Proportion Calculator

What a proportion is and why it matters

A proportion is a statement that two ratios are equal. You write it as a:b = c:d and read it as "a is to b as c is to d." The colon stands for division, so a proportion is the equation a divided by b equals c divided by d, and its whole purpose is to let you find a number you cannot measure directly by measuring something you can.

That idea runs through ordinary errands. If 3 apples cost $2.40, then one apple costs $2.40 divided by 3, which is $0.80, and 7 apples cost 7 times $0.80, which is $5.60. If 2 cups of flour make 16 cookies, one cup makes 8 cookies. If a map is drawn at 1:24,000, then 1 inch stands for 24,000 inches, which is 2,000 feet, and 2 inches stand for 4,000 feet on the ground. Every one of those is a proportion, and the arithmetic underneath is always the same two moves: multiply across, then divide.

The three calculators below all run on that one rule: solve a missing term, split a total by a ratio, and scale a quantity up or down. Everything runs in your browser and nothing you type is sent to a server.

Solving a proportion for the missing term

Enter three of the four terms and the calculator returns the fourth. The tool it uses is called cross multiplication: multiply the two numbers on one diagonal of the proportion and the two numbers on the other diagonal, and the products have to match.

Work it by hand once. Take 3:4 = x:20. Cross multiplying gives 3 times 20 = 4 times x, which is 60 = 4x, so x = 15. The check takes five seconds: 3 times 20 is 60 and 4 times 15 is also 60, the two products agree, so the proportion holds. The calculator does this same swap and then reports both products so you can confirm the answer without trusting it.

A money version: 5 gallons of paint cost $28.75, so 20 gallons cost 4 times $28.75, which is $115.00. The unit rate is $28.75 divided by 5 = $5.75 per gallon, and 20 times $5.75 gives the same $115.00.

Cross multiplication, step by step

When you are new to proportions, the diagonal picture helps. Write a:b = c:d with the terms spaced apart so the a sits above the c and the b sits above the d. The useful diagonals are the ones that pair a with d and b with c, because those two products have to be equal. Everything else follows from that one rule.

The step sequence never changes, and the calculator on this page runs the same four steps in the same order every time.

1. Write the proportion so the unknown term has its own space, for example 3:4 = x:20.
2. Multiply the first and last terms: 3 times 20 = 60.
3. Multiply the middle pair: 4 times x = 4x.
4. Set the two products equal and divide: 60 = 4x, so x = 15.

Two habits keep this clean. First, leave the unknown box empty in the calculator instead of typing a placeholder, so the tool knows which term you want. Second, check the two diagonal products before you leave the answer. If the products differ, the proportion as written was not true, and the fix belongs in the original numbers rather than in the arithmetic.

Splitting a total into parts by a ratio

The second job a proportion does is sharing. Say three roommates split $1,200 in the ratio 2:3:5. The total of the parts is 2 + 3 + 5 = 10, and each part is worth $1,200 divided by 10, which is $120. The first roommate takes 2 parts, the second takes 3, the third takes 5, giving $240, $360 and $600. The shares add back to $1,200 exactly, which is your check.

Ratios with two parts work the same way. A $900 invoice split 3:7 has 10 parts worth $90 each, so the two shares are $270 and $630. Notice that 3:7 and 30:70 describe the same split, and the calculator will treat both the same way, because the part total is what matters, not the size of the numbers.

Percentages are proportions in disguise, and the split tells you the percentage for free. The 2:3:5 split of $1,200 is 20 percent, 30 percent and 50 percent, because each share divided by the total gives 240 / 1200 = 0.20, and so on.

Scaling recipes, mixes, and fuel ratios

When a quantity changes size, the proportion moves with it, and the multiplier is easy to name. A recipe for 4 people uses 1.5 cups of rice. You are cooking for 7, so the scale factor is 7 divided by 4, which is 1.75, and 1.5 cups times 1.75 comes out to 2.625 cups. Double the recipe and the factor is 2, which needs no division at all.

