Long subtraction stacks two numbers in columns and subtracts one place value at a time, starting at the right. The only tricky part is borrowing (regrouping) when a top digit is too small — especially when you have to borrow across zeros. This calculator shows the regrouped digits above the crossed-out originals and explains each column.
How to use the long subtraction calculator
- Enter the minuend (the number you start with) and the subtrahend (the number you take away). Whole numbers and decimals both work.
- The tape shows the difference, how many columns needed regrouping, and an addition check.
- In the layout, crossed-out digits were changed by borrowing; the small blue numbers above them are their new values. Gray zeros are placeholders added to line up decimals.
- Read Column by column for the reasoning behind every borrow.
The column subtraction method
- Write the larger number on top and line up the place values (or decimal points).
- Start with the rightmost column. If the top digit is at least the bottom digit, subtract and write the result.
- If the top digit is smaller, borrow: reduce the digit to the left by 1 and add 10 to the current top digit, then subtract.
- Move left and repeat, remembering that a digit that lent 1 is now one less.
Worked example: borrowing across zeros
Subtract 7,003 − 2,468.
- Ones: 3 is less than 8. The tens digit is 0, so it cannot lend directly — borrowing has to reach the thousands.
- The thousands digit 7 lends 1 and becomes 6. The hundreds 0 becomes 10, lends 1 and becomes 9. The tens 0 becomes 10, lends 1 and becomes 9. The ones 3 becomes 13.
- Now subtract column by column: 13 − 8 = 5, 9 − 6 = 3, 9 − 4 = 5, 6 − 2 = 4.
- The difference is 4,535. Check: 4,535 + 2,468 = 7,003 ✓
Subtracting decimals
Line up the decimal points and add zeros so both numbers have the same number of decimal places. For 5.2 − 4.95, write 5.20 − 4.95:
| Column | Work | Result |
|---|---|---|
| Hundredths | 0 < 5, borrow: 10 − 5 | 5 |
| Tenths | 2 lent 1 → 1, which is < 9, borrow: 11 − 9 | 2 |
| Ones | 5 lent 1 → 4; 4 − 4 | 0 |
The answer is 0.25.
Common mistakes
- Subtracting the smaller digit from the larger in every column. In 52 − 38, doing 8 − 2 = 6 in the ones column gives 26; the correct answer, with borrowing, is 14.
- Forgetting that a digit lent 1. After borrowing, the lending digit is one smaller for its own column.
- Misaligning decimals. 12.5 − 3.25 must be lined up on the point: 12.50 − 3.25 = 9.25.
When signed numbers are involved, the integers calculator explains the sign rules; for dollars and cents, the money math calculator handles rounding to the cent.
Frequently asked questions
What is borrowing in subtraction?
When the top digit in a column is smaller than the bottom digit, you take 1 from the next column to the left. That 1 is worth 10 in the current column, so the top digit grows by 10. It is also called regrouping.
How do you borrow across zeros?
If the next column is 0, it has nothing to lend, so keep moving left until you find a nonzero digit. Borrow from it; every zero you pass becomes 9, and the column that needed help gets 10 more. In 7,003 − 2,468 the two zeros become 9s and the 3 becomes 13.
What happens if the second number is larger?
The calculator subtracts the smaller number from the larger one in the layout and puts a minus sign on the answer. For example, 5 − 12 is worked as 12 − 5 = 7, giving −7.
How can I check a subtraction answer?
Add the difference to the number you subtracted. If you get the number you started with, the answer is right: 4,535 + 2,468 = 7,003.