3
(2–6)
Total Sum
—
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Sources & Methodology
Long addition methodology follows the standard algorithm as defined in Common Core State Standards for Mathematics (CCSSM) and verified against Khan Academy primary arithmetic curriculum.
Khan Academy — Adding Multi-Digit Numbers
Standard curriculum reference for the column addition method, carries, and place value alignment used in this calculator
Common Core State Standards — CCSS.Math.Content.4.NBT.B.4
Fluently add multi-digit whole numbers using the standard algorithm — the authoritative US curriculum definition of long addition
Methodology: Numbers are right-aligned by place value. Each column is summed from right (ones) to left. When a column total ≥ 10, the tens digit(s) are carried to the next column. The final sum is computed using JavaScript's native integer arithmetic. The column working display shows carries above each column for full transparency.
⏱ Last reviewed: April 2026
How to Do Long Addition Step by Step
Long addition (also called column addition or the standard algorithm) is the written method for adding numbers with two or more digits. Numbers are stacked vertically aligned by place value, then each column is added from right to left. When a column sum reaches 10 or more, the extra amount “carries” into the next column.
The Standard Algorithm
Step 1: Stack numbers right-aligned (ones under ones, tens under tens)
Step 2: Add the ones column. If sum ≥ 10 → write ones digit, carry tens digit above next column
Step 3: Add the tens column + any carry. Repeat left through every column
Step 4: The final row is the complete sum
Step 3: Add the tens column + any carry. Repeat left through every column
Step 4: The final row is the complete sum
Worked Example: 345 + 678 + 912
| Column | Digits | Carry In | Total | Write | Carry Out |
|---|---|---|---|---|---|
| Ones | 5 + 8 + 2 | 0 | 15 | 5 | 1 |
| Tens | 4 + 7 + 1 | 1 | 13 | 3 | 1 |
| Hundreds | 3 + 6 + 9 | 1 | 19 | 9 | 1 |
| Thousands | 0 + 0 + 0 | 1 | 1 | 1 | 0 |
Result: 1,935. Verify: 345 + 678 = 1,023; 1,023 + 912 = 1,935 ✔
Rules for Carrying
- If a column sum is 0–9: write the digit, carry 0
- If a column sum is 10–19: write the ones digit, carry 1
- If a column sum is 20–29: write the ones digit, carry 2
- The carry is always the tens digit of the column total
- The last column carry becomes part of the result (a new leading digit)
Adding Numbers With Different Lengths
Right-align all numbers regardless of their digit count. A 3-digit number added to a 6-digit number simply has leading zeros in the higher columns. The algorithm works identically — those columns just add 0 (plus any carry). Never left-align for addition.
💡 Quick Check Method: After computing the sum, estimate by rounding each number to its leading digit. For 345 + 678 + 912 ≈ 300 + 700 + 900 = 1,900. The exact answer 1,935 is close to 1,900, confirming no major error. If your answer is far from the estimate, recheck the carries.
Frequently Asked Questions
Long addition (column addition) is the standard written method for adding numbers with multiple digits. Numbers are stacked vertically aligned by place value — ones under ones, tens under tens — then each column is summed right to left. When a column total exceeds 9, the carry digit moves to the next column. It is the foundation of arithmetic taught worldwide.
1) Write all numbers stacked vertically, right-aligned by place value. 2) Add the ones column. Write the ones digit of the total; carry the tens digit above the tens column. 3) Add the tens column plus any carry. Repeat for each column. 4) If the final (leftmost) column has a carry, write it as the leading digit of the answer.
Carrying (regrouping) happens when a column total is 10 or more. Write the ones digit of the total below the line, and write the tens digit above the next column to the left. For example: 7 + 8 = 15 — write 5, carry 1. The carried 1 is then added into the next column's sum. Without correct carries, the answer will be wrong.
Stack all numbers vertically aligned by place value, regardless of how many there are. Add the ones column of all numbers together. The result may be larger than 9 — that is fine. Write the ones digit of the total; carry all remaining digits (tens and hundreds if needed). Repeat for every column. The method scales to any number of addends.
The most common errors are: 1) Misaligning digits — always align on the right, not the left. 2) Forgetting to add the carry to the next column. 3) Adding the carry twice. 4) Dropping a digit when writing the carry. 5) Not including a number's full digit count — shorter numbers have implied leading zeros in higher columns.
Three methods: 1) Estimate — round each number to its highest place value, sum them, and confirm your answer is close. 2) Reverse check — subtract one addend from the total and verify you recover the remaining sum. 3) Digit sum — add all digits of each addend, sum them together, and compare to the digit sum of the answer (they must match modulo 9).
Yes. Align decimal points vertically rather than right-aligning on the last digit. Pad shorter decimals with trailing zeros so all numbers have the same number of decimal places. Then add column by column exactly as with whole numbers. The decimal point in the answer sits directly below the aligned decimal points.
Mental addition relies on memory and estimation shortcuts — it is fast but error-prone with large numbers. Long addition is a formal written algorithm that tracks carries explicitly, making it reliable for any size numbers. Long addition is slower but guarantees accuracy and leaves a written record of every step for checking.
Right-align all numbers — this automatically places ones under ones, tens under tens, and so on. A 3-digit number aligned with a 6-digit number effectively has three leading zeros in the thousands, ten-thousands, and hundred-thousands columns. The algorithm proceeds normally; those columns simply contribute 0 from the shorter number.
The column method is the formal written algorithm for addition (and also subtraction and multiplication) taught in primary and middle school. For addition, numbers are written in vertical columns aligned by place value, then processed right to left with carries noted above each column. It is also called long addition, vertical addition, or the standard algorithm.
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