Ratio Simplifier Calculator
Simplify any ratio A:B or A:B:C to lowest terms instantly using GCD. Get the decimal value, percentage breakdown, equivalent ratios, and scale to any total. Works for recipes, aspect ratios, finance, and more.
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Reviewed by: Martín Rodríguez (editorial policy ) · Last reviewed:
Result
Simplified Ratio
Decimal Value (A ÷ B)
Percentage Breakdown
Scaled Ratio
Equivalent Ratios (×2, ×3, ×5, ×10)
GCD Used
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A ratio expresses the relative size of two or more quantities. Whether you're mixing concrete (3:2:1 cement:sand:gravel), scaling a recipe, or checking an aspect ratio (1920:1080 = 16:9), unsimplified ratios hide the real relationship. This calculator reduces any ratio to its simplest form using the Greatest Common Divisor (GCD), then shows the decimal value, percentage breakdown, equivalent ratios, and lets you scale to any target total.
When to use this calculator
- Simplify a 2-part or 3-part ratio to lowest terms for a math problem or homework
- Find the decimal and percentage breakdown of ingredients in a recipe or mixture
- Scale a ratio (e.g. 4:6) up or down to hit a specific total quantity (e.g. 500 units)
- Compare financial ratios like debt-to-equity or current ratio in simplified form
- Check aspect ratios for images, screens, or print layouts (e.g. 1920:1080 → 16:9)
- Convert paint or chemical mixing ratios to precise quantities for a given batch size
Common Ratio Simplification Reference
| Original Ratio | GCD | Simplified | Decimal | Use Case |
|---|---|---|---|---|
| 2 : 4 | 2 | 1 : 2 | 0.5 | Scale, probability |
| 6 : 9 | 3 | 2 : 3 | 0.667 | Recipe, mixing |
| 120 : 80 | 40 | 3 : 2 | 1.5 | General proportion |
| 1920 : 1080 | 120 | 16 : 9 | 1.778 | HD/4K aspect ratio |
| 1280 : 720 | 80 | 16 : 9 | 1.778 | HD screen |
| 2560 : 1440 | 160 | 16 : 9 | 1.778 | 2K screen |
| 800 : 600 | 200 | 4 : 3 | 1.333 | Classic monitor |
| 4 : 3 : 2 | 1 | 4 : 3 : 2 | — | 3-part (already simple) |
| 6 : 9 : 15 | 3 | 2 : 3 : 5 | — | 3-part mixture |
| 100 : 75 : 50 | 25 | 4 : 3 : 2 | — | 3-part ingredient mix |
Fuente: Euclidean Algorithm — Wolfram MathWorld / NIST Handbook of Mathematical Functions (2026)
How it works
How to Simplify a Ratio
To simplify a ratio, divide every part by the Greatest Common Divisor (GCD) — the largest integer that divides all parts evenly. The Euclidean algorithm finds the GCD in milliseconds.
Step-by-step:
1. Find GCD of all parts (Euclidean algorithm)
2. Divide each part by the GCD
3. The result is the ratio in its lowest (simplest) form
Formula
gcd(a, b) = b === 0 ? a : gcd(b, a % b) // Euclidean algorithm
gcd3(a, b, c) = gcd(gcd(a, b), c)
A_simple = A / GCD
B_simple = B / GCD
decimal = A / B
pctA = (A / sum) × 100
scaledA = (A / sum) × T // scale to total TWorked Example: 120:80
| Step | Calculation | Result |
|---|---|---|
| GCD | gcd(120, 80) | 40 |
| Simplified | 120÷40 : 80÷40 | 3 : 2 |
| Decimal | 120 ÷ 80 | 1.5 |
| Percentages | 120/200, 80/200 | 60% : 40% |
| Scaled to 500 | (3/5)×500 : (2/5)×500 | 300 : 200 |
3-part example — 6:9:15:
Common Ratio Examples (Quick Reference)
| Original Ratio | GCD | Simplified | Decimal | Use Case |
|---|---|---|---|---|
| 2 : 4 | 2 | 1 : 2 | 0.5 | Scale, probability |
| 6 : 9 | 3 | 2 : 3 | 0.667 | Recipe, mixing |
| 120 : 80 | 40 | 3 : 2 | 1.5 | General proportion |
| 1920 : 1080 | 120 | 16 : 9 | 1.778 | HD/4K aspect ratio |
| 1280 : 720 | 80 | 16 : 9 | 1.778 | HD screen |
| 2560 : 1440 | 160 | 16 : 9 | 1.778 | 2K screen |
| 800 : 600 | 200 | 4 : 3 | 1.333 | Classic monitor |
| 4 : 3 : 2 | 1 | 4 : 3 : 2 | — | 3-part (already simple) |
| 6 : 9 : 15 | 3 | 2 : 3 : 5 | — | 3-part mixture |
| 100 : 75 : 50 | 25 | 4 : 3 : 2 | — | 3-part ingredient mix |
Decimal Input Handling
Inputs like 2.5 : 1.5 are multiplied by 10 → 25 : 15, GCD = 5 → simplified 5 : 3. The calculator detects decimal places automatically.
