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Tool Ratio Simplifier

Enter your ratio using colons, commas, or spaces. The calculator instantly reduces it to its simplest form (lowest terms) and shows the full working plus a visual block diagram comparing the before-and-after proportions.

Enter two or more positive numbers separated by :, commas, or spaces. Example: 12 : 18 or 12, 18, 24

Tip: press Ctrl + Enter to simplify instantly.

Enter a ratio and press Simplify to see the result.

Explained How Ratio Simplification Works

A ratio compares two or more quantities. Simplifying a ratio means expressing it in the smallest possible whole numbers while keeping the same proportion between the parts.

The Core Rule

Step 1: Find the GCD of all parts of the ratio.
Step 2: Divide every part by that GCD.
Result: The ratio is now in its simplest form.
Why it works: Dividing every part of a ratio by the same number preserves the proportion. The GCD is the largest common divisor, so it gets you to the simplest form in a single step.

Handling Decimals

If any part of the ratio contains a decimal, first multiply all parts by 10 until they become whole numbers, then divide by the GCD.

Example: 0.5 : 1.5
Multiply by 10 → 5 : 15
Divide by GCD(5, 15) = 5 → 1 : 3

Handling Fractions

If the ratio contains fractions, multiply all parts by the LCM of the denominators to clear the fractions, then simplify by the GCD.

Example: 1/2 : 3/4
LCM of denominators (2, 4) = 4
Multiply all by 4 → 2 : 3
Already in simplest form → 2 : 3

Reading the Visual Diagram

Each block below represents one unit. The "Before" row shows the raw ratio, and the "After" row shows the simplified ratio. Because both rows use the same proportion, the visual "shape" of the two ratios is identical — just with fewer blocks in the second row.

Reference Common Ratio Simplifications

Original Ratio GCD Simplified Ratio
12 : 1862 : 3
8 : 1242 : 3
15 : 2553 : 5
24 : 36122 : 3
100 : 75254 : 3
1920 : 108012016 : 9
12 : 18 : 2462 : 3 : 4
45 : 60 : 90153 : 4 : 6
0.5 : 1.551 : 3
1/2 : 3/412 : 3
Real-world use: Aspect ratios (like 1920:1080 → 16:9), recipe scaling, gear ratios, and map scales all benefit from simplifying ratios to their lowest terms.

FAQ Frequently Asked Questions

How do you simplify a ratio?

Divide every number in the ratio by their Greatest Common Divisor (GCD). For example, 12:18 becomes 2:3 because GCD(12, 18) = 6, and 12 ÷ 6 : 18 ÷ 6 = 2 : 3.

Can I simplify a ratio with three numbers?

Yes. Find the GCD of all three numbers, then divide each by it. For example, 12:18:24 simplifies to 2:3:4 because GCD(12, 18, 24) = 6.

How do I simplify a ratio with decimals?

Multiply all numbers in the ratio by 10 until they become whole numbers, then simplify by the GCD. For example, 0.5:1.5 → (×10) 5:15 → (÷5) 1:3.

How do I simplify a ratio with fractions?

Multiply all parts of the ratio by the LCM of the denominators to clear the fractions, then simplify by the GCD. For example, 1/2 : 3/4 → (×4) 2:3 (already in simplest form).

What is the simplest form of a ratio?

A ratio is in simplest form when the only common factor of all its parts is 1. For example, 3:4 is in simplest form, but 6:8 is not — it simplifies to 3:4.

Does the order of the numbers matter?

Yes! Ratios are order-sensitive. 2:3 is different from 3:2. The simplification preserves the order while reducing the numbers.

What does the visual diagram show?

Each colored block represents one unit of the ratio. The "Before" row shows the raw numbers as blocks, and the "After" row shows the simplified version. Both rows have the same visual proportions — the second just uses fewer blocks. This makes it easy to see that simplifying a ratio keeps the same relationship between parts.