Ratio Calculator

Work with ratios the easy way. Simplify a ratio to lowest terms, scale it up or down, solve a missing value in a proportion, split a quantity by a ratio, and convert any ratio to a fraction or a percentage — all in one tool, with the working shown.

What Is a Ratio?

A ratio compares two (or more) quantities by division: 3 : 2 means for every 3 units of the first thing, there are 2 of the second. Unlike a fraction, which is one number divided by another, a ratio keeps both parts visible — and that matters. A paint mix of 3 : 2, a recipe of flour to sugar at 4 : 1, and a map scale of 1 : 50,000 are all ratios, and in each case the relationship between the parts is the information.

Ratios have one golden rule: multiply or divide both parts by the same number and the ratio does not change. 3 : 2, 6 : 4, 30 : 20, and 300 : 200 are all the same ratio, just written at different scales. Simplifying a ratio means dividing both parts by their greatest common divisor until no further reduction is possible — 24 : 36 simplifies to 2 : 3, because both divide by 12.

Proportions: When Two Ratios Are Equal

A proportion says two ratios are equal: a : b = c : d. The workhorse for solving them is cross-multiplication: a × d = b × c. If three values are known, the fourth follows immediately — x = (b × c) ÷ a. This is the maths behind unit pricing (“if 3 kg costs $12, what do 7 kg cost?”), map scales, currency-style conversions, and recipe scaling. The discount calculator uses the same proportional thinking for sale prices, and the basic calculator covers the arithmetic.

Proportions also power the “unitary method”: find the value of one unit first, then multiply. If 5 litres cost $8, one litre costs $1.60, and 9 litres cost $14.40. It is slower than cross-multiplication but easier to sanity-check, and for money problems it keeps the units visible at every step.

Ratio, Fraction, and Percent — Three Views of One Idea

To convert a ratio to a percent: add the parts to get the whole, divide each part by the whole, and multiply by 100. A ratio of 3 : 2 has 5 parts, so the shares are 60% and 40%. The Khan Academy ratio lessons build this intuition with visual models, and Wolfram MathWorld gives the formal treatment of ratios and proportions.

Tips for Ratio Problems

• Always simplify first. Working with 2 : 3 instead of 24 : 36 makes every later step easier and errors rarer.
• Keep the order. A ratio of boys to girls is not the same as girls to boys — swapping the parts inverts the meaning.
• Check by adding shares. When splitting a quantity, the shares must add back to the total. If they do not, something went wrong.
• Watch the units. A ratio only makes sense when both parts use the same unit — convert cm to metres (or vice versa) before comparing.
• Scale both parts, never one. Doubling only one side of a recipe does not double the recipe; it changes it.

Worked Examples: Paint, Punch and Profit Share

Paint. A wall paint mixes colour and base in a 3 : 2 ratio, and you need 10 litres total. Total parts are 3 + 2 = 5, so each part is 10 ÷ 5 = 2 litres. That gives 3 × 2 = 6 litres of colour and 2 × 2 = 4 litres of base. The check is instant: 6 + 4 = 10, and 6 : 4 simplifies back to 3 : 2. If you only need 5 litres, each part becomes 1 litre, giving 3 and 2 — the same ratio at half the scale.

Punch. A party punch uses juice, soda, and syrup in the ratio 4 : 2 : 1 (three parts, covered properly below). For 14 litres, total parts are 7, each part is 2 litres, so the mix is 8 litres of juice, 4 of soda, and 2 of syrup. Scaling a ratio never changes its character — a punch mixed 8 : 4 : 2 tastes exactly like one mixed 4 : 2 : 1.

Profit share. Two partners split $5,000 profit in the ratio 2 : 3, matching their investment. Total parts are 5, each worth $1,000, so the shares are $2,000 and $3,000. For money splits with tax or deductions involved, work out the split first, then apply deductions per person — splitting after tax gives a different answer when the partners face different rates, and the salary calculator and percentage calculator help with the per-person figures.

Ratios with Three Parts

Nothing about ratios stops at two parts. A concrete mix of cement, sand, and gravel at 1 : 2 : 4 means for every 1 bucket of cement there are 2 of sand and 4 of gravel. Total parts are 7, so a 70-bucket batch needs 10 buckets of cement, 20 of sand, and 40 of gravel. The method is identical to the two-part case: add all parts, divide the total by that sum to get the value of one part, then multiply by each part in turn.

