Product Calculator

Product Calculator - Multiply Multiple Numbers

Calculate the product of multiple numbers instantly with our free online product calculator. Multiply numbers separated by commas, spaces, or new lines and get the result with step-by-step breakdown.

What is Product?

The product is the result of multiplying two or more numbers together. It's one of the four basic arithmetic operations, alongside addition, subtraction, and division.

Product Formula

Product = a × b × c × ... × n

Example Calculation

Find the product of: 5, 8, 12

Product = 5 × 8 × 12
Product = 40 × 12
Product = 480

Special Cases in Multiplication

Zero Property

Any number multiplied by zero equals zero.

a × 0 = 0
Example: 5 × 8 × 0 = 0

Identity Property

Any number multiplied by one equals itself.

a × 1 = a
Example: 7 × 1 = 7

Negative Numbers

• Negative × Positive = Negative: -5 × 3 = -15
• Positive × Negative = Negative: 5 × (-3) = -15
• Negative × Negative = Positive: (-5) × (-3) = 15

Properties of Multiplication

Commutative Property

The order doesn't change the product.

a × b = b × a
Example: 3 × 5 = 5 × 3 = 15

Associative Property

Grouping doesn't change the product.

(a × b) × c = a × (b × c)
Example: (2 × 3) × 4 = 2 × (3 × 4) = 24

Distributive Property

Multiplication distributes over addition.

a × (b + c) = a×b + a×c
Example: 2 × (3 + 4) = 2×3 + 2×4 = 6 + 8 = 14

Large Numbers and Scientific Notation

When multiplying many numbers or large values, the result can be very large. Scientific notation helps represent these numbers clearly.

Example: 100 × 200 × 300 × 400 = 2,400,000,000

In scientific notation: 2.4 × 10^9

Common Applications

Area and Volume

• Area = length × width
• Volume = length × width × height
• Surface area calculations

Compound Growth

• Compound interest: Principal × (1 + rate)^time
• Population growth
• Bacterial growth

Combinations and Permutations

• Factorial: n! = n × (n-1) × ... × 2 × 1
• Counting possibilities

Practice Problems

Problem 1

Find the product of: 4, 5, 6

Solution: 4 × 5 × 6 = 120

Problem 2

Calculate: 2 × (-3) × 4

Solution: 2 × (-3) × 4 = -24

Problem 3

A room is 12 ft long, 10 ft wide, and 8 ft high. Find the volume.

Solution: 12 × 10 × 8 = 960 cubic feet