Provide any three values below to calculate the fourth in the ratio A : B = C : D.
The ratio calculator on this page does three related jobs. First, it solves a proportion of the form A : B = C : D — enter any three of the four numbers and it finds the missing one. Second, it simplifies the ratio to its lowest whole-number terms and expresses it in the handy 1 : n form and as a percentage. Third, the ratio scaling calculator lets you enlarge or shrink a ratio by any factor, which is exactly what you need when resizing images, scaling recipes, or adjusting a mixture. Whether you are checking homework, resizing a photo, mixing a solution, or comparing quantities, this tool gives fast, exact answers.
Ratios appear everywhere in daily life, often without us noticing: the aspect ratio of a screen, the scale of a map, the proportions in a recipe, gear ratios in machines, and the odds of an event. Understanding and manipulating ratios is a core math skill, and this calculator removes the arithmetic so you can focus on the result.
A ratio is a quantitative relationship between two numbers that shows how many times one value contains another, or how two quantities compare in size. Ratios are usually written with a colon, such as 3:4 ("three to four"), but they can also be written with the word "to" (3 to 4) or as a fraction (¾). The ratio 3:4 tells you that for every 3 units of the first quantity there are 4 units of the second. A ratio can have more than two terms as well — for example, a paint mix might be 1:2:3 for red:blue:white.
Because a ratio describes a relationship rather than an absolute amount, ratios that look different can be equivalent. The ratios 3:4, 6:8, and 600:800 are all the same relationship, just scaled up or down. This equivalence is the key idea behind simplifying ratios and behind proportions.
To solve a proportion, type three of the four boxes in A : B = C : D and leave the unknown blank, then click Calculate. The calculator uses cross-multiplication to find the missing value and also shows the ratio simplified to lowest terms, written as 1 : n, and as a percentage of the total. To scale a ratio, enter the two terms in the Ratio Scaling Calculator, choose Enlarge or Shrink, enter how many times, and click Calculate to see the new ratio.
A proportion is a statement that two ratios are equal, written A : B = C : D. Proportions are the workhorse of ratio math because they let you find an unknown quantity when you know a matching pair. The fundamental rule is cross-multiplication: in any true proportion, A × D = B × C. Rearranging this equation lets you solve for whichever term is missing:
A = (B × C) / D B = (A × D) / C
C = (A × D) / B D = (B × C) / A
For example, in the proportion 3 : 4 = 600 : D, cross-multiplication gives 3 × D = 4 × 600, so D = 2400 / 3 = 800. This is precisely how a cook scales a recipe or how a mapmaker converts a measured distance to real-world scale.
Simplifying (or reducing) a ratio means writing it with the smallest possible whole numbers while keeping the same relationship. The method is the same one used for fractions: divide both terms by their greatest common divisor (GCD). For example, to simplify 6:8, the GCD of 6 and 8 is 2, so dividing both by 2 gives 3:4. To simplify 600:800, the GCD is 200, which again gives 3:4. A ratio is in "lowest terms" when the two numbers share no common factor other than 1. When your ratio contains decimals, you can first multiply both terms by a power of ten to clear the decimals, then reduce. This calculator performs the reduction automatically for whole-number ratios.
Two other useful forms make ratios easier to compare. The 1 : n form rescales the ratio so the first term is 1; for 3:4 this is 1 : 1.333, meaning the second quantity is about 1.33 times the first. This form is ideal for quickly judging relative size and is common in fields like photography and engineering. Ratios can also be turned into percentages: the first term as a share of the whole is A / (A + B). For 3:4, that is 3 / 7 ≈ 42.86%, meaning the first part makes up almost 43% of the total. This calculator shows both forms alongside the simplified ratio so you can see the relationship from every angle.
The Ratio Scaling Calculator multiplies or divides both terms of a ratio by the same factor, which changes the size of the quantities without changing their relationship. Enlarging a ratio multiplies both terms — enlarging 250:280 by 2.5 gives 625:700. Shrinking divides both terms — shrinking 250:280 by 2.5 gives 100:112. Because both terms change by the same factor, the simplified ratio stays the same; only the absolute numbers change. Scaling is exactly what happens when you resize a photo to fit a frame, double a recipe, or reduce a blueprint to a model, and it is the mathematical basis of similar figures in geometry.
