Enter a ratio to reduce it to its simplest form using the Greatest Common Divisor.
Scale a ratio up or down by a multiplier. Useful for recipes, maps, and blueprints.
Find the missing value in a proportion. Enter three values and leave the unknown as blank.
Leave one field empty. Example: A : B = C : ? — fill in A, B, C and leave D blank.
Compare two ratios and find out if they are equivalent, or which is greater.
Split a total amount into parts according to a ratio. Works for 2 or 3 parts.
A ratio calculator lets you simplify, scale, solve, compare, and split ratios without doing the arithmetic by hand. This tool covers all five operations in one place, with worked results and a sum check on every calculation. Whether you are scaling a recipe, solving a proportion for a missing value, or splitting a budget between departments, each tab handles a specific job.
What Is a Ratio?
A ratio compares two or more quantities. It tells you how much of one thing there is relative to another. Written as A : B, it reads “A to B.” If a paint mix uses 3 parts white to 1 part pigment, the ratio is 3:1. That means for every 3 litres of white, you use 1 litre of pigment.
Ratios are not fractions, but they can be expressed as one. The ratio 3:1 is the same as saying the first quantity is 3 times the second, or that white makes up 3/4 of the total mix.
A 3-part ratio like 2:3:1 describes three quantities. The parts add up to a whole. In a business profit split of 2:3:1, for every 6 units of profit, one partner gets 2, another gets 3, and the third gets 1.
Ratios appear in mathematics written as A:B, A to B, A/B, or in the form 1:n (where everything is expressed relative to one unit). Maps, recipes, financial reports, blueprints, and chemical solutions all use one or more of these forms.
Simplify Tab: Reduce a Ratio to Lowest Terms
Enter a ratio and the calculator reduces it to its lowest terms using the Greatest Common Divisor (GCD).
How it works: the GCD is the largest number that divides evenly into all parts. Dividing each part by the GCD gives the simplest equivalent ratio. A ratio is fully simplified when no number greater than 1 divides evenly into all terms — at that point the terms are co-prime.
| Original Ratio | GCD | Simplified |
|---|---|---|
| 12 : 8 | 4 | 3 : 2 |
| 15 : 25 | 5 | 3 : 5 |
| 100 : 75 | 25 | 4 : 3 |
| 9 : 6 : 3 | 3 | 3 : 2 : 1 |
| 48 : 36 : 24 | 12 | 4 : 3 : 2 |
Tick the 3-part ratio checkbox to add a third value. The result also shows the decimal value (A÷B) and the percentage share of A within the whole.
A common mistake is to partially simplify. 12:18 divided by 2 gives 6:9, which looks simpler but is not fully reduced because 6 and 9 share a factor of 3. The correct simplified form is 2:3. This calculator finds the GCD in one step, so the result is always fully reduced.
Scale Tab: Multiply or Divide a Ratio
Scaling multiplies every part of a ratio by the same factor. This keeps the proportions identical while changing the actual quantities.
Enter the ratio and the scale factor. The calculator returns the scaled ratio and the simplified form of the original.
| Original | Factor | Scaled |
|---|---|---|
| 2 : 3 | 4 | 8 : 12 |
| 1 : 2 : 3 | 5 | 5 : 10 : 15 |
| 3 : 4 | 0.5 | 1.5 : 2 |
| 5 : 2 | 3 | 15 : 6 |
A practical example: a concrete mix uses a 1:2:3 ratio of cement, sand, and gravel. To produce 5 times the volume, apply a scale factor of 5. The result is 5:10:15. The proportions stay identical.
Decimal scale factors work too. A scale of 0.5 halves every part. This is useful when reducing a recipe or scaling down a material batch.
Solve Tab: Find a Missing Value in a Proportion
This tab finds a missing value in a proportion. A proportion is a statement that two ratios are equal: A:B = C:D.
Enter any three of the four values and leave one field blank. The calculator uses cross-multiplication to find the unknown.