Mixes follow the same pattern, and this is where ratios get practical. Many small engines run gasoline and oil at 50 parts gasoline to 1 part oil. A US gallon of gas is 128 fluid ounces, so the oil for that tank is 128 divided by 50, which is 2.56 ounces. Paint is often mixed 2 parts base to 1 part thinner, so 5 quarts of base needs 2.5 quarts of thinner for 7.5 quarts of paint in total.

Model and drawing scales are a scale factor too. A 1:87 kit of a car 5 feet long gives a model of 60 inches divided by 87, which is about 0.69 inches. Going the other way, 7 inches on that kit stands for 609 inches of real length, or 50.75 feet.

Proportions in maps, models, and unit prices

Map scales are written as a proportion, and the two numbers carry different kinds of information. In 1:24,000, the 1 is the distance on the map and the 24,000 is the same distance on the ground in the same units. Measuring 2 inches on that map gives you 48,000 inches of real ground, which is 4,000 feet, or about 0.76 miles. The National Institute of Standards and Technology notes that the inch has been exactly 25.4 millimeters since 1959, so metric map scales convert cleanly: 2 inches becomes about 1,219 meters of real distance on a 1:24,000 map.

Unit prices are the same arithmetic in a shop. If 3 identical cans cost $2.40, the unit price is $0.80 each, and you can multiply that by any number to plan a shopping list. Grocery shoppers use this every trip, and so do people pricing cleaning supplies, garden seed, or printer ink. The number that stays fixed is the price for one unit.

Speed is worth one more example, because the units change. 60 miles per hour equals 88 feet per second, because 60 miles is 316,800 feet and an hour is 3,600 seconds. If a conveyor belt moves at 88 feet per second and you need 1,320 feet of belt, the run time is 1,320 divided by 88, which is 15 seconds.

Proportions in government statistics

Public data is full of proportions, and reading them is a matter of dividing one number by another. The 2020 Census apportionment table lists 331,449,281 residents in the 50 states and the District of Columbia. Florida counted 21,538,187 of them, so Florida's share is 21,538,187 divided by 331,449,281, which is 0.06498, or about 6.5 percent of the country. Texas counted 29,145,505, which works out to 8.8 percent, and California counted 39,538,223, which is 11.9 percent.

The Bureau of Labor Statistics uses the same arithmetic in its June 2025 employment situation report. For that month, the civilian labor force was 170,380 thousand people and the civilian noninstitutional population was 273,585 thousand, so the labor force participation rate was 170,380 divided by 273,585, which is 0.6228, and the report rounds that to 62.3 percent. The published rate and your own division agree, which is the quickest way to know you set the proportion up correctly.

A share of a population, a budget, a vote and a market are all the same structure, so the division you just did covers a long list of official numbers.

Mistakes that break proportion problems

Most wrong answers come from a handful of habits rather than from bad arithmetic. Here they are, with the fix for each.

Mixing units inside one ratio. If one side is in cups and the other in tablespoons, the cross products will never match. Convert everything to the same unit first. One US cup is 16 tablespoons, so 3:48 becomes 3:3, and the ratio that looked strange turns out to be 1:1.

Adding when you should multiply. Cross multiplication is multiplication on both diagonals. Adding the diagonals gives you a sum of the four terms, which is not the rule.

Assuming the rate stays fixed when it does not. A quantity priced per unit is a proportion only while the unit price holds. Bulk discounts, shipping tiers, and overtime pay all break the constant rate, and no calculator can rescue a proportion whose rate changed halfway through.

Rounding too early. If you round $2.40 divided by 3 to $0.90 and then multiply by 7, you get $6.30 instead of $5.60. Keep the extra digits through the middle and round only at the end.

Forgetting that a three term proportion is a different shape. 2:3:4 equals x:y:z means three matching pairs, and it needs its own method, usually a scale factor. The two term calculator on this page is for a:b = c:d.