Long Addition Calculator

Add up to 10 numbers with full column-by-column working, carry digits, and step-by-step explanation. Supports whole numbers and decimals.

+ Enter Numbers to Add

Quick Examples

What is Long Addition?

Long addition (also called column addition or the standard algorithm) is a written method for adding two or more numbers of any size. Numbers are stacked vertically, aligned by place value — ones under ones, tens under tens — and addition proceeds column by column from right to left.

When a column's sum exceeds 9, only the ones digit is written in the answer row and the remaining amount is carried to the next column on the left.

Right → Left
Always start at the ones column
Align Columns
Same place value in the same column
Carry the 1
Sum ≥ 10? Write ones, carry tens

How to Do Long Addition — 5 Steps

  1. 1

    Write numbers in a column, right-aligned

    Stack all numbers vertically. For decimals, align the decimal points and pad shorter decimals with trailing zeros.

  2. 2

    Add the rightmost column first

    Sum all digits in the ones column. Write the ones digit of the result below the line. If the sum is ≥ 10, carry the tens digit above the next column.

  3. 3

    Move left, include any carry

    For each next column, add all digits plus the carry from the previous column. Write the ones digit below and carry the rest.

  4. 4

    Decimal point drops straight down

    The decimal point is not added — it simply passes through to the answer row at the same position.

  5. 5

    Bring down any final carry

    After the leftmost column, if a carry remains, write it as the leading digit(s) of the answer.

Worked Examples

Example 1 Simple 2-digit: 45 + 67
  1 1
  4 5
+ 6 7
1 1 2
  • Ones: 5 + 7 = 12 → write 2, carry 1
  • Tens: 4 + 6 + 1 = 11 → write 1, carry 1
  • Hundreds (carry only): write 1  → Answer: 112
Example 2 Three numbers: 248 + 376 + 519
  1 2 1
  2 4 8
  3 7 6
+ 5 1 9
1 1 4 3
  • Ones: 8+6+9 = 23 → write 3, carry 2
  • Tens: 4+7+1+2 = 14 → write 4, carry 1
  • Hundreds: 2+3+5+1 = 11 → write 1, carry 1  → Answer: 1143
Example 3 Decimals: 12.5 + 7.35 + 0.9
   1  1
  1 2 . 5 0
   7 . 3 5
+  0 . 9 0
  2 0 . 7 5
  • Hundredths: 0+5+0 = 5 → write 5
  • Tenths: 5+3+9 = 17 → write 7, carry 1
  • Ones: 2+7+0+1 = 10 → write 0, carry 1
  • Tens: 1+1 = 2 → write 2  → Answer: 20.75
Example 4 Chain carry: 9999 + 1
1 1 1 1
 9 9 9 9
+     1
1 0 0 0 0
  • Each column: 9 + carry = 10 → write 0, carry 1 (repeats 4 times)
  • Final carry of 1 becomes the leading digit → Answer: 10000

Properties of Addition

Commutative

a + b = b + a

Order doesn't matter: 3 + 7 = 7 + 3 = 10

Associative

(a+b)+c = a+(b+c)

Grouping doesn't matter: (2+3)+4 = 2+(3+4)

Identity

a + 0 = a

Adding zero changes nothing: 57 + 0 = 57

Closure

ℤ + ℤ = ℤ

Sum of whole numbers is always a whole number

Common Mistakes to Avoid

Misaligning columns

Always right-align whole numbers (or align decimal points). Writing 25 + 7 with the 7 under the 2 adds tens + ones — a wrong answer.

Forgetting the carry

The carry digit must be added to the very next column on the left. Skipping it is the single most common error in long addition.

Writing the full sum below the line

If a column sums to 17, only write 7 below — not 17. The 1 is the carry for the next column.

Misaligning decimal points

12.5 and 7.35 must be written as 12.50 and 07.35 so the decimal columns match exactly.

Frequently Asked Questions

What is "carrying" in addition?
When the sum of a column is 10 or more, you can only write one digit in that column's answer row. The extra ten (or tens) is "carried" to the next column on the left as a small digit written above. For example, 8 + 7 = 15 → write 5, carry 1.
Can the carry ever be more than 1?
Yes! When adding many numbers, a column sum can exceed 19 — giving a carry of 2 or more. For example, five 9s in a column sum to 45: write 5, carry 4. This calculator always shows the exact carry value above each column.
How do I add numbers with different decimal places?
Align all decimal points vertically, then pad shorter numbers with trailing zeros. E.g., 3.5 + 1.25 → write 3.50 + 1.25. Now every column has a digit and you add normally. The decimal point drops straight into the answer row.
Why do we add right to left instead of left to right?
Carries always move left. Starting from the right means every carry produced can be applied immediately in the very next step. Starting left-to-right would require going back and correcting earlier columns.
How many numbers can I add at once?
Up to 10 numbers. You can mix whole numbers and decimals freely. The calculator automatically aligns decimal points, pads with zeros, and shows every carry digit in the working grid.
What is the difference between long addition and mental addition?
Mental addition uses tricks like rounding or partitioning for small sums. Long addition is the formal written algorithm that works reliably for any size number. Mental methods are faster for small numbers; long addition is safer for large or multi-number sums.

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Place Value Reference

Billions1,000,000,000
Millions1,000,000
Hundred Thou.100,000
Ten Thousands10,000
Thousands1,000
Hundreds100
Tens10
Ones ★1
Tenths0.1
Hundredths0.01
Thousandths0.001

Pro Tips

  • →Estimate first by rounding to the nearest 10 or 100 to catch big errors.
  • →Check by adding bottom-to-top — the same answer confirms it's correct.
  • →Pair numbers that sum to 10, 100, or 1000 first to simplify.
  • →For decimals, count decimal places in the answer to verify.