Ratio Simplifier: How to Simplify Ratios to Simplest Form

Math & Proportions September 5, 2026 · 10 min read

Ratios are the mathematical foundation of proportion, comparison, and scaling. Whether you are blending aggregate for concrete (cement, sand, and stone), mixing two-stroke engine oil at 50:1, computing aspect ratios for 4K video screens, or solving high-school geometry, simplifying ratios to their lowest terms makes complex quantities understandable at a glance.

Reducing ratios involves finding the Greatest Common Divisor (GCD) between all parts. When ratios contain decimals or multiple segments (such as 3-part or 4-part ratios), simplifying by hand can be tedious and prone to calculation mistakes.

Looking for an instant, automated tool to simplify two-term or multi-term proportions into their lowest whole integers? Use the free online Ratio simplifier at simplifyingratiocalculator.com to simplify any ratio, convert decimal ratios, and view step-by-step factors instantly.

Interactive Ratio Simplifier Tool

Enter any 2-part or 3-part ratio (integers or decimals) below to calculate its simplest whole-number form, unit ratio, and percentage breakdown:

Interactive Tool

Ratio Simplifier

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Tip: Decimals like 1.5 : 2.5 will automatically be scaled to whole numbers before simplifying.
Simplified Result
2 : 3
Greatest Common Divisor (GCD): 12
Unit Ratio (1 : n): 1 : 1.5
Unit Ratio (n : 1): 0.67 : 1
Percentages: 40% : 60%
Reduction: 24 ÷ 12 = 2, 36 ÷ 12 = 3 → 2 : 3

What is a Ratio and Why Simplify It?

A ratio compares two or more relative quantities. It indicates how many times one number contains another. Ratios can be expressed in three distinct ways:

Just like fractions, ratios are easiest to understand, communicate, and scale when reduced to their simplest form—meaning all terms are whole integers that share no common divisor other than 1.

The Standard Method: Finding the Greatest Common Divisor (GCD)

The universal technique to simplify any ratio of whole numbers is dividing each term by the Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF):

The Simplification Formula
Simplified Ratio = (A ÷ GCD) : (B ÷ GCD)

Step-by-Step Example: Simplifying 36 : 60

  1. Find the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
  2. Find the factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  3. Identify common factors: 1, 2, 3, 4, 6, 12
  4. The largest common factor (GCD) is: 12
  5. Divide both terms: \(36 \div 12 = 3\) and \(60 \div 12 = 5\)
  6. Result: \(3 : 5\)

How to Simplify Ratios with Decimals

Ratios frequently appear in recipes or lab formulas with decimals, such as \(1.75 : 2.5\). You cannot have decimals in a final simplified ratio.

To eliminate decimals:

  1. Count the maximum number of decimal places across all terms. (For \(1.75 : 2.5\), the maximum is 2 decimal places).
  2. Multiply each term by \(10^n\) (for 2 decimal places, multiply by \(100\)):
    \(1.75 \times 100 = 175\)
    \(2.5 \times 100 = 250\)
  3. Find the GCD of the new whole integers: \(\text{GCD}(175, 250) = 25\).
  4. Divide both terms by 25: \(175 \div 25 = 7\) and \(250 \div 25 = 10\).
  5. Final Simplified Ratio: \(7 : 10\).

Simplifying 3-Part and Multi-Part Ratios

In construction, masonry, and chemical formulations, ratios frequently involve three or more components. For example, a concrete mix containing 15 shovels of cement, 30 shovels of sand, and 45 shovels of crushed stone:

3-Part Ratio Form
15 : 30 : 45  →  (15 ÷ 15) : (30 ÷ 15) : (45 ÷ 15) = 1 : 2 : 3

Every term must be divisible by the single shared GCD across all three terms. If one term cannot be divided by the common factor, the ratio cannot be reduced further.

Common Real-World Ratios Reference Guide

Application Original Ratio Simplified Ratio Interpretation
Concrete Slab Mix 10 : 20 : 30 1 : 2 : 3 1 part cement : 2 parts sand : 3 parts gravel
Brick Mortar Mix 8 : 24 1 : 3 1 part masonry cement : 3 parts sand
2-Stroke Engine Fuel 100 : 2 50 : 1 50 parts gasoline : 1 part 2-cycle oil
HD Video Aspect Ratio 1920 : 1080 16 : 9 16 width units for every 9 height units
Simple Syrup 200 : 200 1 : 1 Equal parts sugar and boiling water
Vinaigrette Dressing 90 : 30 3 : 1 3 parts olive oil : 1 part red wine vinegar

Understanding Unit Ratios (\(1 : n\) and \(n : 1\))

In engineering and economics, comparisons are often simplified into a unit ratio where one number is standardized to exactly 1. For example, in a ratio of \(4 : 5\):

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Frequently Asked Questions

A simplified ratio is a ratio expressed with the smallest possible positive whole integers, where the terms share no common factor other than 1 (their Greatest Common Divisor is 1). For example, 12:18 simplifies to 2:3.

Find the Greatest Common Divisor (GCD) of all numbers in the ratio, then divide every term by that GCD. For example, in 24:36, the GCD is 12. Dividing both by 12 yields the simplified ratio 2:3.

Multiply all terms by 10, 100, or a sufficient power of 10 to eliminate every decimal point, converting them into whole numbers. Once they are whole integers, divide by their greatest common divisor.

Yes. For a 3-part ratio such as A:B:C (like a concrete mix of 10:20:30), find the GCD of all three terms together (GCD is 10) and divide each term by it, resulting in 1:2:3.

A unit ratio is a ratio where one of the terms is scaled to 1 (such as 1:n or n:1). For example, a map scale of 1 inch to 50 miles, or a fuel-to-oil mix ratio of 50:1.