Long Addition Calculator
Add two or more whole numbers or decimals in columns with carrying, shown step by step — every place-value column, each carry, and the final sum.
What is long addition?
Long addition stacks numbers so that matching place values line up in columns, then adds one column at a time from right to left. When a column total passes 9, you carry the extra into the next column — the same idea as trading ten ones for one ten.
Every digit has a place value: in 937, the 9 means 900, the 3 means 30, and the 7 means 7. Adding in columns simply adds the digits that share a place value.
The four steps
- Stack the numbers so ones sit under ones, tens under tens, and so on.
- Add each column from the right.
- Write the ones digit of the column total in the answer.
- Carry the tens digit into the next column when a total is more than 9.
Worked example: 937 + 129 + 248
| Column | Add | Write | Carry |
|---|---|---|---|
| Ones | 7 + 9 + 8 = 24 | 4 | carry 2 |
| Tens | 2 + 3 + 2 + 4 = 11 | 1 | carry 1 |
| Hundreds | 1 + 9 + 1 + 2 = 13 | 3 | carry 1 |
| Thousands | 1 | 1 | — |
So 937 + 129 + 248 = 1,314.
Worked example with decimals: 37.5 + 129.44 + 48.123
Line up the decimal points and pad with trailing zeros so each number has three decimal places: 37.500 + 129.440 + 48.123. Then add column by column exactly as before, starting from the thousandths:
- Thousandths: 0 + 0 + 3 = 3
- Hundredths: 0 + 4 + 2 = 6
- Tenths: 5 + 4 + 1 = 10 → write 0, carry 1
- Ones: 1 + 7 + 9 + 8 = 25 → write 5, carry 2
- Tens: 2 + 3 + 2 + 4 = 11 → write 1, carry 1
- Hundreds: 1 + 0 + 1 + 0 = 2
The result is 215.063.
Chained carries: 99 + 1
Ones: 9 + 1 = 10 → write 0, carry 1. Tens: 9 + 1 = 10 → write 0, carry 1. Hundreds: 1. The carry ripples all the way to a new column, giving 99 + 1 = 100.
Common mistakes
- Columns not aligned — digits end up in the wrong place value.
- Forgetting the carry into the next column.
- Not padding decimals with zeros before adding.
- Decimal points not lined up, which corrupts the whole fractional part.
Where it is used
Column addition adds up bills and expenses, totals quantities across batches, and is the step that combines partial products in long multiplication. It is the additive twin of long subtraction: addition carries, subtraction borrows.
Frequently asked questions
- What is long addition?
- Long addition (or column addition) is adding numbers by stacking them so matching place values line up, then adding one column at a time from right to left and carrying whenever a column total is more than 9. It is the standard written method taught in school.
- What does "carry" mean in addition?
- A carry happens when a column adds up to 10 or more. You write the ones digit of that total in the answer and move the tens digit into the next column to the left. For example, in the ones column 7 + 9 + 8 = 24, so you write 4 and carry 2.
- How do I add decimals in columns?
- Line up the decimal points vertically so tenths sit under tenths and hundredths under hundredths. Pad the shorter numbers with trailing zeros so every number has the same number of decimal places, then add exactly like whole numbers.
- How many numbers can I add at once?
- This calculator adds 2 to 10 numbers at a time. Enter them separated by spaces, commas, or new lines, for example "937 129 248" or "37.5, 129.44, 48.123".
- Why do I add from right to left?
- Adding from the right (the smallest place value) lets each carry flow into the next larger column before you add it. Starting from the left would force you to go back and fix earlier columns every time a carry appears.
- What is the most common mistake in long addition?
- Misaligning the columns. If digits are not stacked by place value — or decimal points are not lined up — you add digits from different places and get the wrong total. Forgetting to add a carry is the second most common slip.
- Is long addition the same as regrouping?
- Yes. "Carrying" and "regrouping" describe the same step — exchanging ten of a smaller unit for one of the next larger unit when a column overflows past 9.