Three-part ratios also explain why order matters even more. Cement, sand, gravel at 1 : 2 : 4 is a usable mix; gravel, sand, cement at 4 : 2 : 1 is a pile of stones with a little cement in it. Labels belong with every part, every time — “1 : 2 : 4” alone is meaningless until you know which number belongs to which material. The same discipline applies to recipes, investment splits, and team workloads: name the parts first, then write the numbers.

One final check belongs on every ratio split: add the shares back together. In the concrete example, 10 + 20 + 40 = 70, the batch you started with. In the profit example, $2,000 + $3,000 = $5,000. If the shares do not add back to the total, a part was miscalculated — usually because the total parts were added wrongly, or one part was multiplied by the wrong value. This single check catches more ratio errors than any other habit, and it takes only a few seconds.

Map Scales: What They Mean on Paper and Ground

A map scale is a ratio of map distance to real distance, and misreading it is how walks become much longer than planned. The table shows what one centimetre on the map represents at common scales.

Reading a scale is a proportion problem: if 4 cm on a 1 : 50,000 map separates two villages, the real distance is 4 × 500 metres = 2,000 metres, or 2 km. The fraction calculator handles the unit conversions when scales mix centimetres, metres, and kilometres.

How to Simplify a Ratio Step by Step

Simplifying a ratio means writing the same comparison with the smallest whole numbers possible. It does not change the relationship between the parts; it only removes a common factor that was hiding the pattern. The ratio 24 : 36 and the ratio 2 : 3 describe exactly the same balance, but 2 : 3 is far easier to picture, scale, and compare. The calculator above does this division for you, but knowing the steps helps you spot mistakes and work confidently without a tool.

1. Write the ratio with labels. Note which number belongs to which part, for example flour : sugar, so the order cannot drift later.
2. Find the greatest common divisor (GCD). This is the largest whole number that divides both parts exactly. For 24 and 36, the GCD is 12.
3. Divide both parts by the GCD. Dividing only one part changes the ratio; dividing both keeps it identical.
4. Check that no common divisor greater than 1 remains. If both new parts still share a factor, divide again.
5. Check by multiplying back. The simplified parts multiplied by the GCD must return the original numbers.

If the GCD is not obvious, divide by any common factor and repeat. For 72 : 96, dividing by 12 gives 6 : 8, and dividing by 2 gives 3 : 4. Dividing directly by the GCD of 24 gives 3 : 4 in one step, because 72 divided by 24 is 3 and 96 divided by 24 is 4. Either route reaches the same simplest form, so use whichever route you can see first.

Ratios with decimals or fractions simplify the same way, after one extra step: clear the decimals or fractions first. The ratio 1.5 : 2.5 becomes 15 : 25 when both parts are multiplied by 10, and then simplifies to 3 : 5. The ratio 0.4 : 1.2 becomes 4 : 12 when both parts are multiplied by 10, and then simplifies to 1 : 3. A ratio written with fractions, such as 1/2 : 3/4, becomes 2 : 3 when both parts are multiplied by 4, because 1/2 multiplied by 4 is 2 and 3/4 multiplied by 4 is 3. In every case the rule is the same: multiply or divide both parts by the same number, never just one.

Equivalent Ratios and How to Spot Them

Equivalent ratios are different writings of the same comparison. The family 2 : 3 includes 4 : 6, 6 : 9, 10 : 15, and 20 : 30, because each one simplifies back to 2 : 3. Recognising equivalent ratios matters whenever a quantity grows or shrinks: a recipe doubled, a mixture made in a larger bucket, or a model built at a bigger scale all use equivalent ratios, not new ones.

• Multiply or divide both parts by the same number. That is the definition of an equivalent ratio, and the only safe way to make one.
• Compare cross-products. Two ratios a : b and c : d are equivalent exactly when a multiplied by d equals b multiplied by c.
• Compare simplified forms. If both ratios simplify to the same simplest form, they are equivalent.
• Compare decimal values. Dividing the first part by the second must give the same decimal for equivalent ratios, for example 2 divided by 3 is 0.6667 in both 2 : 3 and 10 : 15.

The cross-product check settles doubtful cases quickly. For 6 : 9 and 10 : 15, 6 multiplied by 15 is 90 and 9 multiplied by 10 is 90, so the ratios are equivalent. For 4 : 6 and 8 : 10, 4 multiplied by 10 is 40 and 6 multiplied by 8 is 48, so they are not equivalent; 8 : 10 simplifies to 4 : 5, not 4 : 6. When two ratios look close but the cross-products differ, trust the arithmetic, not the appearance.

