Simplify a ratio to lowest terms, solve for an unknown term in a proportion, or scale a ratio to a new total or target value — with full step-by-step work.
Enter a ratio to reduce it to lowest whole-number terms
Choose the unknown term, enter the other three, and solve the proportion
Enter a base ratio and a target to scale every term proportionally
This free ratio calculator simplifies any ratio to its lowest whole-number terms, solves for an unknown term in a proportion using cross-multiplication, and scales a ratio up or down to a target total or target term value — all with full step-by-step working shown. A ratio compares two or more quantities of the same kind, such as 2 cups of flour to 3 cups of sugar, and understanding how to reduce, solve, and scale ratios is essential in cooking, construction, finance, and standardized test prep. This ratio calculator with steps supports two-term and three-term ratios, decimal inputs, and shows the exact GCD or scale factor behind every answer.
Three tools in one: Simplify a Ratio reduces any 2- or 3-term ratio to lowest terms and shows its decimal equivalent, percentage split, and GCD; Solve for X (Proportions) finds any missing term in A:B = C:X using cross-multiplication; and Scale a Ratio multiplies every term by a factor so the ratio hits a target total or a target value for one specific term.
Students learning proportional reasoning, teachers building practice problems, home cooks and professional bakers scaling recipes, tradespeople mixing concrete or chemical solutions to the correct proportions, photographers and video editors preserving aspect ratios, and finance students comparing ratios like debt-to-equity all benefit from a fast, verified ratio calculation.
Ratios let you compare quantities independent of scale — a 2:3 flour-to-sugar ratio works whether you're baking one cookie or a thousand. Proportional reasoning (recognizing that two ratios are equal) underlies unit conversion, map reading, recipe scaling, and financial analysis. Getting the order and scale factor right avoids costly mistakes, from a botched recipe to a miscalculated concrete mix.
Bakers and chefs scale recipes for different serving sizes. Contractors mix cement:sand:gravel ratios for concrete batches. Cartographers and hikers convert map-scale ratios (like 1:50,000) into real-world distances. Photographers and screen designers preserve width:height aspect ratios when resizing. Analysts compare financial ratios such as price-to-earnings or debt-to-equity in simplified form.
How this ratio calculator simplifies, solves, and scales your numbers
Dividing every term by their greatest common divisor keeps the same proportion while using the smallest possible whole numbers, exactly like simplifying a fraction.
Because A:B = C:X means A/B = C/X, cross-multiplying (A×X = B×C) turns the proportion into a simple one-step algebra problem for whichever term is unknown.
Multiplying every term of a ratio by the same factor changes its scale but never its underlying proportion — 2:3 and 8:12 describe the identical relationship.
From picking a tool to verifying the result
Pick Simplify a Ratio, Solve for X (Proportions), or Scale a Ratio.
Type in the A and B terms, and an optional third term C for a three-term ratio.
Select whether A, B, C, or X is unknown, then fill in the other three values.
Scale to a desired total, or scale so one specific term hits a target value.
The calculator applies the matching ratio formula instantly and displays the result.
Check the simplified ratio, solved value, or scaled ratio along with the full step-by-step working, and confirm it by reversing the calculation.
Simplifying a 12:18:24 concrete mix, then scaling it to a 100 kg batch
A concrete recipe calls for cement, sand, and gravel in the ratio 12:18:24 by weight. First reduce this to its simplest form, then scale it up to make a 100 kg batch.
Explanation: Reducing 12:18:24 to 2:3:4 first makes the scaling math simpler and reveals the true underlying proportion — 2 parts cement, 3 parts sand, 4 parts gravel. Scaling that reduced ratio to a 100 kg batch gives roughly 22.22 kg cement, 33.33 kg sand, and 44.44 kg gravel, which sum back to 100 kg.
What each tool's output actually represents
| Result Field | What It Means | Example Reading |
|---|---|---|
| Simplified Ratio | The same proportion expressed in the smallest possible whole numbers | 12:18:24 simplifies to 2:3:4 |
| Decimal (A ÷ B) | The two-term ratio expressed as a single number for direct comparison | 2:3 → 0.6667 |
| Percentage Split | Each term's share of the total, useful for reporting proportions | 2:3 → 40% / 60% |
| GCD Used | The largest number every term was divided by to reach lowest terms | GCD(12,18,24) = 6 |
| Solved Value (X) | The missing term that makes both sides of the proportion equal | 3:4 = 15:20 → solved C = 15 |
| Scale Factor | The multiplier applied to every term to reach the target | Factor ×11.11 for a 100 kg batch |
Reading the sign: a scale factor greater than 1 means the ratio was scaled up; a factor less than 1 means it was scaled down to a smaller total or term value.
Typical ranges: a GCD of 1 means the entered ratio was already in lowest terms — no further simplification is possible.
Manual verification: add the scaled or simplified terms back together and confirm the sum matches the target total, or plug a solved proportion value back into A:B = C:X to confirm both sides are equal.
Where accurate ratio math genuinely matters
Check ratio, proportion, and scaling word problems step by step.
Practice the ratio and proportion questions common in aptitude and entrance exams.
Scale ingredient ratios up or down while keeping flavor proportions correct.
Scale cement:sand:gravel or dilution ratios to a larger or smaller batch size.
Convert a map or model scale ratio into real-world distances or dimensions.
Resize a photo, video, or screen resolution while preserving its width:height ratio.
Compare simplified debt-to-equity, price-to-earnings, or current ratios.
Mix paint, cleaning solutions, or fuel blends to the correct proportion.
Scale fertilizer or nutrient solution ratios to a tank or garden bed size.
Scale a building or object's dimensions to a model or blueprint ratio.
Divide a dataset into training and testing sets using a chosen ratio, like 80:20.
Balance protein:carb:fat ratios in a meal plan.
Simplify and compare conversion, click-through, or cost ratios across campaigns.
What this ratio calculator does well, and where manual judgment is still needed
Three related but distinct concepts
| Term | Definition | Example |
|---|---|---|
| Ratio | Compares two or more quantities of the same kind, with no units of its own | 2:3 (flour:sugar) |
| Proportion | A statement that two ratios are equal | 2:3 = 8:12 |
| Rate | Compares two quantities of different kinds and keeps the units | 60 miles per hour |
Summary: This ratio calculator gives you an instant, free way to simplify a ratio to lowest terms, solve for a missing term in a proportion, and scale a ratio to a new total or target value — all with the formula and steps shown. Pair it with related tools like the GCF Calculator and Fraction Calculator for a fuller picture of proportional math.
Common questions about ratios, proportions and scaling
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