The formula depends on which value is missing:
| Unknown | Formula |
|---|---|
| A | A = B × C ÷ D |
| B | B = A × D ÷ C |
| C | C = A × D ÷ B |
| D | D = B × C ÷ A |
| Known Values | Missing | Answer |
|---|---|---|
| 3 : 4 = ? : 12 | A | 9 |
| 5 : ? = 10 : 8 | B | 4 |
| ? : 6 = 5 : 3 | A | 10 |
| 7 : 3 = 14 : ? | D | 6 |
This tab is useful for map scales, unit conversions, and proportion problems in school maths or engineering. It is also the fastest way to check whether a scaled-up recipe or material mix keeps the same proportions as the original.
Compare Tab: Check If Two Ratios Are Equivalent
Enter two separate ratios. The calculator converts both to decimal form (A÷B), then compares them directly.
If the decimal values are equal, the ratios are equivalent. If not, it returns which ratio is greater.
| Ratio 1 | Ratio 2 | Decimal 1 | Decimal 2 | Result |
|---|---|---|---|---|
| 3 : 4 | 6 : 8 | 0.75 | 0.75 | Equivalent |
| 2 : 3 | 3 : 4 | 0.667 | 0.75 | Ratio 2 is greater |
| 5 : 2 | 7 : 3 | 2.5 | 2.333 | Ratio 1 is greater |
| 1 : 2 | 2 : 4 | 0.5 | 0.5 | Equivalent |
Two ratios that look different can describe the same relationship. 3:4 and 6:8 are equivalent because both simplify to 3:4 and both equal 0.75 as a decimal. You can also confirm equivalence by cross-multiplication: if A × D = B × C, the ratios are equal.
Split Tab: Divide a Total by a Ratio
Enter a total amount and a ratio. The calculator divides the total into shares according to the ratio parts.
The method: add the ratio parts to get the total shares. Divide the total amount by that sum to find the value of one share. Multiply by each ratio part to get each person’s or category’s amount.
Example: split £500 in the ratio 2:3.
| Step | Working | Result |
|---|---|---|
| Add parts | 2 + 3 | 5 parts total |
| One part | £500 ÷ 5 | £100 per part |
| Share A | 2 × £100 | £200 |
| Share B | 3 × £100 | £300 |
| Check | £200 + £300 | £500 ✓ |
| Total | Ratio | Part A | Part B | Part C |
|---|---|---|---|---|
| 100 | 1 : 1 | 50 | 50 | — |
| 200 | 3 : 2 | 120 | 80 | — |
| 600 | 1 : 2 : 3 | 100 | 200 | 300 |
| 90 | 2 : 1 : 3 | 30 | 15 | 45 |
The calculator shows a sum check confirming the parts add back to the total. Tick the 3-part checkbox to split into three portions.
How to Find Equivalent Ratios
Equivalent ratios express the same relationship using different numbers. To find an equivalent ratio, multiply or divide every part by the same non-zero number.
Starting from 2:3, multiplying both parts by 4 gives 8:12. Multiplying by 7 gives 14:21. All three — 2:3, 8:12, and 14:21 — are equivalent.
| Factor | Equivalent Ratio |
|---|---|
| ×2 | 4 : 6 |
| ×3 | 6 : 9 |
| ×5 | 10 : 15 |
| ×10 | 20 : 30 |
To confirm two ratios are equivalent without a calculator: cross-multiply. If A × D = B × C, the ratios A:B and C:D are the same. For 2:3 and 8:12: 2 × 12 = 24 and 3 × 8 = 24. Equal, so they are equivalent.
Use the Compare tab to check equivalence quickly, or the Scale tab to generate a specific equivalent ratio by applying a factor.
How to Convert a Ratio to a Percentage
Two steps. First, express the ratio as a fraction by putting the first part over the total of all parts. Then multiply by 100.
Example: the ratio 3:2. Total parts = 5. Part A as a fraction = 3/5. As a percentage: 3/5 × 100 = 60%. Part B = 2/5 × 100 = 40%.
| Ratio | Total Parts | Part A % | Part B % |
|---|---|---|---|
| 1 : 1 | 2 | 50% | 50% |
| 1 : 3 | 4 | 25% | 75% |
| 3 : 2 | 5 | 60% | 40% |
| 2 : 3 : 5 | 10 | 20% | 30% / 50% |
The Simplify tab shows the percentage share of Part A automatically alongside the simplified ratio. For 3-part ratios, check each part using the same method: divide each part by the total of all parts and multiply by 100.
