Long Multiplication Calculator (partial products, step by step)

Understanding the long multiplication calculator — concept and principle

This calculator multiplies two whole numbers by the standard written method, showing each partial product, the placeholder zeros and the final addition. It also counts the partial products and the digits of the answer. Use it to check homework, teach the method or verify a hand calculation.

One partial product per digit of 27, shifted by its place value, then added.

How it is calculated

Multiply the top number by the ones digit of the bottom number: the first partial product.
Multiply by the tens digit and add one zero on the right (it is really × 10).
Continue for hundreds (two zeros) and so on.
Add all the partial products.

The principle

Long multiplication is the distributive property applied to place values: 4,836 × 27 = 4,836 × (20 + 7) = 4,836 × 7 + 4,836 × 20. Each digit of the multiplier stands for a number of tens, hundreds and so on, which is why its partial product is shifted left with placeholder zeros. Adding the shifted pieces rebuilds the full product.

Worked example

Default inputs: 4,836 × 27.

Ones place: 7 × 4,836 = 33,852.
Tens place: 2 × 4,836 = 9,672 → with zeros added: 96,720.
Add the partial products: 33,852 + 96,720 = 130,572.
Product: 130,572, from 2 partial products, with 6 digits.

Each point is the calculator re-run with only “First number (multiplicand)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

First number (multiplicand)	Product
1,209	32,643
2,418	65,286
3,627	97,929
4,836	130,572
6,045	163,215
7,254	195,858
9,672	261,144

How to read the result

Estimate to check: 5,000 × 27 = 135,000, slightly above the answer because 4,836 is a bit under 5,000. The number of digits in a product is the sum of the digits of the factors or one less: here 4 + 2 = 6.

Common mistakes

Forgetting the placeholder zero on the second partial product.
Losing a carry inside a partial product.
Misaligning the partial products before adding.
Multiplying by the tens digit as if it were ones.

Keep in mind: Enter whole numbers only. For decimals, multiply as whole numbers and then place the decimal point by counting decimal places.

Frequently asked questions

Why do we add a zero in long multiplication?

Because the tens digit means tens: multiplying by 2 in the tens place is multiplying by 20.

What is 4,836 × 27?

130,572.

How can I check a long multiplication?

Estimate with rounded numbers, or swap the two numbers and multiply again.

Sources: OpenStax, Prealgebra 2e (2020), §1.4 Multiply Whole Numbers

Checked 9 Nov 2026. OpenStax, Prealgebra 2e (2020), §1.4 Multiply Whole Numbers (multiply the top number by the ones digit, then by the tens digit and so on; insert a zero as a placeholder with each additional partial product; add the partial products).

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