Part-to-Part vs Part-to-Whole: Do Not Mix Them Up

This distinction causes more ratio errors than any other. A part-to-part ratio compares one part with another part: 3 : 2 compares the first part with the second part. A part-to-whole comparison compares one part with the total: 3 out of 5 compares the first part with all five parts combined. Both describe the same situation, but the numbers mean different things, and swapping them gives wrong fractions and wrong percentages.

• Part-to-part: 3 boys to 2 girls in a group. The ratio is 3 : 2, and the group has 5 children in total.
• Part-to-whole: 3 out of 5 children in that group are boys. The fraction is 3/5, which is 60 percent.
• Part-to-part: 4 parts concentrate to 1 part water in a cleaning mix. The ratio is 4 : 1, and the mix has 5 parts in total.
• Part-to-whole: 4 out of 5 parts of that mix are concentrate. The fraction is 4/5, which is 80 percent.

A related trap is reading a ratio as if it were already a fraction of the whole. The ratio 3 : 2 written as a division, 3 divided by 2, equals 1.5, but 1.5 is not the share of the whole; it only says the first part is one and a half times the second part. The share of the whole is 3 divided by 5, which is 3/5 or 60 percent. Keeping the words part-to-part and part-to-whole in mind at the start of a problem prevents this mistake before any numbers are written down. The fraction calculator is useful when the shares need further fraction arithmetic.

Converting a Ratio to a Fraction or a Percent

Converting a ratio is a short, fixed routine. Once the total number of parts is known, each share is simply its part divided by that total, and a percent is that same share multiplied by 100. The routine works for two parts, three parts, or any number of parts, and it is the bridge between ratio form and the fraction and percent forms used in most reports and labels.

1. Add all the parts to get the total. For 7 : 3, the total is 10.
2. Divide each part by the total to get its fraction of the whole. For 7 : 3, the fractions are 7/10 and 3/10.
3. Multiply by 100 for a percent. For 7 : 3, the percents are 70% and 30%.
4. Simplify the fraction and check the total. The fractions must add to 1 and the percents must add to 100.

The reverse conversion is just as useful. A split given as percents becomes a ratio by writing the percents as ratio parts and simplifying: 75% and 25% become 75 : 25, which simplifies to 3 : 1. Likewise, 20% and 80% become 20 : 80, which simplifies to 1 : 4, and 12.5% and 87.5% become 125 : 875, which simplifies to 1 : 7, because 125 multiplied by 7 is 875. Going the other way, 1 : 9 becomes 10% and 90%, because the total is 10 parts and 1/10 is 10% while 9/10 is 90%. The percentage calculator handles the percent arithmetic whenever a conversion involves awkward numbers.

• 1 : 1 is 50% and 50%, because the two equal parts make halves of the whole.
• 1 : 3 is 25% and 75%, because the total is 4 parts and each part is worth 25%.
• 3 : 1 is 75% and 25%, the same split with the order reversed.
• 2 : 3 is 40% and 60%, because the total is 5 parts and each part is worth 20%.
• 9 : 1 is 90% and 10%, because the total is 10 parts and each part is worth 10%.

Proportions and Cross-Multiplication Worked Through

A proportion is an equation between two ratios, and cross-multiplication is the reliable way to solve it. In the proportion a : b = c : d, the cross-products a multiplied by d and b multiplied by c must be equal. If three of the four values are known, the fourth follows from a single division, and the answer can always be checked by simplifying both ratios to see that they match.

1. Write the proportion with matching order. The first part of each ratio must describe the same kind of quantity, and so must the second part.
2. Cross-multiply. Multiply the outer values together and the inner values together, and set the products equal.
3. Divide to isolate the unknown. Divide the known product by the number multiplying the unknown.
4. Check by simplifying. Both ratios in the completed proportion must simplify to the same simplest ratio.