Real-World Uses for Ratios
Ratios show up across almost every field. Some common applications:
| Field | Example Use |
|---|---|
| Cooking | Scale a recipe from 4 to 10 servings using the Scale tab |
| Finance | Split profits or investments by agreed ratio using the Split tab |
| Architecture and maps | Convert blueprint or map measurements using the Scale or Solve tab |
| Chemistry | Mix solutions in correct concentration ratios |
| Photography and design | Maintain aspect ratios when resizing images |
| Education | Solve proportion problems in maths exams using the Solve tab |
| Construction | Mix concrete, mortar, or paint in correct ratios |
| Business | Divide costs, revenue, or resources between departments |
| Medicine and pharmacy | Calculate drug dilution ratios and dosage concentrations |
| Odds and probability | Express and compare odds in gambling, insurance, and risk modelling |
Frequently Asked Questions
What is the difference between a ratio and a fraction?
A ratio compares two quantities to each other. A fraction compares a part to a whole. The ratio 3:4 means 3 of one thing for every 4 of another. The fraction 3/4 means 3 parts out of a total of 4 parts. They use different reference points, but both express a proportional relationship.
How do you simplify a ratio?
Find the Greatest Common Divisor (GCD) of all parts. Divide every part by the GCD. The result is the simplified ratio. For 18:12, the GCD is 6. Dividing both by 6 gives 3:2. A ratio is fully simplified when no number greater than 1 divides evenly into all terms.
What does it mean for two ratios to be equivalent?
Two ratios are equivalent when they describe the same proportional relationship. 2:4 and 1:2 are equivalent because both simplify to 1:2 and both equal 0.5 as a decimal. You can also test equivalence by cross-multiplying: if A × D = B × C, the ratios A:B and C:D are equivalent.
Can ratios contain decimals?
Yes. A ratio like 1.5:2 is valid. The calculator accepts decimal inputs across all five tabs. If you prefer whole numbers in your result, multiply both parts by the same factor to clear the decimals. 1.5:2 becomes 3:4 when multiplied by 2.
What is a 3-part ratio?
A 3-part ratio compares three quantities. Written as A:B:C, it divides something into three portions. A concrete mix of 1:2:3 means 1 part cement, 2 parts sand, 3 parts gravel. The Simplify, Scale, and Split tabs all support 3-part ratios via the checkbox.
How does the Solve tab find the missing value in a proportion?
It uses cross-multiplication. In the proportion A:B = C:D, the rule is A × D = B × C. If one value is unknown, rearrange the formula to isolate it. For example, if D is missing: D = B × C ÷ A. The calculator identifies which value is blank and applies the correct formula automatically.
What is the difference between a ratio and a proportion?
A ratio is a comparison of two quantities: 3:4. A proportion is a statement that two ratios are equal: 3:4 = 6:8. The Solve tab works with proportions. The Simplify and Compare tabs work with individual ratios.
Can I use this calculator for map scales?
Yes. Map scales are ratios. A scale of 1:50,000 means 1 unit on the map equals 50,000 units in the real world. Use the Scale tab to find real distances from map measurements, or the Solve tab to find what distance on the map corresponds to a known real-world distance.
How do you convert a ratio to a percentage?
Divide each part by the total of all parts, then multiply by 100. For a ratio of 3:2, the total parts are 5. Part A = 3/5 × 100 = 60%. Part B = 2/5 × 100 = 40%. The Simplify tab shows the percentage share of Part A automatically alongside every result.
What is the GCD and why does it matter for simplifying ratios?
GCD stands for Greatest Common Divisor, also called Greatest Common Factor (GCF). It is the largest whole number that divides evenly into all parts of a ratio. Dividing every part by the GCD reduces the ratio to its lowest terms in one step. For 48:36, the GCD is 12. Dividing both by 12 gives 4:3. Using any smaller common factor — like 6 — would not fully simplify the ratio, leaving 8:6 instead of 4:3.
How do you split an amount in a given ratio?
Add the ratio parts to find the total number of shares. Divide the amount by the total shares to find the value of one share. Multiply each ratio part by one share’s value to get each portion. For £900 split in the ratio 1:2:3: total parts = 6, one part = £150. Shares are £150, £300, and £450. The Split tab does this calculation and confirms the parts sum to the original total.
