Adding a long list by hand is slow and error-prone, and a phone calculator gives you no record of what you typed. Paste the numbers here instead: the sum calculator totals them, counts them, finds their average and prints a running total after each value, so you can spot exactly where a typo crept in.
How to use the sum calculator
- Paste or type your numbers. Put one per line, or separate them with spaces, tabs, commas or semicolons.
- Leave out thousands separators (write 1250, not 1,250) and currency symbols other than a leading minus sign for negatives.
- Read the total on the tape. The count, mean, smallest and largest values and the sum of squares appear beneath it, and the running-total table lists the sum after every entry.
The summation formula
Adding a list is written with the Greek capital sigma, Σ:
The running total after the kth value is the partial sum Sₖ = x₁ + … + xₖ, and the mean is simply the sum divided by the count:
Worked example
Five receipts from a trip: $125.50, $89.99, $42.00, $310.25 and $18.75.
| # | Amount | Running total |
|---|---|---|
| 1 | 125.50 | 125.50 |
| 2 | 89.99 | 215.49 |
| 3 | 42.00 | 257.49 |
| 4 | 310.25 | 567.74 |
| 5 | 18.75 | 586.49 |
The total is $586.49 for five receipts, an average of 586.49 ÷ 5 = $117.30 each (117.298 before rounding to cents).
Tips for accurate totals
Check your count first
The most common mistake when totaling a list is a missing or doubled entry, not an addition error. Compare the count on the tape with the number of items you expect. If a bank statement lists 23 transactions and the calculator counts 22, look for a line that pasted together with its neighbor.
Use the running total to reconcile
When a total does not match a statement or invoice, compare running totals line by line. The first place they diverge points to the entry that differs. This is the same technique bookkeepers use with a paper adding-machine tape; the adding machine offers a keypad version.
Watch the decimals
Binary floating-point arithmetic, which every computer uses, cannot represent most decimal fractions exactly. Adding 0.1 ten times in many programs gives 0.9999999999999999. This calculator uses compensated (Kahan–Babuška) summation, which tracks the rounding error as it goes, and displays the result rounded to 12 significant digits, so money and measurement totals come out clean.
Sums of squares and beyond
The sum of squares, Σx², shown on the tape, feeds directly into variance and standard deviation formulas. If your goal is an average where some entries count more than others — credit hours, quantities, portfolio weights — switch to the weighted average calculator. For the arithmetic, geometric and harmonic means of the same list, use the mean calculator.
Frequently asked questions
How do I add a column from a spreadsheet?
Select the cells, copy, and paste into the box. Each cell lands on its own line, and the calculator adds them all. Remove any header text first, since words are not numbers.
Why can't I use commas inside numbers?
Commas separate values in the list, so 1,250 would be read as the two numbers 1 and 250. Type 1250 instead, or put each number on its own line without thousands separators.
Can I add negative numbers?
Yes. Type a minus sign before the number, as in -42.50. The tape then shows the sum of the positive values and of the negative values separately, which is handy for checking a ledger of credits and debits.
Why does a spreadsheet sometimes show tiny errors like 0.30000000000000004?
Computers store decimals in binary, and most decimal fractions cannot be stored exactly. This calculator uses compensated summation and rounds the display to 12 significant digits, so ordinary money amounts add up the way you expect.