Math

Ratio Calculator & Simplifier

Calculator Free · Private

Reviewed by: Hacé Cuentas editorial team (política editorial ) · Last reviewed: 28 abr 2026

Was this calculator helpful?

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 analyzing financial data, 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, and lets you scale to any target total.

Last reviewed: May 12, 2026 Verified by Hacé Cuentas Team Source: Khan Academy — Ratios and Proportions, NIST Digital Library of Mathematical Functions — Greatest Common Divisor, Euclidean Algorithm — Wolfram MathWorld, Common Core State Standards for Mathematics — Ratios and Proportional Relationships 100% private

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

How it works

2 min read

What is a ratio?

A ratio expresses the relative size or proportion between two or more quantities. It shows how many times one value contains another—for example, 3:2 means the first quantity is 1.5 times the second. Ratios simplify comparison and scaling in recipes, mixtures, and data analysis.

How It Works

A ratio compares quantities. Simplifying means dividing every part by the Greatest Common Divisor (GCD) — the largest integer that divides all parts evenly. For decimal inputs, the calculator first converts to integers by multiplying by the appropriate power of 10.

Formula

// Step 1: find GCD of two numbers (Euclidean algorithm)
gcd(a, b) = b === 0 ? a : gcd(b, a % b)

// Step 2: for three parts
gcd3(a, b, c) = gcd(gcd(a, b), c)

// Step 3: simplified parts
A_simple = A / GCD
B_simple = B / GCD
C_simple = C / GCD   // only for 3-part ratios

// Step 4: decimal value (2-part only)
decimal = A / B

// Step 5: percentage breakdown
pctA = (A / sum) × 100
pctB = (B / sum) × 100
// etc.

// Step 6: scale to total T
scaledA = (A / sum) × T
scaledB = (B / sum) × T

Worked Example

Input: 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 = 60%, 80/200 = 40%	60% : 40%
Scaled to 500	(3/5)×500 : (2/5)×500	300 : 200

3-part example: 6 : 9 : 15

GCD(6,9,15) = 3

Simplified: 2 : 3 : 5

Percentages: 20% : 30% : 50%

Decimal Input Handling

Inputs like 2.5 : 1.5 are multiplied by 10 → 25 : 15, GCD = 5 → simplified 5 : 3.

Limitations & When NOT to Apply

Zero values: A ratio with any part equal to 0 is undefined or degenerate. The calculator returns an error message.

Negative values: Ratios are defined for positive quantities only. Negative inputs are rejected.

Irrational relationships: If A and B share no common integer factor (e.g. 1 : √2), this integer GCD approach will report GCD = 1 and the ratio cannot be simplified further.

Scaling precision: When scaling to a non-divisible total (e.g. 3:2 to total 7), the results are decimal approximations — round to practical units as needed.

Three-part vs. two-part: The decimal value output (A÷B) is only meaningful for 2-part ratios.

Frequently asked questions

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%.

How does the GCD simplification work?

The Greatest Common Divisor (GCD) is found using the Euclidean algorithm: repeatedly replace the larger number with the remainder when divided by the smaller, until the remainder is 0. Dividing all ratio parts by the GCD gives the simplest form.

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. The decimal output (A÷B) is omitted for 3-part ratios as it is not a single meaningful value.

What does 'scale to total' mean?

It redistributes the simplified ratio so the parts add up to your target. For 3:2 scaled to total 100: A = (3/5)×100 = 60, B = (2/5)×100 = 40. Useful for recipes, mixtures, or budgets.

What does 'scale to Part A' mean?

It fixes Part A at your target value and scales the other parts proportionally. For 3:2, if you want Part A = 150: multiplier = 150/3 = 50, so Part B = 2×50 = 100. Result: 150:100.

Why does 1920:1080 simplify to 16:9?

GCD(1920, 1080) = 120. Dividing: 1920÷120 = 16, 1080÷120 = 9. This is the standard widescreen aspect ratio used by HD and 4K displays.

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, result: 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 relationship — useful for scaling up without a calculator.

Is a ratio the same as odds (like 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 both parts are already in simplest form?

If GCD equals 1, the ratio is already fully simplified and no reduction is possible. The calculator will display GCD = 1 and show the original ratio as the simplified result.