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Interval Merge Calculator

Reviewed by Calculator Editorial Team

An Interval Merge Calculator helps you efficiently combine overlapping time ranges, intervals, or date ranges into non-overlapping intervals. This is particularly useful in scheduling, project management, and data analysis where you need to visualize or process time-based data.

What is Interval Merge?

Interval merging is the process of combining overlapping or adjacent intervals into a set of non-overlapping intervals. This is a fundamental operation in computer science and data processing, often used in algorithms that deal with time-based data.

For example, if you have the intervals [1,3], [2,6], and [8,10], merging them would result in [1,6] and [8,10]. The overlapping intervals [1,3] and [2,6] are combined into [1,6] because they overlap at point 2-3.

Key Concepts

Intervals are typically represented as pairs of numbers [start, end], where start ≤ end. The merge operation combines intervals that overlap or are adjacent. The result is a list of intervals where no two intervals overlap.

How to Use the Calculator

Using the Interval Merge Calculator is straightforward:

  1. Enter your intervals in the input field, separated by commas. Each interval should be in the format [start,end].
  2. Click the "Calculate" button to merge the intervals.
  3. View the merged intervals in the result panel below.
  4. Optionally, view a visualization of the intervals using the chart.

Input Format

Enter intervals in the format [start,end]. For example: [1,3],[2,6],[8,10]

Formula Explained

The interval merge algorithm works as follows:

  1. Sort all intervals based on their start time.
  2. Initialize an empty list to store merged intervals.
  3. Iterate through the sorted intervals:
    • If the current interval overlaps with the last interval in the merged list, merge them by updating the end time of the last interval to be the maximum of both end times.
    • Otherwise, add the current interval to the merged list.
  4. Return the merged list.

Algorithm Steps

1. Sort intervals by start time.
2. Initialize merged list.
3. For each interval in sorted list:
  a. If overlaps with last in merged, merge them.
  b. Else, add to merged list.
4. Return merged list.

Worked Examples

Let's look at a couple of examples to understand how interval merging works.

Example 1: Simple Overlapping Intervals

Input: [1,3],[2,6],[8,10]

Step 1: Sort intervals (already sorted).

Step 2: Merge [1,3] and [2,6] → [1,6].

Step 3: [8,10] doesn't overlap → add to list.

Result: [1,6],[8,10]

Example 2: Adjacent Intervals

Input: [1,4],[4,6],[8,10]

Step 1: Sort intervals (already sorted).

Step 2: Merge [1,4] and [4,6] → [1,6].

Step 3: [8,10] doesn't overlap → add to list.

Result: [1,6],[8,10]

Input Intervals Merged Intervals
[1,3],[2,6],[8,10] [1,6],[8,10]
[1,4],[4,6],[8,10] [1,6],[8,10]
[1,4],[2,3],[5,8],[6,7] [1,4],[5,8]

Frequently Asked Questions

How do I enter intervals into the calculator?

Enter intervals in the format [start,end], separated by commas. For example: [1,3],[2,6],[8,10].

What happens if intervals are not sorted?

The calculator automatically sorts intervals by their start time before merging.

Can I merge intervals that are not overlapping?

Yes, the calculator will merge adjacent intervals (where end of one equals start of another).

What if I enter invalid intervals?

The calculator will show an error message if intervals are invalid (e.g., start > end).