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Ratio simplifier
Divide every term by their greatest common divisor — two-part or three-part ratios.
CALCULATOR · MATH · RATIOS
Ratio Simplifier
A ratio is in lowest terms when its numbers share no common divisor above 1 — and finding that divisor is the whole job. Enter two or three terms (decimals welcome: 1.5:2.5 becomes 3:5), and the calculator finds the greatest common divisor, divides every term by it, and shows each step. The default 12:18 reduces to 2:3: same proportion, smallest whole numbers, ready for a recipe, a scale model, or a homework check.
The 60-second rule
Find the GCD of all the terms, then divide every term by it. At the defaults, GCD(12,18) = 6, so 12:18 becomes 2:3. You know you are done when the reduced terms share nothing: GCD(2,3) = 1. Decimals are cleared first — 1.5:2.5 is multiplied by 10 to make 15:25, then reduced to 3:5.
The worked example, line by line
Defaults: 12:18. Step 1 — find the greatest common divisor: GCD(12,18) = 6. Step 2 — divide each term: 12÷6 = 2, 18÷6 = 3. Step 3 — verify: GCD(2,3) = 1, so 2:3 is final.
Decimal input: 1.5:2.5 — one decimal place, so multiply both terms by 10: 15:25. GCD(15,25) = 5. 15÷5 = 3, 25÷5 = 5 → 3:5.
Three-part: 6:9:12 — GCD(6,9,12) = 3. 6÷3 : 9÷3 : 12÷3 = 2:3:4.
Branches: 100:75 → GCD(100,75) = 25 → 4:3. 0.75:1.25 — two decimal places, multiply by 100: 75:125, GCD(75,125) = 25 → 3:5. A repeating-ish input like 0.33:0.66 → ×100 → 33:66, GCD 33 → 1:2.
Output · formula · meaning
| Output | Formula | What it means |
|---|---|---|
| Simplified ratio | each term ÷ GCD(all terms) | 2:3 at the defaults — the same proportion in the smallest whole numbers. |
| Greatest common divisor | largest integer dividing every scaled term | 6 for 12:18 — the one number the whole simplification hangs on. |
| Scale factor | 10 ^ (most decimal places) | 10 for 1.5:2.5 — what clears the decimals before the GCD runs (15:25). |
| Original ratio | your terms joined with : | 12:18 — exactly what you typed, before any math. |
Who uses this
- The recipe scaler: halving a recipe that calls for a 12:18 flour-to-sugar mix? The 2:3 version scales to any batch size without a single long division.
- The map and model builder: a 6:9:12 plan reduced to 2:3:4 keeps every proportion true when the model gets built at a different size.
- The student: checking that 100:75 really reduces to 4:3 — and showing GCD(100,75) = 25 as the work earns the marks.
- The finance analyst: ratio analysis lives on reduced ratios — a 100:75 debt-to-equity comparison reads instantly as 4:3.
Accuracy & limitations
The GCD math is exact. The one soft spot is decimal input: decimals are scaled to integers and rounded (up to 6 decimal places), which cleans up floating-point quirks — but very long decimals get rounded, so an input like 0.3333:0.6666 lands on 1:2 as intended. Irrational ratios such as 1:π cannot be expressed exactly in whole terms; the calculator gives the best whole-number approximation your decimals allow. Terms must be positive — negative terms and an all-zero ratio are rejected with a message.
Cite this calculatorBright Side Kit. “Ratio Simplifier.” brightoolbox.com, 2026.
Bright Side Kit. "Ratio Simplifier." https://brightoolbox.com/ratio-simplifier/ Accessed October 23, 2026.Frequently asked questions
How do you simplify a ratio?
Divide every term by their greatest common divisor. For 12:18, GCD(12,18) = 6, so 12÷6 : 18÷6 = 2:3. The calculator above does all three steps for you.
Can you simplify a ratio with three numbers?
Yes — the same rule applies to any number of terms. Enter the third term in field C: 6:9:12 has GCD(6,9,12) = 3, so it reduces to 2:3:4. Leave C blank for an ordinary two-part ratio.
How do you simplify a ratio with decimals?
Clear the decimals first, then find the GCD. 1.5:2.5 — multiply both by 10 to get 15:25, GCD(15,25) = 5, so the answer is 3:5. 0.75:1.25 works the same way with ×100: 75:125 → 3:5.
What is the GCD of 12 and 18?
6. The divisors of 12 are 1, 2, 3, 4, 6, 12; the divisors of 18 are 1, 2, 3, 6, 9, 18 — and 6 is the largest number on both lists. That is why 12:18 simplifies to 2:3.
How do I know a ratio is fully simplified?
When the terms share no common divisor above 1 — that is, their GCD is 1. 2 and 3 share nothing, so 2:3 cannot go further. If your reduced terms still share a divisor, divide again.
What is the difference between simplifying a ratio and simplifying a fraction?
It is the same GCD idea in different notation: the fraction 12/18 reduces to 2/3, and the ratio 12:18 reduces to 2:3. If your problem is written with a fraction bar, try our fraction simplifier instead.