Ratio Calculator

Simplify ratios and find decimal equivalents.

Value A

Value B

How to Use

Enter ratio values

Input the two or three parts of your ratio. Whole numbers and decimals are both accepted.

Simplify the ratio

The tool divides all parts by their GCF to reduce the ratio to its simplest form.

Solve proportions if needed

Enter three known values in A:B = C:? form to find a missing fourth value by cross-multiplication.

Use the result in your application

Apply the simplified ratio or scaled proportion to cooking, mixing, maps, finance, or engineering.

Understanding Ratios

Ratios compare the size of one number to another.

Real-World Examples & Use Cases

Cooking and Recipe Scaling

Recipes use ratios that must stay constant when scaling up or down. A bread dough recipe requiring flour and water in a 5:3 ratio: for 2kg flour, water needed = 2 × (3/5) = 1.2kg. Scaling a recipe for 4 people up to serve 18: multiply all ingredients by 18/4 = 4.5. When mixing spice blends, sauce ratios, or cocktail recipes, ratios express the proportional relationship between components that must be maintained regardless of total quantity.

Financial and Business Ratios

Finance relies on ratios: debt-to-equity ratio of 3:1 means $3 of debt per $1 of equity. A current ratio of 2:1 means $2 of current assets per $1 of current liabilities. Price-to-earnings (P/E) ratio of 25:1. Gross margin ratio = gross profit : revenue. These ratios allow comparison across companies of different sizes. Expressing financial metrics as simplified ratios enables analysts to benchmark performance without being distracted by absolute dollar amounts.

Map Scales and Technical Drawing

Maps and engineering drawings use scale ratios to represent real-world dimensions: a 1:50,000 map means 1 unit on the map represents 50,000 of the same units in reality. 1cm on the map = 50,000cm = 500m = 0.5km. Architects use scales like 1:100 (1cm = 1m) or 1:50 (1cm = 50cm). When measuring distances on maps or preparing technical drawings, the ratio calculator helps convert between map measurements and ground-truth distances accurately.

Mixing Solutions and Chemical Dilutions

Laboratory and industrial mixing requires precise ratio maintenance. Diluting a concentrated solution 1:9 with water means 1 part concentrate per 9 parts water (10% concentration). For 500ml final volume: 50ml concentrate + 450ml water. Paint mixing, concrete proportions (cement:sand:aggregate = 1:2:3 by volume), pesticide dilutions, and cleaning solutions all express mixing instructions as ratios. The ratio calculator verifies proportions and scales them to your required total volume.

How It Works

Ratio simplification and proportion solving: Simplifying a ratio A:B: 1. Find GCF(A, B) 2. Simplified ratio = (A/GCF):(B/GCF) Example: 24:36 → GCF(24,36) = 12 → 2:3 For three-part ratios A:B:C: 1. Find GCF(A, B, C) = GCF(GCF(A, B), C) 2. Divide all three parts by GCF Solving proportions (A:B = C:D): - Cross multiply: A × D = B × C - Solve for unknown: D = (B × C) / A Converting ratio to percentage/decimal: - A:B total parts = A + B - A as percentage = A/(A+B) × 100 - B as percentage = B/(A+B) × 100 Example: 3:5 → total 8 parts → 3/8 = 37.5%, 5/8 = 62.5% Equivalent ratios multiply or divide all parts by the same factor: 2:3 = 4:6 = 6:9 = 10:15 (all equivalent)

Frequently Asked Questions

What is the difference between a ratio and a fraction?▼

A fraction represents a part of a whole: 3/4 means 3 parts out of 4 total parts. A ratio compares two separate quantities: 3:4 means for every 3 of one thing, there are 4 of another. The ratio 3:4 does NOT mean 3/4 of a whole — it means the first quantity is 3 and the second is 4 (total is 7). However, ratios can be expressed as fractions: 3:4 means the first quantity is 3/7 and the second is 4/7 of the combined total.

How do I convert a ratio to a percentage?▼

Add all ratio parts to get the total. Divide each part by the total and multiply by 100. For ratio 2:3:5: total = 10 parts. First part = 2/10 = 20%. Second part = 3/10 = 30%. Third part = 5/10 = 50%. This is used in portfolio allocation (30:40:30 stocks/bonds/cash), recipe percentages (baker's percentages), and business mix reporting.

Can ratios include decimals or fractions?▼

Yes, though ratios are usually expressed as whole numbers after simplification. If you have a ratio of 1.5:2, multiply both by 2 to get the equivalent whole-number ratio 3:4. For fraction ratios like (1/2):(1/3), multiply both by the LCM of denominators (6) to get 3:2. The process of clearing fractions and decimals from ratios is called 'rationalizing the ratio' and produces the clearest form for communication and calculation.

What does it mean for a ratio to be in its simplest form?▼

A ratio is in its simplest form when GCF(A, B) = 1 — meaning A and B share no common factors other than 1 (they are co-prime). Examples: 6:10 simplifies to 3:5 (GCF=2). 15:25 simplifies to 3:5 (GCF=5). 7:11 is already simplest (GCF=1). Simplest form is preferred because it reveals the fundamental proportional relationship most clearly, without unnecessary scale inflation.

How do golden ratio and aspect ratios relate to this calculator?▼

The golden ratio (approximately 1.618:1 or φ:1) appears throughout art, architecture, and nature. Common aspect ratios — 16:9 (widescreen video), 4:3 (traditional screens), 1:1 (square), 3:2 (DSLR photos), 2.39:1 (cinema) — define how width and height relate in display formats. When designing graphics or video frames, entering pixel dimensions and simplifying the ratio reveals the aspect ratio. A 1920×1080 image simplifies to 16:9; a 1440×1080 image simplifies to 4:3.

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