two points in a coordinate system. It is essential for math, engineering, navigation, computer graphics, and data science.

★

Why It's Useful

Skip manual arithmetic and instantly find the precise distance between any two coordinates in 2D or 3D space.

⌖

Coordinate Systems

Works with Cartesian coordinates (x, y) for planes and (x, y, z) for volumes, the most common system in science and engineering.

∑

Built On Math

Uses the Euclidean distance formula derived from the Pythagorean theorem to deliver accurate, reliable results every time.

How to Calculate Distance Between Two Points

Follow five simple steps to find the distance between any pair of coordinates.

Identify Coordinates

Note (x₁, y₁) and (x₂, y₂), or include z for 3D.

Find Differences

Subtract: (x₂ − x₁), (y₂ − y₁), (z₂ − z₁).

Square Each

Square each difference to remove negatives.

Add Squares

Sum all of the squared values together.

Square Root

Take the square root to get the distance.

Distance Formula

The Euclidean distance formula in 2D and 3D space.

2D Distance

d = √((x₂ − x₁)² + (y₂ − y₁)²)

3D Distance

d = √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²)

x₁, y₁, z₁Coordinates of Point A

x₂, y₂, z₂Coordinates of Point B

dDistance between A & B

Example Distance Calculations

See exactly how the formula works step by step.

Example 1 — 2D

A (2, 3)

B (8, 11)

d = √((8 − 2)² + (11 − 3)²)
  = √(36 + 64)
  = √100
  = 10

Distance = 10

Example 2 — 3D

A (1, 2, 3)

B (4, 6, 9)

d = √((4 − 1)² + (6 − 2)² + (9 − 3)²)
  = √(9 + 16 + 36)
  = √61
  ≈ 7.81

Distance ≈ 7.81

Real-World Use Cases

Distance calculations power dozens of industries.

📡

GPS Navigation

Calculate route distances and proximity between geographic coordinates.

📐

Surveying

Measure land boundaries and reference distances between survey points.

🏗️

Construction

Verify dimensions and spatial relationships in building plans.

⚙️

Engineering

Solve mechanical and structural problems involving coordinate geometry.

🎮

Computer Graphics

Drive rendering, collision detection, and 3D modeling calculations.

📊

Data Science

Power clustering, KNN, and similarity metrics in machine learning.

Why Use a Distance Calculator

Save time, reduce errors, and learn the math behind every result.

⚡

Faster Calculations

Get instant results without juggling pen, paper, and a scientific calculator.

✓

Improved Accuracy

Eliminate arithmetic mistakes with automated precision computations.

🎓

Educational Learning

See the formula and breakdown to understand the steps, not just the answer.

📈

Coordinate Analysis

Quickly analyze the relationship between any two data points.

🗺️

Mapping Support

Use for cartography, geofencing, and spatial planning tasks.

🛠️

Engineering Ready

Trustworthy results for CAD, robotics, and physics calculations.

Frequently Asked Questions

Everything you need to know about the Distance Calculator.

What is a distance calculator?

A distance calculator is an online tool that uses the Euclidean distance formula to compute the straight-line distance between two points in 2D or 3D space.

How do you calculate distance between two points?

Subtract each pair of coordinates, square the differences, sum them, and take the square root: d = √((x₂−x₁)² + (y₂−y₁)²).

What is the Euclidean distance formula?

The Euclidean distance formula computes the shortest straight-line distance between two points using the Pythagorean theorem extended to n dimensions.

How do I calculate 3D distance?

Use d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²). It simply adds the z-axis term to the 2D formula.

Can this calculator calculate coordinate distance?

Yes. Enter Cartesian coordinates for two points in either 2D or 3D mode and the calculator returns the exact distance.

What units can I use?

You can display the result in meters, kilometers, miles, feet, or yards — switch units at any time.

Calculate Distance Instantly

Use our free Distance Calculator to quickly find the distance between two points in 2D or 3D space.

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