Ratio Calculator
Simplify ratios, divide a quantity by ratio, or solve for a missing value in an equivalent ratio.
Leave the value you want to solve for as ? — exactly one of the four boxes should contain it.
Breakdown
How to Use the Ratio Calculator
Our Ratio Calculator is a free, all-in-one tool for working with ratios. Simplify a ratio to its lowest terms, split any amount — money, ingredients, time, or shares — between two or three parts of a ratio, or solve for a missing value in an equivalent ratio (proportion). Every result comes with a full step-by-step breakdown, so you can see exactly how the answer was calculated.
What Is a Ratio?
A ratio compares two or more quantities, showing how much of one thing there is compared to another. Ratios are written with a colon, such as 2:3, meaning for every 2 units of the first quantity there are 3 units of the second. Ratios are used everywhere in daily life, from mixing paint and recipes to splitting bills, scaling recipes, calculating gear ratios, and working out map scales.
How to Simplify a Ratio
To simplify a ratio, divide every term by the highest common factor (HCF) of all the terms, also known as the greatest common divisor (GCD). For example, the ratio 8:12 has an HCF of 4, so dividing both terms by 4 gives the simplified ratio 2:3. Our calculator does this automatically, even for ratios that include decimals or a zero term, by scaling every term to a whole number first.
| Original Ratio | HCF | Simplified Ratio |
|---|---|---|
| 8:12 | 4 | 2:3 |
| 15:25 | 5 | 3:5 |
| 18:24:30 | 6 | 3:4:5 |
| 1.5:2 | 0.5 | 3:4 |
| 0:5 | 5 | 0:1 |
How to Divide a Quantity by a Ratio
To split an amount according to a ratio, add up the ratio parts to find the total number of units, then divide the amount by that total and multiply by each part. For example, to split £600 in the ratio 2:3, add the parts together (2 + 3 = 5), divide £600 by 5 to get £120 per unit, then multiply by each part: 2 × £120 = £240 and 3 × £120 = £360. Our calculator handles this instantly for two-part or three-part ratios.
How to Find a Missing Value in a Ratio (Proportion)
When two ratios are equal, such as A:B = C:D, this is called a proportion. To find a missing value, use cross-multiplication: A × D = B × C. Rearranging this equation lets you solve for whichever value is unknown. For example, if 4:9 = 20:D, then D = (9 × 20) ÷ 4 = 45. This method is commonly used for scaling recipes, converting measurements, and solving similar-triangle problems.
Common Ratio Uses
- Recipes and cooking: scaling ingredient quantities up or down while keeping the same proportions.
- Splitting bills or profits: dividing rent, business profits, or inheritance between parties in an agreed ratio.
- Mixing solutions: paint, concrete, cleaning products and fertiliser are often mixed in a stated ratio.
- Maps and scale drawings: a map scale of 1:25,000 means 1 unit on the map equals 25,000 units in real life.
- Aspect ratios: screens and photos use ratios like 16:9 or 4:3 to describe width-to-height proportions.
- Finance: financial ratios such as loan-to-value or debt-to-income are simplified and compared the same way.
Frequently Asked Questions
How do you simplify a ratio?
Find the highest common factor (HCF) of all the terms in the ratio, then divide every term by that number. For example, 10:15 has an HCF of 5, so it simplifies to 2:3.
How do you split money by a ratio?
Add the ratio parts together to get the total number of units, divide the amount by that total to find the value of one unit, then multiply each ratio part by that unit value. For example, £500 split 3:2 gives £300 and £200.
What does A:B = C:D mean?
It means the ratio of A to B is the same as the ratio of C to D — the two ratios are equivalent, or “in proportion.” You can find any one of the four values if you know the other three, using cross-multiplication: A × D = B × C.
Can a ratio have three or more terms?
Yes. A ratio can compare any number of quantities, for example 2:3:5. The same simplification method applies — divide every term by the highest common factor of all the terms.
What is the difference between a ratio and a fraction?
A ratio compares two or more separate quantities to each other, such as 2:3. A fraction represents a part of a single whole, such as 2/5. A ratio of 2:3 corresponds to fractions of 2/5 and 3/5 of the total.
How do I convert a ratio to a percentage?
Add the ratio parts together to get the total, then divide each part by that total and multiply by 100. For example, the ratio 1:4 has a total of 5, so the parts represent 20% and 80% of the whole.
Does the calculator work with decimal ratios?
Yes. Enter decimal values such as 1.5:2 and the calculator automatically scales them to whole numbers before simplifying, giving you an accurate lowest-terms result.
Can a ratio term be zero?
Yes, as long as not every term is zero. For example, 0:5 is a valid ratio and simplifies to 0:1. A ratio where every term is zero, such as 0:0, is not mathematically meaningful and cannot be simplified.