CALCULATE WITH CONFIDENCE

Averages & Means

Average, Sum & Count Calculator

Solve any one of average, sum, or positive whole count from the other two.

Averages & Means

Solve average, sum, or count

Bidirectional exact relationship
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example

Average

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Feedback

Understand the subject

How are average, sum, and count connected?

Average, sum, and count are three views of the same relationship. Know any two and you can solve the third—provided the count is a real positive whole number.

The relationship

The defining relationship

Sum is the total of all values; count is how many values there are; average is the equal-share value.

See the idea

One identity, three possible solves

Worked example

Recover the total

An average of 12 across 8 values means the total is 12 × 8 = 96. In reverse, 96 divided by 8 gives 12.

Interpret with care

Choose the relationship that fits

A result of 2.4 for a count is not a valid count of observations. Also, a sum of 0 and average of 0 do not identify one unique positive count.

For a side-by-side view of the classical means, use the Mean Comparison Calculator.

Quick guide

How to use this calculator

  1. Choose the quantity to solve.
  2. Enter the other two known quantities.
  3. For a count result, check that the implied result is a positive whole number.

Calculation method

Use one three-part identity

Sum equals average multiplied by count. The calculator rearranges this identity exactly and classifies impossible or indeterminate count cases.

Worked example

Recover a total

An average of 12 across 8 values corresponds to a sum of 96.

sum = average × count = 12×8 = 96

Supported inputs

Precision and limits

Count

Entered or solved counts must be positive whole numbers no greater than 1,000,000.

Exactness

Finite decimals are evaluated as exact rational values.