Summation (Sum) Calculator

What this calculator does

You have a list of numbers and you just want the total. This adds them all up, however many there are, and however messy the mix of decimals and negatives.

Paste your numbers in and it gives you how many there were and their sum. It runs right here in the browser.

Using the calculator

1. Enter your numbers, separated by commas, spaces, or line breaks: 1.618, 2, 3.14, -8.5.
2. Press Calculate.

You get the count of numbers and their total, with large results comma-grouped so they stay readable. Reset clears the box.

Summation, and the sigma symbol

Summation is just the formal word for adding a set of numbers together, and the total is called the sum. In maths you will often see it written with a big Greek letter sigma, which looks like this: Σ. It is not as scary as it looks. The sigma simply says "add up all the terms", with little notes above and below it telling you where to start and stop. So this tool is a summation machine: you hand it the terms, it hands you the Σ.

Because addition does not care about order, you can list your numbers in any sequence at all and the total comes out the same. The tool just runs straight down the list adding as it goes.

A worked example

Take 5, 8, 12 and 3. Adding left to right: 5 + 8 = 13, then 13 + 12 = 25, then 25 + 3 = 28. Shuffle them to 3, 12, 5, 8 and you still land on 28, because the order of adding never changes a sum. Decimals and negatives work exactly the same way, so a list like 1.618, 2, 3.14, -8.5 simply adds to -1.742.

Sums with a pattern

This tool adds any numbers you give it, no pattern required. But some sums follow a rule so neat that you do not have to list every term, because a formula gives the total in one step. If your numbers go up by a fixed step or multiply by a fixed ratio, the sum of series calculator totals them from just a few facts. And two special cases have their own shortcuts and their own tools: the sum of cubes and the sum of consecutive squares, both of which turn out to be surprisingly beautiful.

Questions people ask

How do I add a long list of numbers quickly?

Paste them all in, separated by commas or spaces, and the tool returns the total in one step, so there is no adding by hand.

What does the sigma symbol mean?

The Greek letter Σ is shorthand for summation. It means "add up all the terms", with the numbers above and below it marking where to start and finish.

Does the order of the numbers matter?

No. A sum is the same whatever order you add the numbers in, so you can enter them however you like.

Does it handle decimals and negative numbers?

Yes, in any mix. Negatives are subtracted from the running total as you would expect.

How do I separate the numbers?

Commas, spaces or line breaks all work.

References

A note on the idea. Summation is the addition of a sequence of numbers to give a total, written compactly with the sigma symbol Σ, and it is one of the most basic operations in mathematics. For further reading, see Summation.

1. Summation notation, the use of the Greek letter Σ to denote the sum of a set or sequence of terms.