An everyday check shows the same method at work. If 3 kilograms cost 12 dollars, the unit price is 12 divided by 3, which is 4 dollars per kilogram, and 7 kilograms cost 7 multiplied by 4, which is 28 dollars. As a proportion, 3 : 12 = 7 : x gives 3x = 84, so x is 28, the same answer. Currency conversion follows the same pattern when a rate is stated: at an example rate of 1 dollar to 0.86 euro, 50 dollars convert to 43 euro, because 50 multiplied by 0.86 is 43. Real exchange rates change constantly, so always use the current rate for a real conversion, which the currency converter is built to handle. For the arithmetic itself, the scientific calculator covers the multiplication and division in longer proportion problems.

Scaling Recipes, Mixtures and Models

Scaling is the most common real use of equivalent ratios. To make more or less of something without changing its character, multiply every part by the same factor. A dough mixed at a flour-to-water ratio of 5 : 3 needs 240 grams of water for 400 grams of flour, because each part is worth 80 grams and 3 parts are 240 grams, making 640 grams of dough in total. Doubling the batch multiplies both parts by 2, giving 800 grams of flour and 480 grams of water, or 1,280 grams of dough, at exactly the same ratio.

A squash drink mixed at 1 part concentrate to 4 parts water shows the same idea on a smaller scale. With 50 millilitres of concentrate, the water needed is 200 millilitres, giving 250 millilitres of drink. Doubling gives 100 millilitres of concentrate and 400 millilitres of water, or 500 millilitres of drink. Halving gives 25 millilitres of concentrate and 100 millilitres of water. In each case the taste stays the same because the ratio stays the same, while the total changes by the scale factor.

Scale models use ratios in the opposite direction: the model is smaller, so the ratio describes how many real units one model unit represents. A 1 : 24 model car of a real car 4.8 metres long is 20 centimetres long, because 480 centimetres divided by 24 is 20 centimetres. A 1 : 72 model aircraft of a real aircraft 36 metres long is 50 centimetres long, because 3,600 centimetres divided by 72 is 50 centimetres. Reversing the calculation, a 15 centimetre model at 1 : 24 represents a real length of 360 centimetres, or 3.6 metres, because 15 multiplied by 24 is 360.

• Scale every part, never just one. Changing one part alone changes the recipe, the mix, or the model.
• Keep the units identical before scaling. Convert metres to centimetres, or kilograms to grams, before any multiplication.
• Label every part. A bare pair of numbers invites the order to be swapped halfway through the scaling.
• Check that the simplified ratio is unchanged. If the scaled ratio does not simplify back to the original, the scaling went wrong.
• Check that the total scaled by the same factor. Doubling each part must double the total, and halving each part must halve it.

When a scaled quantity involves money, the same proportional check applies to the cost: doubling a batch doubles the ingredient cost at the same unit prices, and the basic calculator is enough for the multiplication involved.

Aspect Ratios: Screens, Photos and Paper

An aspect ratio describes the shape of a rectangle as width to height. A 16 : 9 screen is 16 units wide for every 9 units tall, which is wider than a 4 : 3 screen at 4 units wide for every 3 units tall. Aspect ratios explain why the same photo looks different on a phone, a television, and a printed page: the content is the same, but the rectangle it must fill has a different shape, so part of it is cropped or letterboxed.

Every size in the table simplifies to its stated ratio: 1920 divided by 120 is 16 and 1080 divided by 120 is 9, while 1024 divided by 256 is 4 and 768 divided by 256 is 3. The 21 : 9 ratio also simplifies further to 7 : 3, because both parts divide by 3, but manufacturers keep the 21 : 9 name because it describes the ultrawide shape more directly. Finding a missing dimension is a proportion problem: a 16 : 9 image 1,920 pixels wide is 1,080 pixels tall, because 1,920 divided by 16 is 120 and 120 multiplied by 9 is 1,080. A 4 : 3 image 1,600 pixels wide is 1,200 pixels tall, because 1,600 divided by 4 is 400 and 400 multiplied by 3 is 1,200. A 3 : 2 image 900 pixels tall is 1,350 pixels wide, because 900 divided by 2 is 450 and 450 multiplied by 3 is 1,350.

• Video: most modern video is 16 : 9, so older 4 : 3 footage shows bars at the sides on a widescreen display.
• Photography: a 3 : 2 camera photo cropped to a 1 : 1 square loses part of the width, so keep the subject centred when a square crop is planned.
• Presentations: slides made at 4 : 3 shown on a 16 : 9 screen leave empty space unless the slide size is changed to match.
• Printing: a print size with a different aspect ratio from the photo file forces a crop, a border, or a stretched image, and stretching distorts the picture.

