Long Addition Calculator (column addition with carrying, step by step)

Understanding the long addition calculator — concept and principle

This calculator adds whole numbers in columns, the way it is taught in primary school, and explains every column: the digits added, the digit written down and the amount carried. It also counts the carries. Use it to check homework, teach carrying or verify a written sum.

Work right to left; anything over 9 in a column carries into the next column.

How it is calculated

Line the numbers up by place value: ones under ones, tens under tens.
Add the ones column first.
If a column adds up to 10 or more, write its last digit and carry the rest to the next column on the left.
Repeat for each column, including the carried amount, until all columns are done.

The principle

In base 10, ten ones make one ten, ten tens make one hundred, and so on. A column total of 21 ones is really 2 tens and 1 one, so the 1 stays in the ones column and the 2 moves to the tens. Carrying is just regrouping to keep every column below 10. Adding from the right is necessary because a carry can change the column to its left.

Worked example

Default inputs: 4,837 + 2,596 + 978 (3 numbers).

Ones place: 7 + 6 + 8 = 21 → write 1, carry 2.
Tens place: 3 + 9 + 7 + 2 (carried) = 21 → write 1, carry 2.
Hundreds place: 8 + 5 + 9 + 2 (carried) = 24 → write 4, carry 2.
Thousands place: 4 + 2 + 2 (carried) = 8 → write 8.
Sum: 8,411, with 3 carries.

How to read the result

Check by estimating: about 4,800 + 2,600 + 1,000 = 8,400, close to 8,411. With three or more numbers, a column total can exceed 19, so the carry can be 2 or more, as in every column here.

Common mistakes

Misaligning numbers with different numbers of digits, such as putting 978 under the thousands.
Forgetting to add the carry.
Writing the whole column total instead of its last digit.
Starting from the left.

Keep in mind: Enter whole numbers; separators such as commas are ignored, but a misplaced digit changes the answer.

Frequently asked questions

What is carrying in addition?

Moving the tens of a column total to the next column on the left.

Can the carry be more than 1?

Yes, when three or more numbers are added; here each carry was 2.

How do I check a long addition?

Estimate with rounded numbers, or add the columns in the opposite order.

Sources: OpenStax, Prealgebra 2e (2020), §1.2 Add Whole Numbers

Checked 9 Nov 2026. OpenStax, Prealgebra 2e (2020), §1.2 Add Whole Numbers (write the numbers so each place value lines up vertically; add the digits in each place value from right to left; if a sum in a place value is more than 9, carry to the next place value).

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