Ratio Calculator

What a ratio is, and the two ways to read it

A ratio compares two amounts by division. The ratio 3 to 4, written 3 : 4, is the same statement as the fraction 3 / 4 and the decimal 0.75. That single number is the whole idea: for every 3 of the first thing, there are 4 of the second.

The trap is that a ratio can be read two ways. As part to part, 3 : 4 says three of one thing next to four of another, so the group holds 7 items in total. As part to whole, 3 of every 7 items are the first kind, which is 3 / 7 = 42.9 percent. Both readings are correct, and they answer different questions. A class with 3 girls for every 4 boys has 3 / 7 of its students girls, not 3 / 4.

Order matters. 3 : 4 is 0.75 and 4 : 3 is 1.33, and those describe opposite situations. The first number always belongs to the thing named first, so write the names down before you start moving numbers around.

Worked example: solving the missing value

A proportion sets two ratios equal: A : B = C : D. When three of the four values are known, the fourth comes out by cross multiplication, which means multiplying the diagonal pairs and then dividing by the remaining number.

Take 3 : 4 = x : 20. The diagonal pair 3 x 20 = 60, and the other diagonal is 4 x x. Setting them equal gives 60 = 4 x, so 60 / 4 = 15, and the missing value is 15. Checking it back: 15 / 20 is also 0.75, so the two ratios match.

The same move works when the unknown sits in another place. For 2 : 3 = 5 : x, the diagonals are 2 x x and 3 x 5. So 2 x x = 15, and 15 / 2 = 7.5. A result in decimals is normal: ratios do not have to land on whole numbers.

The calculator above leaves exactly one box empty and fills it, which is the same arithmetic written once instead of four times. If you leave two or more boxes empty there is no unique answer, and it says so instead of guessing.

Worked example: scaling a recipe

Rice is the classic two to three: two parts rice to three parts water by volume. Scaling it is a proportion problem. To cook 5 cups of rice, set 2 : 3 = 5 : x, so 3 x 5 = 15 and 15 / 2 = 7.5 cups of water.

Doubling both sides never changes the ratio: 4 : 6 and 6 : 9 both reduce to 2 : 3, and all three have the same decimal value of 0.667. That is why doubling a recipe works, and why halving works in the other direction. Add the same number to both sides, on the other hand, and the ratio shifts: 2 : 3 becomes 4 : 5, which is 0.8, not 0.667.

Weight based recipes use the same math with a different ratio. Coffee is brewed anywhere from about 1 : 15 to 1 : 18 by weight, so 20 grams of coffee wants 300 to 360 grams of water. The coffee to water ratio calculator works that one out in grams and keeps the units straight.

Simplifying ratios with the greatest common factor

Simplifying means dividing both numbers by their greatest common factor until nothing divides evenly except 1. For 36 : 48, the greatest common factor is 12, and 36 / 12 = 3 with 48 / 12 = 4, so the ratio reduces to 3 : 4. For 48 : 180, the factor 12 also works, giving 4 : 15.

Decimals need one extra step. Multiply both sides by the same power of ten until both are whole numbers, then reduce: 2.5 : 5 becomes 25 : 50 after multiplying by 10, and that reduces to 1 : 2. The calculator does this automatically, up to six decimal places. When the factors are not obvious, the GCF calculator lists them all.

Not every ratio wants simplifying. A map scale of 1 : 25,000 is written in its raw form on purpose, because 25,000 is the number you multiply by. A 16 : 9 screen ratio is already in lowest terms. Simplifying helps when you want the shape of the relationship, not when you want the working number.

Splitting a total by parts

When a total is shared in a given ratio, the work runs through parts, not percentages. For a two part mix, add the parts to get the number of shares, divide the total by that number, then multiply back up. Paint thinned 1 : 4 in a 10 liter batch has 5 parts in total, so 10 / 5 = 2 liters per part. The hardener takes 1 part, 2 liters, and the base takes 4 parts, 2 x 4 = 8 liters.

Three part mixes work the same way. Concrete at 1 : 2 : 3 cement, sand and gravel has 6 parts, so a 60 kilogram batch gives 60 / 6 = 10 kilograms per part: 10 kilograms of cement, 20 of sand and 30 of gravel. Splitting money follows the identical pattern. To divide 100 dollars in a 2 : 3 ratio, 100 / 5 = 20 dollars per part, so the shares are 40 and 60.

Ratios in the wild: screens, maps, money, health

Ratios with three or more terms scale the same way: multiply every term by the same number, or divide every term by the same factor. A 1 : 2 : 3 mix doubled is 2 : 4 : 6, and the proportions hold at any batch size.

Official statistics lean on the same arithmetic. The employment to population ratio divides the number of employed people by the civilian noninstitutional population, and it stood at 59.2 percent in September 2026, according to the Bureau of Labor Statistics Employment Situation release. A ratio written as one number over another is how a labour market gets summarized in a single line.

Screens are the ratio most people meet first. A 16 : 9 display is 16 / 9 = 1.78 units wide for every unit of height, and a 4 : 3 screen is 1.33. The aspect ratio calculator handles that same ratio in pixels and frames, resizing an image so the shape stays intact. This page works with plain numbers, so use it when you know the quantities but not the pixels.

Map scales are ratios written on every hiking map. At 1 : 25,000, one centimeter on the paper stands for 25,000 centimeters on the ground, and 25,000 / 100 = 250 meters. Four centimeters of trail on that map is 4 x 25,000 = 100,000 centimeters, which is one kilometer.

Lending uses a ratio too. Debt to income divides monthly debt payments by monthly gross income. A household paying 2,100 dollars a month against 4,800 dollars of income sits at 2,100 / 4,800 = 0.4375, or 43.75 percent. The 2014 general qualified mortgage rule in the United States drew its line at 43 percent; the Consumer Financial Protection Bureau later replaced that hard cutoff with price based thresholds, and lenders still quote 43 percent as a benchmark.

Health measurements are ratios as well: waist to hip circumference, waist to height, and body mass index all divide one measurement by another. A 32 inch waist with 40 inch hips is 32 / 40 = 0.8, a number with its own risk bands. The waist to hip ratio calculator covers the measurement side of that one.

Mistakes that break ratio problems

Ratios are simple to compute and easy to bend. Four mistakes cover most of the wrong answers.

• Adding the same number to both sides. 2 : 3 with 1 added to each term becomes 4 : 5, which is 0.8, not 0.667. A ratio survives multiplication and division, not addition.
• Reading part to part as part to whole. 3 : 4 with girls and boys means 3 of every 7 students, not 3 of 4. The denominator changes depending on which question you are asking.
• Mixing units. Two cups of rice to three cups of water is a volume ratio. Two cups of rice to 300 grams of water is a different statement until both sides are converted to the same unit.
• Percent confusion. 3 : 4 is 75 percent when you divide the first term by the second, and 42.9 percent when you divide it by the group total. Name the denominator before quoting a percentage.
• Rounding mid step. Rounding 2 : 3 to 0.67 early and a 300 liter batch loses about a liter by the end. Keep the fraction until the final answer.

The check that catches all of them: put the numbers back into the proportion and see whether both sides give the same decimal. 3 : 4 = 15 : 20 passes because 0.75 matches 0.75. Any wrong answer fails that test somewhere.