Ratio vs Rate: A Small Difference That Matters

A ratio compares two quantities, often measured in the same unit, such as 3 parts paint to 2 parts water. A rate compares two quantities measured in different units, such as kilometres per hour or dollars per kilogram, and it is usually reduced to a unit rate: the value for exactly one unit of the second quantity. The distinction matters because a rate always carries its units with it, while a ratio is a pure comparison that only makes sense once the units and the order are known.

• Ratio examples: paint mixed 3 : 2, a map scale of 1 : 50,000, a screen with an aspect ratio of 16 : 9, a class split of boys to girls at 3 : 2.
• Ratio examples with three parts: concrete mixed 1 : 2 : 4, a punch mixed 4 : 2 : 1, an investment split 2 : 3 : 5.

• Rate examples: a car travelling at 60 kilometres per hour, flour priced at 4 dollars per kilogram, a typist producing 60 words per minute.
• Rate examples from everyday totals: a car covering 360 kilometres on 8 litres, which is 45 kilometres per litre, and a reader finishing 240 words in 4 minutes, which is 60 words per minute.

Unit rates are found by division, and they make comparisons honest. Flour at 12 dollars for 3 kilograms costs 4 dollars per kilogram, because 12 divided by 3 is 4. A journey of 150 kilometres in 2.5 hours averages 60 kilometres per hour, because 150 divided by 2.5 is 60. A rate can be written in ratio form with units attached, such as 60 kilometres : 1 hour, but dropping the units turns it back into a bare number that no longer says what was measured. When a rate involves pay, the salary calculator converts between hourly, weekly, and monthly figures using the same unit-rate idea.

Ratios in Everyday Life

Ratios appear wherever two amounts must stay in balance: in kitchens, shops, gyms, workshops, and sports grounds. The settings change, but the maths does not. Every example below is the same three moves: write the ratio with labels, find the value of one part or the unit rate, and multiply by the parts needed, checking that the shares add back to the total.

Cooking and Baking

Cooks rely on ratios because a recipe that works for four people must still work for ten, and a sauce that works in a small pan must still work in a large pot. A vinaigrette at 3 parts oil to 1 part vinegar uses 150 millilitres of oil and 50 millilitres of vinegar for 200 millilitres of dressing, because the total is 4 parts and each part is 50 millilitres. Scaling to 400 millilitres doubles both parts to 300 millilitres and 100 millilitres. Bread dough, pastry, stock, and pancake batter all behave the same way: change the scale, keep the ratio, and the result keeps its character. The basic calculator covers the scaling arithmetic when a recipe is multiplied by an awkward factor such as 1.5.

Money and Shopping

Shoppers use ratios whenever they compare pack sizes, and the honest comparison is the unit rate, not the pack price. A 500 gram pack costing 4.00 dollars costs 0.80 dollars per 100 grams, because 4.00 divided by 5 is 0.80. A 750 gram pack costing 5.25 dollars costs 0.70 dollars per 100 grams, because 5.25 divided by 7.5 is 0.70. The second pack costs more at the till but less per 100 grams, so it is the better value if the extra food will be used. The same part-to-whole thinking gives the debt-to-income ratio: monthly debt payments of 500 dollars against gross monthly income of 2,500 dollars give 500 divided by 2,500, which is 20 percent, or a ratio of 1 : 5. Sale prices use proportional thinking too, and the discount calculator works them out directly.

Health and Fitness

Health and fitness plans often describe targets as shares of a total, which is ratio thinking in percent form. A daily intake of 2,000 kilocalories split with 30 percent from protein gives 600 kilocalories from protein, because 2,000 multiplied by 30 and divided by 100 is 600, and at 4 kilocalories per gram of protein that is 150 grams, because 600 divided by 4 is 150. The same intake with 50 percent from carbohydrate gives 1,000 kilocalories, which is 250 grams at 4 kilocalories per gram, because 1,000 divided by 4 is 250. These are planning figures for a stated split, not medical advice for any individual, and personal targets depend on age, activity, and health. For the calorie and energy side of the plan, the calorie calculator and the TDEE calculator estimate daily needs, and the BMI calculator gives the related body mass index figure.

