Distance Calculator 2D

  • Enter the X and Y coordinates for Point 1 and Point 2.
  • Click "Calculate Distance" to find the distance between the two points.
  • Results will be displayed as a chart, text, and in the Calculation History section below.
  • Click "Clear Results" to clear both the chart and the history.
  • Click "Copy Result" to copy the latest result to the clipboard.
Distance Result:

Calculation Details:

Formula used: Distance = √((X2 - X1)^2 + (Y2 - Y1)^2)

Explanation: The formula calculates the Euclidean distance between two points in a 2D plane. It measures the straight-line distance between Point 1 (X1, Y1) and Point 2 (X2, Y2).

Detailed Calculation: The calculation involves finding the difference in X and Y coordinates, squaring them, summing the squares, and taking the square root of the sum to get the distance.

Calculation History:

    What is 2D Distance?

    The 2D distance, also known as the Euclidean distance, between two points (x1, y1) and (x2, y2) in a two-dimensional plane can be calculated using the following formula:

    Distance = √((x2 – x1)^2 + (y2 – y1)^2)


    • (x1, y1) are the coordinates of the first point.
    • (x2, y2) are the coordinates of the second point.
    • √ denotes the square root operation.
    • (x2 – x1)^2 represents the squared difference of the x-coordinates.
    • (y2 – y1)^2 represents the squared difference of the y-coordinates.

    All Formulae Related to 2D Distance

    1. Euclidean Distance:
      • Formula: √((x2 – x1)^2 + (y2 – y1)^2)
      • Calculates the straight-line distance between two points in a 2D plane.
    2. Manhattan Distance:
      • Formula: |x2 – x1| + |y2 – y1|
      • Calculates the distance between two points in a grid-like fashion, where you can only move horizontally or vertically (no diagonal movement).
    3. Minkowski Distance:
      • Formula: [Σ(|xi – yi|^p)]^(1/p) for i = 1 to n (for n-dimensional space)
      • Generalizes distance calculation by introducing a parameter ‘p’. When p=1, it’s the Manhattan distance; when p=2, it’s the Euclidean distance.
    4. Chebyshev Distance (Chessboard Distance):
      • Formula: max(|x2 – x1|, |y2 – y1|)
      • Measures the distance when movement is allowed in all directions (horizontal, vertical, diagonal).
    5. Hamming Distance (for binary vectors):
      • Formula: Σ(|xi – yi|) for i = 1 to n
      • Measures the difference between two binary vectors of equal length.
    6. Cosine Distance (for vectors):
      • Formula: 1 – (Σ(xi * yi) / (sqrt(Σ(xi^2)) * sqrt(Σ(yi^2))))
      • Measures the cosine of the angle between two vectors, used in vector space similarity analysis.
    7. Jaccard Distance (for sets):
      • Formula: 1 – (|A ∩ B| / |A ∪ B|)
      • Measures the dissimilarity between two sets by comparing their intersection and union.

    Applications of 2D Distance Calculator in Various Fields

    A 2D distance calculator, which computes distances between points in a two-dimensional space, finds applications in various fields. Here are some common areas where it is utilized:

    1. Geographic Information Systems (GIS):
      • Calculating distances between geographical coordinates to determine travel distances, shortest routes, or proximity analysis for mapping and navigation.
    2. Computer Graphics:
      • Determining the distance between pixels or vertices in 2D images, which is essential for rendering, image processing, and computer games.
    3. Robotics:
      • Robot path planning, obstacle avoidance, and control algorithms use 2D distance calculations to ensure safe and efficient movement.
    4. Machine Learning and Data Analysis:
      • Feature engineering: Calculating distances between data points for clustering, dimensionality reduction, or similarity analysis.
    5. Statistics:
      • In hypothesis testing and data analysis, distance measures can help assess the similarity or dissimilarity between data points or samples.

    Benefits of Using the 2D Distance Calculator

    Using a 2D distance calculator offers several benefits in a wide range of applications and fields. Here are some of the key advantages:

    1. Accuracy: 2D distance calculators provide precise measurements, ensuring accurate results in applications where precise spatial relationships are critical, such as geographic analysis and engineering.
    2. Efficiency: They automate the distance calculation process, saving time and effort compared to manual calculations, especially when dealing with large datasets or complex geometries.
    3. Consistency: Calculations are consistent and repeatable, reducing the likelihood of human errors that can occur with manual measurements.
    4. Versatility: 2D distance calculators can handle various distance metrics, allowing users to choose the most appropriate measure for their specific needs, whether it’s Euclidean, Manhattan, Minkowski, or others.
    5. Speed: These calculators can quickly process a large number of distance calculations, making them suitable for real-time or near-real-time applications, such as robotics and navigation.
    6. Optimization: In fields like logistics and supply chain management, distance calculators help optimize routes, reducing transportation costs and delivery times.


    1. “Beyond Cartesian Coordinates: Distance Measures in Riemannian Geometry and Computer Graphics” by SIGGRAPH Asia
    2. “From Robotics to Path Planning: Distance Metrics in Sensor Fusion and Autonomous Systems” by IEEE Transactions on Robotics and Automation

    Last Updated : 27 February, 2024

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