Ratio Calculator

Simplify ratios to lowest terms, check equivalence with cross-multiplication, or reduce width×height to a clean aspect ratio like 16:9—all in your browser.

Simplify 12:18

GCD = 6 → divide both terms → 2:3

Equivalent?

2:3 and 8:12 match because 2×12 = 3×8 = 24

Privacy

Runs locally in your browser—no upload

Simplify ratio

Reduce a:b to lowest terms using the greatest common divisor (GCD).

Simplify

Compare

Aspect ratio

Simplified ratio

12:182:3

Decimal (first ÷ second): 0.666667

GCD used: 6

How this result was calculated
  1. Ratio: 12 : 18
  2. GCD(12, 18) = 6
  3. Divide both terms: 12÷6 : 18÷6 = 2:3
  4. Decimal (first ÷ second): 0.666667

Press C to copy when not typing in a field.

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By Muhammad Abdullah Rauf · Founder, EverydayTools.proUpdated 2026-05-20

What is a ratio calculator?

A ratio calculator simplifies a:b to lowest terms using the greatest common divisor (GCD) and checks whether two ratios are equivalent by cross-multiplication (a×d = b×c)—all in your browser.

A ratio expresses how two quantities compare, written as a:b (read “a to b”). Unlike a fraction a/b, ratios often stay in colon form for recipes, maps, betting odds, and mix ratios. Simplifying means dividing both terms by their GCD so no smaller whole-number ratio represents the same proportion—12:18 becomes 2:3 because GCD(12, 18) = 6.

To see if two ratios match without converting to decimals, cross-multiply: a:b equals c:d when a×d equals b×c. Example: 2:3 and 8:12 are equivalent because 2×12 = 24 and 3×8 = 24. This calculator runs locally in your browser; your numbers are not uploaded to EverydayTools servers.

Use the fraction calculator when you need arithmetic on fractions, or the percentage calculator when converting a ratio to a percent of a whole.

Quick answers

Concise answers for common searches — definitions, steps, and comparisons.

How do you simplify 12:18?

GCD(12, 18) = 6. Divide both terms: 12÷6 = 2, 18÷6 = 3. Simplified ratio: 2:3.

When are two ratios equivalent?

Ratios a:b and c:d are equivalent when a×d = b×c. Example: 2:3 and 8:12 because 2×12 = 3×8 = 24.

Is the ratio calculator private?

Yes. Calculations run locally in your browser; your inputs stay on your device and are not uploaded.

What is the ratio formula for simplification?

Divide both terms by GCD(a, b): simplified a:b = (a÷g):(b÷g). Equivalence: a:b = c:d when a×d = b×c.

Ratio simplification

Divide both terms by GCD; equivalence uses cross-multiplication with floating-point tolerance for decimals.

Formula

Simplified a:b = (a÷g):(b÷g) where g = GCD(a,b)
Equivalent when |a×d − b×c| < ε

Assumptions

  • Terms are numeric and b (and d when comparing) are non-zero

Limitations

  • Does not solve for an unknown term in a proportion (a:b = c:x) — set up algebra manually or use a dedicated proportion solver

How to use Ratio Calculator

  1. Enter the first ratio

    Type the two terms a and b (e.g. 12 and 18). The second term cannot be zero.

  2. Read the simplified ratio

    The tool divides both terms by the GCD and shows the reduced ratio, decimal value (a÷b), and the GCD used.

  3. Compare a second ratio (optional)

    Enable comparison and enter c:d. The calculator cross-multiplies to show equivalent or not, with the cross-products displayed.

  4. Copy or apply the result

    Use 2:3 in recipes, scale drawings, or homework checks. For fraction math (add/multiply), open the fraction calculator instead.

Ratio Calculator examples

Simplify 12:18

Input

12 : 18

Output

2 : 3 (decimal ≈ 0.667)

GCD(12, 18) = 6. Divide both terms: 12÷6 = 2, 18÷6 = 3.

