Long Multiplication Calculator

Name: Long Multiplication Calculator
Author: Jitendra Kumar

Multiply long integers or decimals with exact products, paper-style partial products, carry steps, and decimal placement work.

Last Updated: May 2026

Product

10,368

Partial products

Decimal places

Digit steps

Multiplication Inputs

Enter two nonnegative whole numbers or decimals. Commas and dollar signs are ignored, and the product is calculated exactly after decimal alignment.

Multiplicand

Multiplier

Long Multiplication Work

    384
x    27
-------
   2688
+  7680
-------
  10368

Single-Digit Carry Steps

Step	Places	Carry in	Raw product	Write	Carry out
4 x 7	ones by ones	0	28	8	2
8 x 7	tens by ones	2	58	8	5
3 x 7	hundreds by ones	5	26	6	2
4 x 2	ones by tens	0	8	8	0
8 x 2	tens by tens	0	16	6	1
3 x 2	hundreds by tens	1	7	7	0

Partial Products

Multiplier digit	Base multiplication	Partial	Shifted partial
7 in the ones place	384 x 7	2,688	2,688
2 in the tens place	384 x 2	768	7,680

Arithmetic Notice

This calculator is for educational arithmetic and exact nonnegative multiplication. It ignores common formatting marks such as commas and dollar signs, but it does not evaluate formulas or mixed-sign expressions.

Checked by Jitendra Kumar

Long Multiplication Calculator is checked for formula labels, source links, and result limits.

Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.

Sources & methodology · Review standards

How to Use the Long Multiplication Calculator

Enter two nonnegative factors. You can use whole numbers or decimals, and you may leave commas or dollar signs in pasted values.

Review the long multiplication layout, partial products, single-digit carry steps, and decimal placement note. The work follows the standard right-to-left paper method.

Step 1: Enter the multiplicand
This is the first factor, or the number being multiplied by each digit of the multiplier.
Step 2: Enter the multiplier
Each digit of this factor creates one partial product row.
Step 3: Review partial products
Check each multiplier digit, base multiplication, and shifted place-value row.
Step 4: Place the decimal
For decimals, add the decimal places in both factors and put that many places in the product.

How This Long Multiplication Calculator Works

Long multiplication breaks a problem into partial products. Each digit of the multiplier is multiplied by the multiplicand, and each row is shifted according to that digit’s place value.

Decimal multiplication uses the same whole-number work. The calculator removes decimal points, multiplies the whole-number factors exactly, then places the decimal point by counting the decimal digits from both original factors.

The carry table shows the small digit-by-digit products inside each partial product. Each raw product writes its ones digit and carries the tens part into the next digit.

Long Multiplication Guide

Core Formulas

Concept	Formula	Use
Multiplication	a x b = product	Combines equal groups or repeated addition.
Partial product	multiplicand x one multiplier digit x place value	Builds each row in long multiplication.
Digit step	digit x digit + carry in	Creates the written digit and next carry.
Carry out	floor(raw product / 10)	Moves tens from a digit step into the next column.
Decimal product	decimal places in factor 1 + decimal places in factor 2	Places the decimal point in the final product.

Examples

Problem	Product	Notes
384 x 27	10,368	384 x 7 plus 384 x 20.
12.49 x 8.6	107.414	Multiply 1249 x 86, then place 3 decimal digits.
987654321987654321 x 123456789	121,932,631,234,567,900,112,635,269	Large integer multiplication is exact.

Multiplication Context

Long multiplication is a place-value algorithm. It works because multiplying by a multi-digit number is the same as multiplying by each place-value part and adding the results.

For example, multiplying by 27 means multiplying by 7 and by 20. The shifted partial product represents the tens place in the multiplier.

Keep the research moving with Long Addition Calculator, Modulo Calculator, Fraction Calculator, and Scientific Calculator.

Frequently Asked Questions

Long multiplication is the paper method that multiplies one factor by each digit of the other factor, shifts each partial product by place value, and adds the partial products.

Yes. It removes decimal points, multiplies the resulting whole numbers, then restores the decimal point using the combined number of decimal places in both factors.

Yes. It uses exact integer-style arithmetic for the whole-number work, so large products are not rounded by floating-point math.

A partial product is one row of long multiplication. It is made by multiplying the multiplicand by a single digit of the multiplier and shifting by that digit’s place value.

Carry out is the tens part of a single digit multiplication step. For example, 8 x 7 = 56 writes 6 in the current column and carries 5 to the next digit.

This calculator focuses on standard paper-style long multiplication for nonnegative factors. Use a scientific calculator for mixed-sign arithmetic.