When a Ratio Is Already in Simplest Form
If GCD = 1, no further reduction is possible. For example, 7:11 — no common factor — GCD = 1, already simplest.
Limitations
Frequently asked questions
How do you simplify a ratio?
Divide all parts of the ratio by their Greatest Common Divisor (GCD). For example, to simplify 120:80, find GCD(120, 80) = 40, then divide: 120÷40 = 3 and 80÷40 = 2. Result: 3:2.
What is the GCD and how is it calculated?
The Greatest Common Divisor (GCD) is the largest positive integer that divides all parts of the ratio without a remainder. It is calculated using the Euclidean algorithm: repeatedly replace the larger number with the remainder when divided by the smaller, until the remainder is 0. For example, gcd(120, 80): 120 mod 80 = 40 → 80 mod 40 = 0 → GCD = 40.
What is a ratio and how is it different from a fraction?
A ratio compares two or more quantities (e.g. 3:2), while a fraction expresses one part over a whole (e.g. 3/5). The ratio 3:2 means for every 3 units of A there are 2 units of B. As a fraction of the total, A is 3/5 = 60%.
Why does 1920:1080 simplify to 16:9?
GCD(1920, 1080) = 120. Dividing: 1920÷120 = 16, 1080÷120 = 9. The 16:9 ratio is the standard widescreen aspect ratio used by HD, Full HD, and 4K displays. Similarly, 1280:720 and 2560:1440 also simplify to 16:9.
Can I simplify a 3-part ratio like 6:9:15?
Yes. The calculator finds GCD(6, 9) = 3, then GCD(3, 15) = 3. Dividing each part by 3 gives 2:3:5. This works for any 3-part ratio — the GCD is applied across all three parts.
What does 'scale to total' mean?
It redistributes the simplified ratio so the parts add up to your target total. For 3:2 scaled to total 100: A = (3/5)×100 = 60, B = (2/5)×100 = 40. Useful for recipes, mixtures, or splitting a budget.
Can I use decimal inputs like 2.5:1.5?
Yes. The calculator detects the maximum number of decimal places and multiplies all parts by the corresponding power of 10 (here ×10 → 25:15). Then it applies GCD normally. GCD(25, 15) = 5 → simplified to 5:3.
What equivalent ratios does the calculator show?
It multiplies the simplified ratio by 2, 3, 5, and 10. For 3:2, equivalents are 6:4, 9:6, 15:10, and 30:20. All represent the same proportion — useful for scaling without a calculator.
Is a ratio the same as odds in probability?
Odds express a ratio of favorable to unfavorable outcomes, so they use the same math. Odds of 3:2 mean 3 favorable to 2 unfavorable, which is 60% probability. This calculator simplifies odds ratios correctly.
What if the ratio is already in simplest form?
If GCD equals 1, the ratio is already fully simplified — no reduction is possible. The calculator will display GCD = 1 and show the original ratio as the result. For example, 7:11 has GCD = 1 and cannot be simplified.
Sources & references
- Khan Academy — Ratios and Proportions (6th Grade) — Khan Academy (2026)
- Euclidean Algorithm — Wolfram MathWorld — Wolfram Research (2026)
- NIST Handbook of Mathematical Functions — Greatest Common Divisor — National Institute of Standards and Technology (NIST) (2026)
- Common Core State Standards — Ratios and Proportional Relationships (Grade 6) — Common Core State Standards Initiative (2026)
Methodology & trust
Editorial
Calculadora de matemática revisada por el equipo editorial de Hacé Cuentas, contrastada con Khan Academy — Ratios and Proportions (6th Grade), según nuestra política editorial y metodología.
Updates
Última revisión: June 20, 2026. Los parámetros se verifican periódicamente con las fuentes citadas.
Privacy
Calculations run 100% in your browser. We do not store or transmit your data.
Limitations
Indicative results. For critical decisions, consult a professional.
📌 How to cite this calculator
Rodríguez, M. (2026). Ratio Simplifier Calculator. Hacé Cuentas. https://hacecuentas.com/ratio-simplifier-calculator
Contenido bajo licencia CC-BY 4.0 — reutilizable citando la fuente con enlace a Hacé Cuentas.