Sum Calculator

What this calculator does

Use it to:

1. Sum a data set — any count of numbers, including decimals and negatives.
2. Long addition — the same total for non-negative numbers, with stacked place-value steps and carries.

A sum is simply the total after addition. You might sum people per floor to get building occupancy, line items on a receipt, or a statistics sample before computing a mean.

How to enter numbers

Accepted layouts (all become the same list):

Do not use a comma as a thousands separator. Write 7890, not 7,890. If you enter 7,890, it is read as 7 + 890 = 897 and the result includes a non-blocking warning.

Sum formula

Sum = sum(i=1)ⁿ xᵢ = x₁ + x₂ + ⋯ + xₙ

The arithmetic mean is the same total divided by the count:

barx = 1/nsum(i=1)ⁿxᵢ

which is also:

Mean = Sum/n

Sum mode shows both the total and the mean so you can move straight into average-style checks without a second tool. When the mean is a repeating decimal it is labelled with ≈ (for example 256.25 / 9 ≈ 28.4722).

Long addition

Long addition is addition by place value:

1. Stack the numbers and align columns (ones under ones, tenths under tenths).
2. Add each column from right to left.
3. Write the ones digit of the column total; carry any tens to the next column on the left.

Whole-number example: 937 + 129 + 2248

    937
    129
+  2248
  -----
   3314

• Ones: 7 + 9 + 8 = 24 → write 4, carry 2
• Tens: 2 + 3 + 2 + 4 = 11 → write 1, carry 1
• Hundreds: 1 + 9 + 1 + 2 = 13 → write 3, carry 1
• Thousands: 1 → write 1

Decimal example: 37.5 + 129.44 + 48.123

Align decimal points (pad with zeros if needed), then add the same way:

   37.500
  129.440
+  48.123
  -------
  215.063

How the engine adds

• Plain decimals (including mixed signs) are added in base-10, so 0.1 + 0.2 = 0.3 exactly — not the IEEE-754 sequential total 0.30000000000000004.
• Scientific notation (1e3, 2e-12) uses Neumaier compensated summation, which is more stable than naive left-to-right addition when large and small terms cancel.
• Long addition is the schoolbook place-value algorithm with carrying. It matches the exact decimal total for non-negative addends.

Worked sum example

Numbers: -66.25, -37.5, 40, 42, 47, 53, 54, 59, 65

−66.25 + (−37.5) + 40 + 42 + 47 + 53 + 54 + 59 + 65 = 256.25

Count = 9 · mean ≈ 28.4722.

Agent / API notes

• Capability engine sum · page /calc/math/add · REST /api/v1/calc/sum (alias /api/v1/calc/add) · calculation_version 1.0.2
• Share URL: ?mode=sum|long&sumInput=… is server-rendered (the HTML includes the computed sum, not an empty result shell).
• Published input separators: comma and whitespace (spaces, tabs, new lines). Semicolons and pipes may be accepted by the parser but are not part of the published contract.
• Non-blocking warning: THOUSANDS_SEPARATOR_AMBIGUITY when a comma group looks like thousands grouping (7,890 → 7 + 890).
• Stable errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_MODE, VALUE_MUST_BE_NON_NEGATIVE, UNSUPPORTED_FORMAT, TOO_MANY_VALUES, TOO_MANY_DIGITS.

Tips

• Prefer Sum when you only need a total or mean.
• Prefer Long addition when teaching place value or checking handwritten work.
• For percent of a total, use the Percentage Calculator after you have the sum.
• Pair with Subtraction, Multiplication, or Division for the other basic operations.