Range Notes

Published on: September 29, 2026

This Range Calculator finds how far apart the largest and smallest values in a list are, and shows the working line by line. Sorting the values puts the two ends where they can be read off directly, and subtracting the smaller from the larger gives the distance between them. The range uses only those two values, so it says nothing about the ones between. Following the same pattern every time makes the range easy to check and repeat.

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the smallest and the largest value.
  4. Write the formula.
  5. Substitute the largest and the smallest into the formula.
  6. Subtract to get the range.

Formula:

\(\text{Range} = \text{Maximum} - \text{Minimum}\)
See Example 1 Hide Example 1

Problem

\(10,\; 14,\; 18,\; 22\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the smallest and the largest value.
  4. Write the formula.
  5. Substitute the largest and the smallest into the formula.
  6. Subtract to get the range.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding how far apart the largest and smallest of \(10,\; 14,\; 18,\; 22\) are.

\(10,\; 14,\; 18,\; 22\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(10,\; 14,\; 18,\; 22\).

\(10,\; 14,\; 18,\; 22\)

Step 3

Step 3 - Take the smallest and the largest value.

In this problem: The sorted list starts at \(10\) and ends at \(22\), so those are the smallest and largest values.

\(\text{Minimum} = 10,\; \text{Maximum} = 22\)

Step 4

Step 4 - Write the formula.

In this problem: The range is the distance between the two ends, which is what is left after taking the smallest away from the largest.

\(\text{Range} = \text{Maximum} - \text{Minimum}\)

Step 5

Step 5 - Substitute the largest and the smallest into the formula.

In this problem: Replacing \(\text{Maximum}\) with \(22\) and \(\text{Minimum}\) with \(10\) gives \(\text{Range} = 22 - 10\).

\(\text{Range} = 22 - 10\)

Step 6

Step 6 - Subtract to get the range.

In this problem: Subtracting gives \(22 - 10 = 12\).

\(\text{Range} = 22 - 10 = 12\)

Final Answer

\(\text{Range} = 12\)
See Example 2 Hide Example 2

Problem

\(1,\; 3,\; 3,\; 7\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the smallest and the largest value.
  4. Write the formula.
  5. Substitute the largest and the smallest into the formula.
  6. Subtract to get the range.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding how far apart the largest and smallest of \(1,\; 3,\; 3,\; 7\) are.

\(1,\; 3,\; 3,\; 7\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(1,\; 3,\; 3,\; 7\).

\(1,\; 3,\; 3,\; 7\)

Step 3

Step 3 - Take the smallest and the largest value.

In this problem: The sorted list starts at \(1\) and ends at \(7\), so those are the smallest and largest values.

\(\text{Minimum} = 1,\; \text{Maximum} = 7\)

Step 4

Step 4 - Write the formula.

In this problem: The range is the distance between the two ends, which is what is left after taking the smallest away from the largest.

\(\text{Range} = \text{Maximum} - \text{Minimum}\)

Step 5

Step 5 - Substitute the largest and the smallest into the formula.

In this problem: Replacing \(\text{Maximum}\) with \(7\) and \(\text{Minimum}\) with \(1\) gives \(\text{Range} = 7 - 1\).

\(\text{Range} = 7 - 1\)

Step 6

Step 6 - Subtract to get the range.

In this problem: Subtracting gives \(7 - 1 = 6\).

\(\text{Range} = 7 - 1 = 6\)

Final Answer

\(\text{Range} = 6\)
See Example 3 Hide Example 3

Problem

\(6,\; 15,\; 9,\; 21\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the smallest and the largest value.
  4. Write the formula.
  5. Substitute the largest and the smallest into the formula.
  6. Subtract to get the range.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding how far apart the largest and smallest of \(6,\; 15,\; 9,\; 21\) are.

\(6,\; 15,\; 9,\; 21\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(6,\; 9,\; 15,\; 21\).

\(6,\; 9,\; 15,\; 21\)

Step 3

Step 3 - Take the smallest and the largest value.

In this problem: The sorted list starts at \(6\) and ends at \(21\), so those are the smallest and largest values.

\(\text{Minimum} = 6,\; \text{Maximum} = 21\)

Step 4

Step 4 - Write the formula.

In this problem: The range is the distance between the two ends, which is what is left after taking the smallest away from the largest.

\(\text{Range} = \text{Maximum} - \text{Minimum}\)

Step 5

Step 5 - Substitute the largest and the smallest into the formula.

In this problem: Replacing \(\text{Maximum}\) with \(21\) and \(\text{Minimum}\) with \(6\) gives \(\text{Range} = 21 - 6\).

\(\text{Range} = 21 - 6\)

Step 6

Step 6 - Subtract to get the range.

In this problem: Subtracting gives \(21 - 6 = 15\).

\(\text{Range} = 21 - 6 = 15\)

Final Answer

\(\text{Range} = 15\)
See Example 4 Hide Example 4

Problem

\(12,\; 4,\; 18,\; 7,\; 10\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Sort the values from smallest to largest.
  3. Take the smallest and the largest value.
  4. Write the formula.
  5. Substitute the largest and the smallest into the formula.
  6. Subtract to get the range.

Step 1

Step 1 - Set up the problem.

In this problem: We are finding how far apart the largest and smallest of \(12,\; 4,\; 18,\; 7,\; 10\) are.

\(12,\; 4,\; 18,\; 7,\; 10\)

Step 2

Step 2 - Sort the values from smallest to largest.

In this problem: Putting the values in order from smallest to largest gives \(4,\; 7,\; 10,\; 12,\; 18\).

\(4,\; 7,\; 10,\; 12,\; 18\)

Step 3

Step 3 - Take the smallest and the largest value.

In this problem: The sorted list starts at \(4\) and ends at \(18\), so those are the smallest and largest values.

\(\text{Minimum} = 4,\; \text{Maximum} = 18\)

Step 4

Step 4 - Write the formula.

In this problem: The range is the distance between the two ends, which is what is left after taking the smallest away from the largest.

\(\text{Range} = \text{Maximum} - \text{Minimum}\)

Step 5

Step 5 - Substitute the largest and the smallest into the formula.

In this problem: Replacing \(\text{Maximum}\) with \(18\) and \(\text{Minimum}\) with \(4\) gives \(\text{Range} = 18 - 4\).

\(\text{Range} = 18 - 4\)

Step 6

Step 6 - Subtract to get the range.

In this problem: Subtracting gives \(18 - 4 = 14\).

\(\text{Range} = 18 - 4 = 14\)

Final Answer

\(\text{Range} = 14\)