Add numbers
Result
Steps
How long addition works
- Line up by place value. Ones under ones, tens under tens, decimal points in a straight vertical line.
- Add right to left. Start at the smallest place value (rightmost column) and move left.
- Carry the excess. When a column sums to 10 or more, write the ones digit and carry the rest into the next column.
Worked examples
Example: 456 + 789
456 + 789 = 1,245
Classic two-number carry walk.
Line up the numbers by place value: 456, 789.
Ones column: 6 + 9 = 15 → write 5, carry 1
Tens column: 5 + 8 + carry 1 = 14 → write 4, carry 1
Hundreds column: 4 + 7 + carry 1 = 12 → write 12
Done — the sum is 1245.
Example: 99.5 + 0.75
99.5 + 0.75 = 100.25
Decimal alignment: pad to 99.50 + 00.75.
Line up the numbers by place value: 99.50, 00.75.
Hundredths column: 0 + 5 = 5 → write 5, carry 0
Tenths column: 5 + 7 = 12 → write 2, carry 1
Ones column: 9 + 0 + carry 1 = 10 → write 0, carry 1
Tens column: 9 + 0 + carry 1 = 10 → write 10
Done — the sum is 100.25.
Example: 1234 + 5678 + 91
1234 + 5678 + 91 = 7,003
Three addends, one column at a time.
Line up the numbers by place value: 1234, 5678, 0091.
Ones column: 4 + 8 + 1 = 13 → write 3, carry 1
Tens column: 3 + 7 + 9 + carry 1 = 20 → write 0, carry 2
Hundreds column: 2 + 6 + 0 + carry 2 = 10 → write 0, carry 1
Thousands column: 1 + 5 + 0 + carry 1 = 7 → write 7
Done — the sum is 7003.
Example: 0.1 + 0.2
0.1 + 0.2 = 0.3
Exactly 0.3 — no floating-point dust.
Line up the numbers by place value: 0.1, 0.2.
Tenths column: 1 + 2 = 3 → write 3, carry 0
Ones column: 0 + 0 = 0 → write 0
Done — the sum is 0.3.
Why carrying works
Each column is worth ten times the column to its right. So when the ones column adds to 15, that is really 1 ten and 5 ones — the 5 stays, and the 1 ten moves into the tens column where it belongs. Carrying is just regrouping by place value, which is why the method never fails no matter how many digits or addends you stack.
Frequently asked questions
What is long addition?
Long addition (also called column addition or vertical addition) is a written method for adding numbers digit by digit. You stack the numbers so each place value lines up, then add one column at a time from right to left, carrying any excess into the next column.
How do you do long addition step by step?
First, write the numbers in a column so ones sit under ones and tens under tens. Then add each column starting from the rightmost one. If a column sums to 10 or more, write down its ones digit and carry the rest into the next column to the left.
What does “carry the 1” mean in addition?
It means a column added up to 10 or more, so you keep only the ones digit in that column and move the extra ten (the “1”) into the next column left, where it counts as one unit of that larger place value. For example, in 456 + 789 the ones column is 6 + 9 = 15, so you write 5 and carry 1.
How do you add decimal numbers with long addition?
Line up the decimal points so tenths sit under tenths and hundredths under hundredths. Pad shorter decimals with trailing zeros (99.5 becomes 99.50), then add column by column exactly like whole numbers, keeping the decimal point in the same position in the answer.
Can you add more than two numbers at once?
Yes. Stack all the numbers in one column and add each place-value column from top to bottom. A column can sum to 20 or more — in that case you carry 2 (or more) into the next column. This calculator accepts up to 10 numbers.
Why do you start adding from the right?
Because carrying moves left: a column’s excess must be known before the column to its left can be finished. Working from the smallest place value (rightmost) toward the largest guarantees every carry lands in the right column.
What if a column adds up to 20 or more?
Write the ones digit and carry the rest. If a column sums to 27, you write 7 and carry 2, because 27 is 2 tens and 7 ones. The same rule scales: a sum of 35 means write 5, carry 3.
Why does 0.1 + 0.2 equal 0.30000000000000004 on a computer?
Most programming languages store decimals in binary floating point, which cannot represent 0.1 exactly, so tiny rounding errors leak into the answer. This calculator adds digit by digit exactly like you would on paper, so 0.1 + 0.2 is precisely 0.3.
How can I check a long addition answer?
Add the columns a second time, estimate first by rounding each number, or re-add the addends in a different order — the sum must be identical every time. This calculator’s step list makes re-checking each column easy.
How is long addition different from a normal calculator?
A normal calculator only shows the final answer. Long addition shows every column, every carry, and every intermediate sum, which is why teachers use it to teach place value — and why it is the best way to find exactly where a hand calculation went wrong.
Can long addition handle very large numbers?
Yes, the method works for any number of digits. This calculator supports integers up to 24 digits and decimals up to 12 decimal places, far beyond typical school problems.
What is the difference between carrying and borrowing?
Carrying belongs to addition: excess from a column moves left into the next column. Borrowing belongs to subtraction: a column that is too small takes ten from the column to its left. They are mirror images of the same place-value idea.
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