Long addition — also called column addition — is the paper method for adding numbers: stack them so the place values line up, add one column at a time from right to left, and carry whatever does not fit into the next column. This calculator draws the layout with the carries in small blue digits above each column and explains every column in words.
How to use the long addition calculator
- Type the numbers to add, one per line. Commas for thousands are fine (4,768), and decimals are allowed.
- The sum appears on the tape along with the number of columns and the largest carry.
- The layout shows the numbers aligned by place value. Gray zeros are placeholders added so decimals line up.
- Column by column describes each step: the digits in that column, any carry coming in, the total, the digit written and the carry going out.
The column addition method
- Align the numbers by place value: ones under ones, tens under tens. For decimals, line up the decimal points.
- Add the rightmost column. If the total is 9 or less, write it below.
- If the total is 10 or more, write its last digit and carry the rest to the next column.
- Move one column left and add the digits plus the carry. Repeat until every column is done.
- Write any final carry at the front of the answer.
Worked example
Add 4,768 + 925 + 3,089.5.
Line up the decimal points and treat the whole numbers as 4,768.0 and 925.0.
| Column | Work | Write | Carry |
|---|---|---|---|
| Tenths | 0 + 0 + 5 = 5 | 5 | 0 |
| Ones | 8 + 5 + 9 = 22 | 2 | 2 |
| Tens | 6 + 2 + 8 + 2 = 18 | 8 | 1 |
| Hundreds | 7 + 9 + 0 + 1 = 17 | 7 | 1 |
| Thousands | 4 + 3 + 1 = 8 | 8 | 0 |
Reading the written digits from the top of the table up gives 8,782.5.
Why carrying works
Each column is worth ten times the column to its right. A total of 22 in the ones column is really 2 ones and 2 tens, so the 2 tens belong in the tens column. Carrying is just regrouping ten of one place value into one of the next. The same idea runs in reverse when you borrow in long subtraction.
Checking your answer
- Estimate first. 4,768 + 925 + 3,089.5 is roughly 4,800 + 900 + 3,100 = 8,800, so 8,782.5 is reasonable.
- Add in a different order. Addition is commutative, so adding from the bottom up should give the same total.
- Use subtraction. The sum minus one of the addends should equal the sum of the others.
For quick running totals with a printed tape, the adding machine is faster; for a list of many values with the count and average, use the sum calculator. This tool is for seeing — and learning — the method.
Frequently asked questions
What does carrying mean in addition?
When a column adds up to 10 or more, only the ones digit is written in that column. The tens part is carried to the next column on the left as an extra amount to add. For example, if the ones column totals 22, write 2 and carry 2 to the tens.
Can the carry be bigger than 1?
Yes. With two numbers the carry is never more than 1, but with three or more numbers a column can total 20 or more, so you may carry 2, 3 or even more. Adding twelve 9s in one column gives 108, which writes 8 and carries 10.
How do you add decimals in a column?
Line up the decimal points, not the last digits. Fill the empty places at the right with zeros so every number has the same number of decimal places, add as usual, and put the decimal point in the answer directly below the others.
How many numbers can I add at once?
Up to 12 numbers with up to 30 digits each. Because the calculator works digit by digit rather than with floating-point math, the answer is exact even for very long numbers.