One of the most common everyday uses of ratios is the aspect ratio — the ratio of a rectangle's width to its height. Screens, images, and videos all have an aspect ratio, and matching it correctly prevents stretching, squishing, or black bars. Some of the most familiar aspect ratios include:
The ratio calculator is handy for resizing while keeping the aspect ratio intact: enter the known aspect ratio and one dimension, leave the other blank, and it computes the matching value. For instance, to fit a 16:9 image into a 1280-pixel width, solve 16 : 9 = 1280 : D to get a height of 720 pixels.
Ratios are woven into countless practical tasks:
These three ideas are related but distinct. A fraction expresses a part of a whole, such as 3/7 of the total. A ratio compares two separate quantities, such as 3:4, and does not have to be part-to-whole — it can be part-to-part. A rate is a special ratio that compares quantities with different units, such as miles per hour or price per pound. A part-to-part ratio like 3:4 can be rewritten as part-to-whole fractions (3/7 and 4/7), which is how the percentage form is derived. Recognizing which form a problem calls for makes ratio math much clearer.
Ratios are not limited to two quantities. A ratio like 1:2:3 compares three parts at once — for example, a mortar mix of 1 part cement to 2 parts lime to 3 parts sand. The same rules apply: to scale a multi-term ratio, multiply every term by the same factor; to simplify it, divide every term by their common greatest divisor. To find the total number of parts, add all the terms together (1 + 2 + 3 = 6 parts), then each term as a fraction of the whole tells you its share. If you are working with an actual quantity — say 12 cups of mixture — divide it by the total parts (12 ÷ 6 = 2 cups per part) and multiply by each term to get 2 cups cement, 4 cups lime, and 6 cups sand. While this calculator focuses on two-term ratios and proportions, these principles extend directly to any number of terms, which is why ratios are so useful in cooking, construction, and chemistry where several ingredients must stay in balance.
Perhaps the most famous ratio of all is the golden ratio, approximately 1 : 1.618, denoted by the Greek letter phi (φ). It arises when a line is divided so that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller part. The golden ratio appears throughout art, architecture, and nature — from the proportions of classical buildings and Renaissance paintings to the spiral arrangement of seeds in a sunflower and the shells of certain mollusks. Designers and photographers often use it, along with the related "rule of thirds," to create compositions that feel naturally balanced. You can explore it with this calculator by entering the ratio in the 1:n form and comparing your own proportions against 1 : 1.618.
Set up the proportion A : B = C : D with the known values, then cross-multiply: A × D = B × C. Solve the resulting equation for the unknown term. This calculator does it automatically when you leave one of the four boxes blank.
Divide both terms by their greatest common divisor. For 12:18, the GCD is 6, so the simplified ratio is 2:3. A ratio is fully simplified when the two numbers have no common factor other than 1.
It is the ratio rewritten so the first term equals 1, making the second term show how many times larger it is. For 3:4, dividing both by 3 gives 1 : 1.333, so the second quantity is about 1.33 times the first.
Add the terms to get the whole, then divide each term by the whole and multiply by 100. In 3:4 the whole is 7, so the first part is 3/7 ≈ 42.86% and the second is 4/7 ≈ 57.14%.
Enlarging multiplies both terms by the scale factor, making the numbers bigger; shrinking divides both terms, making them smaller. Either way the underlying relationship — the simplified ratio — stays the same.
Yes. Ratios can include decimals, such as 1.5:2. To simplify a decimal ratio to whole numbers, multiply both terms by the same power of ten to clear the decimals, then reduce by the greatest common divisor.
This Ratio Calculator is provided for educational and general informational purposes. Results are computed with standard proportion and ratio math and displayed to high precision; round them as appropriate for your use. Always double-check critical calculations independently.