Sport and Games

Sport reports are full of ratios, even when they are written as percents or records. A team with 18 wins and 12 losses has a win-to-loss ratio of 3 : 2, because both numbers divide by 6, and a win percent of 60 percent, because 18 out of 30 games is 18 divided by 30, which is 0.60. A team that scored 45 goals and conceded 30 has a goals ratio of 3 : 2, because both numbers divide by 15, and a possession split of 60 percent to 40 percent is the same 3 : 2 ratio, because both percents divide by 20. Averages sit beside ratios in sports reporting: a batter averaging runs per innings, or a bowler averaging runs per wicket, is a rate, and the average calculator works those out from match totals.

• Gardening: fertiliser mixed at a stated ratio of concentrate to water must be measured by volume, not guessed, or plants get too much or too little.
• DIY and decorating: paint, stain, and concrete mixes all state ratios on the container, and the batch size changes while the ratio stays fixed.
• Classrooms: a teacher-to-pupil ratio of 1 : 15 means 30 pupils need 2 teachers, because 30 divided by 15 is 2.
• Photography and design: aspect ratios and crop ratios decide how an image fills a frame, as described above.
• Maps and travel: a scale ratio turns centimetres on paper into kilometres on the ground, as described above.
• Business splits: partners, investors, and teams split money, work, and rewards by agreed ratios, and the shares must add back to the total.

Common Mistakes With Ratios and How to Avoid Them

Most ratio mistakes are not arithmetic slips; they are setup mistakes made before the arithmetic starts. Each mistake below changes the answer quietly, so the result looks plausible while being wrong. Reading through them before a problem, and checking the setup after it, catches the majority of errors.

• Scaling only one part. Doubling 2 : 3 by doubling only the first part gives 4 : 3, which is a different ratio. Doubling both parts gives 4 : 6, which simplifies back to 2 : 3.
• Swapping the order. A flour-to-sugar ratio of 4 : 1 is not a sugar-to-flour ratio of 4 : 1; reversed, it is 1 : 4. Always write the labels with the numbers.
• Treating part-to-part as part-to-whole. In a 3 : 2 split, the first share is 3/5 of the whole, not 3/2. Dividing 3 by 2 gives 1.5, which compares the parts with each other, not with the total.
• Adding instead of multiplying. Adding 2 to both parts of 3 : 2 gives 5 : 4, which is not equivalent to 3 : 2. Equivalent ratios are made by multiplying or dividing both parts, never by adding.
• Mixing units. A ratio of 1 metre to 50 centimetres is not 1 : 50. Converted to centimetres it is 100 : 50, which simplifies to 2 : 1. Convert first, compare second.
• Stopping before the simplest form. Dividing 24 : 36 by 6 gives 4 : 6, which is correct but not finished; dividing by the GCD of 12 gives 2 : 3. Check that no common divisor greater than 1 remains.
• Rounding too early. Rounding an intermediate decimal can shift the final answer, especially in proportions and money splits. Keep fractions exact until the last step, then round the final shares: a 1 : 3 split of 100 dollars is 33.33 dollars and 66.67 dollars, which add back to 100.00 dollars.

The single best habit is the add-back check: shares from a split must total the original amount, a scaled recipe must simplify back to the original ratio, and a solved proportion must have equal cross-products. If any check fails, the setup is wrong, not the check, so re-read the labels and the order before redoing the arithmetic.

Practice Problems With Answers

Try each problem without the calculator first, then use the calculator above to confirm the answer. Working by hand builds the judgement that tells you whether a calculator answer is plausible, and the checking steps in the table show exactly what to verify. Change one number in any problem and solve it again; the method stays the same while the arithmetic changes, which is how the skill becomes flexible.

• Check a simplification by multiplying the simplified parts by the GCD to recover the original numbers.
• Check a proportion by cross-multiplying the completed proportion and confirming the two products are equal.
• Check a split by adding the shares together and confirming they equal the original total.
• Check a conversion by adding the percents together and confirming they equal 100.

Frequently Asked Questions

Can a ratio be written as a decimal?

Yes, by dividing the first part by the second: 3 : 2 becomes 1.5. But the decimal throws away information — 1.5 could also be 6 : 4 or 30 : 20, and it hides how many parts each side has. Use the decimal for comparing ratios quickly, and keep the ratio form whenever the parts themselves matter.

What does a 1 : 1 ratio mean?

Equal parts. A 1 : 1 mix is half of each, a 1 : 1 split divides a total into two equal halves, and a 1 : 1 map is life size. It is also the ratio where fraction, percent, and ratio all agree most simply: 1/2 each, 50% each.

