Long Multiplication Calculator
Multiply two numbers the written way, with every partial product shown.
Long multiplication breaks one number into its place values and multiplies by each in turn.
How the long multiplication calculator works
Long multiplication breaks one number into its place values and multiplies by each in turn. For 342 × 27 you compute 342 × 7 and 342 × 20, then add.
The shift is what people forget. Multiplying by the tens digit produces a partial product ten times larger, so it is written one place to the left — the trailing zero that is often left implicit in the way the method is taught.
Formula: a × b = Σ (a × each digit of b × its place value)
Worked examples
| Inputs | Product | Note |
|---|---|---|
| 342 × 27 | 9234 | 9,234 |
| A single-digit multiplier | 3648 | 3,648 |
| Three digits by three | 56088 | 56,088 |
FAQFrequently asked questions
What is long multiplication?
The written method: multiply by each digit of the second number in turn, shifting each partial product one place left, then add.
Why does the second row shift left?
Because that digit stands for tens, so its partial product is ten times larger. The shift is the ×10.
What is a partial product?
The result of multiplying by one digit of the second number, before the partial products are added together.
How do I check the answer?
Estimate by rounding both numbers to one significant figure — 342 × 27 is roughly 300 × 30 = 9,000, close to 9,234.
Does the order matter?
No — multiplication is commutative, though putting the number with fewer digits second gives fewer rows to add.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.