Ratio Calculator

A ratio says how much of one thing there is for every so much of another, and it keeps saying the same thing however large or small you make it. That is the whole trick behind every job this ratio calculator does. Simplifying divides every term by the same number. Sharing an amount multiplies every term by the same number. Scaling a mix does the same again. Type one part per row, as many as eight, and the table beside the answer shows each part in lowest terms, as a fraction of the whole, as a percent, as a share of any amount you enter and at any new size you choose.

How a ratio is reduced to lowest terms

A ratio is in its simplest form when no whole number bigger than 1 divides every term exactly. To get there, find the greatest common divisor of all the terms and divide each one by it. For 8 : 12 : 4 the largest number that goes into all three is 4, so the ratio becomes 2 : 3 : 1. For 12 : 16 : 20 it is also 4, giving 3 : 4 : 5. The rule is the same for three, four or eight parts. The only change is that the divisor has to work for every term, not just the first two, which is why 3 : 6 : 8 cannot be simplified at all. Three and six share a factor of 3, but eight does not, so the greatest common factor of the set is 1.

Decimals and fractions need one step first, because a divisor only makes sense for whole numbers. The calculator multiplies every term by the smallest number that clears all the decimals and fractions, then divides out the common factor. With 1.2 : 0.8 that multiplier is 5, giving 6 : 4, which reduces to 3 : 2. Multiplying by 10 instead gives 12 : 8 and the same answer, which is how most textbooks show it. With 1/2 : 3/4 the multiplier is 4 and the answer is 2 : 3 straight away. Mixed numbers such as 1 1/2 work too: 1 1/2 : 2 becomes 3 : 4.

Sharing an amount in a ratio

Sharing is three steps. Add the terms to get the total number of parts. Divide the amount by that total to get the value of one part. Multiply each term by the value of one part. Share $48 in the ratio 3 : 1 : 2 and there are 6 parts, each worth $8, so the shares are $24, $8 and $16. Share $50 in 2 : 3 : 5 and there are 10 parts worth $5 each, giving $10, $15 and $25. Add the shares back up every time. If they do not come to the amount you started with, a part was left out of the total, which is the most common mistake on three way splits: dividing by the sum of two terms when there are three.

The ratio does not need to be simplified before sharing, because 6 : 2 : 4 and 3 : 1 : 2 split any amount identically. The calculator reduces it anyway so the working shows the smallest honest numbers.

When the amount will not split evenly

Split $100 three ways equally and every share is $33.333 recurring. Round each one to the cent and you have handed out $99.99. The cent has not vanished, the rounding has simply refused to place it. This calculator uses the largest remainder rule, the same idea used to allocate seats in some elections: round every share down, then give the leftover units one at a time to the shares whose dropped remainders were largest. $100 in 1 : 1 : 1 becomes $33.34, $33.33 and $33.33, and the column adds back to exactly $100. The note under the answer says how many leftover units were placed, so you can see when it happened. On one bill a stray cent is trivial, but the same ratio applied across months of rent or hundreds of invoice lines turns a cent into a real discrepancy. Choose whole units, one, two or three decimal places to match what you are dividing: whole units for sweets or people, two places for money.

Scaling a ratio up or down

Scaling keeps every relationship and changes the size. Pick the part you know the new value for, type that value, and every other part follows by the same scale factor. A concrete mix of cement, sand and gravel at 1 : 2 : 3 with 7 buckets of sand needs a factor of 3.5, so the batch is 3.5 : 7 : 10.5 buckets. Other mixes use 1 : 2 : 4, and the method is identical. A pancake batter of 3 parts flour to 2 parts milk made four times over is 12 : 8. Doubling or halving a recipe is the same operation with a factor of 2 or 0.5, and so is resizing an image: fix the width in pixels and the scaled column gives the height that keeps the shape.

Part to part, part to whole, fractions and percents

A ratio compares parts with each other. A fraction compares a part with the whole. In a class where boys and girls are 2 : 3, the ratio of boys to girls is 2 : 3, but boys are 2/5 of the class, because the whole is 2 + 3 = 5 parts. That is why the fraction column divides each term by the total, never by the other term. Percent is the same fraction multiplied by 100. A mixture of 5 : 9 : 4 : 2 has 20 parts, so it is 25%, 45%, 20% and 10%, and 200 litres of it holds 50, 90, 40 and 20. A 1 : 4 dilution works the same way: one part concentrate and four of water make five parts, so the concentrate is a fifth of the bottle, not a quarter.

Order matters too. Boys to girls at 2 : 3 is girls to boys at 3 : 2, and the name you give each row in the calculator is there so the table cannot be read the wrong way round.

Convert units before you compare

A ratio has no unit of its own, which only works if every term was measured in the same one. 45 minutes to 2 hours is not 45 : 2. Convert first: 45 minutes to 120 minutes reduces to 3 : 8. 750 g to 3 kg is 750 : 3000, which is 1 : 4. The calculator cannot see units, so it trusts that every row uses the same one.

The 1 : n form

Some ratios read best with one side fixed at 1. Divide every term by the smallest and you get the unit ratio shown in the working: 4 : 5 is 1 : 1.25. Map scales are written this way, where 1 : 63,360 means one inch on the map is one mile on the ground. Coffee brewing is another. The Specialty Coffee Association's Golden Cup guideline is 55 g of coffee per litre of water. Enter 55 and 1000 and the calculator reduces it to 11 : 200, which is 1 : 18.18, close to the 1 : 18 many brewers quote.

Aspect ratios and screens that are almost 16:9

An aspect ratio is width to height, reduced. YouTube's standard player is 16:9, and so are its 1920 × 1080 and 3840 × 2160 sizes. Enter 1920 and 1080 and the calculator divides by 120 to give 16 : 9. Not every screen reduces so tidily. The 1366 × 768 laptop panel that resolution tables list as roughly 16:9 actually reduces to 683 : 384, a decimal of 1.7786 against 1.7778, about 0.05% wide of true 16:9. YouTube's own 854 × 480 size is 427 : 240 for the same reason: 480 × 16 ÷ 9 is 853.33, which is not a whole pixel. With two parts entered, the calculator reports the exact ratio, the nearest named one and how far apart they are. It also recognises names that are deliberately left unreduced: a 1280 × 800 panel is strictly 8 : 5, but screens call it 16:10 so it reads directly against 16:9.

Ultrawide monitors are sold as 21:9, but the common 2560 × 1080 panel reduces to 64 : 27, about 2.37 to 1, while 21 : 9 is 2.33. The 3440 × 1440 panel is 43 : 18. On phones the shape turns around: Instagram's portrait feed post is 4:5 at 1080 × 1350, and Reels and Stories are 9:16 at 1080 × 1920. Cinema uses decimal ratios against 1, 1.85:1 for flat widescreen and 2.39:1 for anamorphic, and the calculator accepts those as typed. Fix the height at 1080 and a 1.85:1 frame is 1998 pixels wide.

Mixes written as one number to another

Two stroke fuel is sold as 50:1, which means 50 parts gasoline to 1 part oil. A US gallon is 128 fluid ounces, so scaling 50 : 1 until the gasoline is 128 gives 2.56 oz of oil, the figure mixing charts give, usually rounded to 2.6. Note what the ratio is not: the oil is 1 part of 51 in the can, about 1.96% of the mix, not 2%. The same distinction applies to any dilution printed on a bottle.

What belongs on other pages

If you know three values of two equal ratios and need the fourth, or need to decide whether two quantities move together or against each other, that is a proportion, and the proportion calculator solves it. Percent change and percent of a number are on the percentage calculator, and adding or multiplying fractions is on the fraction calculator.