Compare 2:3 and 8:12

Input

2:3 vs 8:12

Output

Equivalent

2×12 = 24 and 3×8 = 24 — cross-products match.

Non-equivalent check

Input

3:4 vs 2:3

Output

Not equivalent

3×3 = 9 but 4×2 = 8 — cross-products differ.

Who uses Ratio Calculator?

Common real-world scenarios where this tool saves time.

Recipe scaling

Reduce ingredient ratios like 6:9 to 2:3 before doubling or halving a recipe.

Map and model scales

Confirm whether two scale statements (e.g. 1:50 vs 2:100) represent the same proportion.

Classroom and homework checks

Verify simplified ratios and equivalence without manual GCD division.

Mix ratios and dilution

Normalize paint, coolant, or chemical mix ratios to lowest terms before scaling volume.

Workflow guides

Step-by-step chains that connect related tools for common tasks.

Recipe ratio then scale

  1. Simplify the ingredient ratio here (e.g. 6:9 → 2:3).
  2. Scale portions with the Fraction Calculator if you need fractional cups or batch multiplication.

Reference tables

Ratio calculator vs fraction vs percentage

Pick the right EverydayTools calculator for your task.

ToolBest for
Ratio CalculatorSimplify a:b and test if two ratios are equivalent
Fraction CalculatorAdd, subtract, multiply, or divide fractions
Percentage CalculatorConvert between percent, fraction, and decimal parts of a whole

Common mistakes to avoid

Swapping terms thinking order does not matter

2:3 and 3:2 are different ratios. Keep the same order as your problem statement (e.g. flour:sugar).

Comparing by decimal rounding only

Use cross-multiplication for exact equivalence; decimals can hide small differences.

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Frequently Asked Questions

How do you simplify a ratio?

Divide both terms by their greatest common divisor (GCD). Example: 12:18 → GCD is 6 → 12÷6 = 2 and 18÷6 = 3, so the simplified ratio is 2:3.

How do you know if two ratios are equal?

Cross-multiply: a:b equals c:d when a×d = b×c. Example: 2:3 and 8:12 are equivalent because 2×12 = 24 and 3×8 = 24.

What is the difference between a ratio and a fraction?

A ratio a:b compares two quantities and is often left in colon form. A fraction a/b usually means “a parts of b equal parts of a whole.” The same numbers can look different in context—use this tool for simplifying ratios; use the fraction calculator for adding or multiplying fractions.

Can ratios include decimals?

Yes. Enter decimal terms; the calculator still finds a GCD on rounded integers where applicable and shows the decimal value a÷b for comparison.

Does the ratio calculator upload my numbers?

No. All simplification and comparison runs locally in your browser. Nothing is sent to EverydayTools servers.

Is this ratio calculator free?

Yes—free with no signup, no usage limits, and no ads required to see your result.

Can I simplify aspect ratios like 1920×1080?

Yes. Use Aspect mode (or enter width and height as the two terms). 1920:1080 simplifies to 16:9—the same GCD method as any other ratio.

Privacy, accuracy, and trust

Privacy

Ratio terms and comparison inputs stay in your browser. Results are computed with JavaScript on your device—nothing is uploaded to EverydayTools.

Accuracy

Uses the Euclidean algorithm for GCD and cross-multiplication for equivalence. Decimal display is for convenience; equivalence uses exact cross-products when possible.

For financial, medical, or safety-critical mix ratios, verify with domain-specific guidelines.

Related Tools

More free tools for the same workflow.

Fraction Calculator

Free fraction calculator with steps: add, subtract, multiply, divide, simplify, and show mixed/decimal forms instantly. Fast, private, no signup.

Scientific Calculator

Use a scientific calculator for trigonometry, logarithms, powers, roots, and constants with DEG/RAD support and instant browser-based results.

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Reviewed by EverydayTools Editorial Team on 2026-05-20.