Long Multiplication Calculator
Multiply two numbers step-by-step. See partial products, alignment, carries, and final product instantly, supporting decimals and negatives clearly with explanations.
Equation Preview
Helping Notes
- Stack numbers right-aligned; multiply each digit of the multiplier by the whole multiplicand.
- Write each partial product one row lower, shifted left by its digit place; then add them all.
- For decimals, ignore points while multiplying, then place the decimal with total decimal places from both inputs.
- Negatives: one negative → negative product; two negatives → positive product.
Results
Final Product
Partial Products
Long Multiplication Steps
Error
What is Long Multiplication Calculator?
A Long Multiplication Calculator automates the traditional column method for multiplying multi‑digit numbers. It breaks the problem into smaller digit‑by‑digit products, aligns them by place value, and accumulates carries to build the final result. This mirrors the manual algorithm taught in schools, but eliminates arithmetic slips and speeds up larger problems. The method relies on decomposing each number into base‑10 digits and summing all partial products at the correct powers of ten.
About the Long Multiplication Calculator
The calculator accepts integers (and, optionally, decimals) and displays every step: the partial products, carry values, and a neat column layout. It emphasizes place‑value alignment, making it ideal for learners, teachers, and anyone verifying homework or financial calculations. You will see each row correspond to a single digit of the second factor, shifted appropriately, then a running total. When decimals are used, the tool counts decimal places after multiplication and positions the decimal point correctly in the final answer.
How to Use this Long Multiplication Calculator
- Enter the first number and the second number in the input fields.
- Choose integer or decimal mode if available, then confirm the number of decimal places (optional).
- Click the calculate button to generate partial products and the running total.
- Study the step table: each row multiplies by a single digit of the second number and shifts by its place.
- Review the final sum and, if decimals are present, note the total decimal places applied to the product.
Examples
Example 1: 247 × 36
Multiply 247 by 36. First compute the row for 6, then for 3 tens, and add.
Example 2: 1.25 × 0.48
Ignore decimals during steps, then place the decimal with total places p+q = 2+2 = 4.
Example 3: 5087 × 64
Two rows: multiply by 4, then by 6 tens, shift and add.
FAQs
Does this work for very large numbers?
Yes. The algorithm scales well; the tool handles large inputs and displays all partial products and carries clearly.
Can I multiply decimals?
Yes. Multiply as integers, then shift the decimal point by the total number of decimal places from both factors.
How are carries managed?
Each column computes a sum, extracts the ones digit as the result, and propagates the quotient to the next column.
Why do rows shift to the left?
Shifts reflect place value: tens, hundreds, and so on. Each additional zero represents a higher power of ten.
Is long multiplication faster than lattice methods?
They are comparable. Long multiplication is more common in curricula, while lattice can be more visual for some learners.
What if a digit is zero?
The partial product row becomes zero. The calculator either hides it or shows a row of zeros for transparency.
Will I see intermediate sums?
Yes. The step table shows each partial product and the cumulative total so you can verify every stage.
Can I copy the steps for homework?
Absolutely. The layout matches the standard column format, making it easy to transfer steps to paper neatly.
Does the method handle negative numbers?
Yes. The sign of the product is negative if exactly one factor is negative; otherwise, the product is positive.
What about rounding?
The product itself is exact. Any rounding should be applied afterward according to your desired precision or context.
Are there limits on input length?
Practical limits depend on device memory. The algorithm itself supports arbitrarily long integers in principle.
How do I verify the final answer?
Estimate using leading digits and place value, or check by reversing the factors and re‑multiplying to confirm.
Can I use this for currency calculations?
Yes. Treat values as decimals with fixed places, then position the decimal accurately in the final product.