What is the difference between a ratio and a fraction?

A fraction is one number over another (3/5 of a whole). A ratio compares two parts (3 : 2). They convert freely: a 3 : 2 ratio means shares of 3/5 and 2/5.

How do I simplify a ratio?

Divide both parts by their greatest common divisor. 24 : 36 shares GCD 12, so it simplifies to 2 : 3.

How do I solve a proportion with a missing value?

Cross-multiply: in a : b = c : x, a × x = b × c, so x = (b × c) ÷ a.

How do I split money by a ratio?

Add the parts to get the total parts, divide the money by that, then multiply by each part. $100 split 3 : 2 gives $60 and $40.

Can a ratio have more than two parts?

Yes — 2 : 3 : 5 works the same way: add all parts (10), and each share is its part over 10 of the total.

The questions below cover the cases that come up once the basics are comfortable: zeros, decimals, fractions, unit ratios, odds, and comparing ratios that do not look alike at first glance. Each answer uses only the rules already covered on this page, applied to a slightly trickier starting point.

Can a ratio include zero?

A ratio can include a zero part, but only in the first position with care: 0 : 5 means none of the first thing and 5 parts of the second, which simplifies to 0 : 1 when both parts are divided by 5. A zero in the second position, such as 5 : 0, cannot be used as a divisor, so it does not form a usable ratio for division or proportion work. A ratio of 0 : 0 is meaningless, because there is nothing to compare and no total to share. In practice, if a zero appears, check whether the measurement is genuinely zero or whether a value is missing.

Can a ratio include decimals or fractions?

Yes. Ratios with decimals or fractions are simplified by clearing the decimals or fractions first, then dividing by the GCD as usual. The ratio 1.5 : 2.5 becomes 15 : 25 when both parts are multiplied by 10, and then 3 : 5. The ratio 1/2 : 3/4 becomes 2 : 3 when both parts are multiplied by 4. The ratio 0.25 : 0.75 becomes 25 : 75 when both parts are multiplied by 100, and then 1 : 3. The fraction calculator helps when the fractional parts need arithmetic of their own.

What is a ratio in simplest form?

A ratio is in simplest form when its parts share no common divisor greater than 1, so no further division of both parts by a whole number is possible. The ratio 10 : 15 is not in simplest form because both parts divide by 5, giving 2 : 3, and 2 and 3 share no divisor greater than 1, so 2 : 3 is in simplest form. Simplest form is the standard way to state a ratio for comparison, because equivalent ratios all reduce to the same simplest form and can then be recognised as the same comparison.

How do I write a ratio as 1 to something?

Divide both parts by the first part. This unit ratio form is useful when the first quantity is the reference: 10 : 4 becomes 1 : 0.4, because 10 divided by 10 is 1 and 4 divided by 10 is 0.4. Likewise, 8 : 2 becomes 1 : 0.25, because 8 divided by 8 is 1 and 2 divided by 8 is 0.25, and 6 : 9 becomes 1 : 1.5, because 6 divided by 6 is 1 and 9 divided by 6 is 1.5. The form reads naturally as for every 1 unit of the first thing, there are 0.4, 0.25, or 1.5 units of the second.

Is a ratio the same as odds?

Odds are a ratio, but they compare favourable outcomes with unfavourable outcomes, not a part with a whole. Odds of 3 : 2 in favour mean 3 favourable outcomes for every 2 unfavourable ones, so the probability is 3 out of 5, or 60 percent, because 3 divided by 5 is 0.60. Odds against would be written the other way round, 2 : 3. The distinction is in the reading, not in the arithmetic: the same numbers mean different things depending on whether the second number is the other part or the number of outcomes against.

How do I compare two ratios?

Simplify both ratios first, then compare by cross-multiplication or by decimal value. To compare 3 : 4 with 5 : 7, cross-multiply: 3 multiplied by 7 is 21 and 4 multiplied by 5 is 20, and since 21 is greater than 20, 3 : 4 is the larger ratio. By decimals, 3 divided by 4 is 0.75 and 5 divided by 7 is about 0.714, which gives the same conclusion. Either method works; cross-multiplication avoids rounding, while decimals are quicker for a rough comparison. If the ratios simplify to the same form, they are equal, however different they first looked.

Disclaimer: This calculator is for general maths education and everyday problems. For engineering or financial ratios, verify with the relevant professional standard.