Ratio Simplifier

Proportions without the noise

A ratio is two numbers and a relationship; simplification is discovering the smallest pair that keeps that relationship intact. This tool divides both numbers by their greatest common divisor (GCD) — the largest number that goes into both — and prints the result as "smaller:larger simplified", with the GCD shown in the detail line as proof of work. Simplified is not cosmetic: recipes, screens and carousels scaled from 1,920 × 1,080 all inherit the compact 16:9; a ratio that stays unscaled is the first domino of many measurement drifts downstream.

What the page deliberately does not do: convert a ratio into a percentage (that needs the Percentage Points Calculator for gap language, or a division performed on your side), nor mix different units — 3 kg per 4 pieces and 3:4 pieces are different claims even though both contain a 3 and a 4. And decimals: the tool rounds to whole numbers first, so 7.5 : 15 should be scaled up (75 : 150 → 1 : 2) by hand before it is entered.

A worked example, step by step

Problem: a monitor is 1,920 × 1,080 px. Simplify the aspect ratio.

1. Both numbers factor cleanly: their GCD is 120.
2. Divide the width: 1,920 ÷ 120 = 16.
3. Divide the height: 1,080 ÷ 120 = 9.
4. Clean result: 16:9.
5. Consequence: any resize that keeps 16:9 keeps the picture undistorted — 1,440 × 810, 960 × 540, all the same shape.

The tool reports the GCD (120) explicitly, which is the number you would need a factor tree to find by hand. For 28:64 the GCD is 4, and the ratio lands at 7:16 when rewriting a doorway footprint or a paper size; checking the GCD is how you catch "7:16 guesses" that don't actually divide the originals.

Ratios you meet every day

The 15 × 45 row matters in kitchens: a ratio that survives simplification (1 : 3) scales to a triple batch with no rounding at all — 300 g to 900 g stays exactly 1 : 3.

From the number to the decision

Keep the simplified pair and the originals side by side in any shared note: "1,920 × 1,080 = 16:9" tells the designer both the shape policy and where it came from, which avoids re-measuring for every new screen size. Scale operations ride on the untouched pair too: a 1:3 dilution from 15:45 scales to 300:900 for a triple batch with no rounding at all, whereas a stale "about 1:3" invites underspill. When one side changes — a wider tray, a larger wall — re-enter the new pair rather than nudging one number, because a changed side quietly changes the shape the simplified ratio claims to describe.

And mind the two deliberate blind spots: the simplified ratio is a proportion, not a size (16:9 covers both phone screens and billboards), and it carries no percentage meaning ("2:1" is not "50%") — those belong to the What Percent Is X of Y page or the Percentage Points Calculator. State which units both sides reference, and the ratio stays usable for whatever follows: prints, screens, mixes or scale drawings.

Mistakes that break proportions

• Reading the order backwards. 5 : 3 and 3 : 5 are different shapes; the tool keeps your left-to-right order, so label what each number means before typing.
• Comparing different units. Grams and grams, ribbons and ribbons; simplifying "300 g : 0.5 kg" returns a result about the wrong problem.
• Adding to one side only. Multiplying or adding to just one number changes the relationship; if the shape matters, scale both sides or run the changed pair again.
• Treating 2:1 as 50%. Percentage language needs a denominator decision ("2 of every 3"); keep the ratio form for shape and scale work.
• Trusting rounded replicas. A "roughly 16:9" of 1,915 × 1,082 is not the tool's 16:9; put the real pixel numbers in.

Keep exploring

• GCD & LCM Calculator — the GCD on its own, plus LCM for shared schedules.
• What Percent Is X of Y? — turn the pair into a share of the whole.
• Unit Price Comparison — compare two prices per the same unit, a ratio in money terms.
• Guide: Grades, Fractions and Proportions.