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Formula
? = (B × C) ÷ A
- A, B
- the two terms of the known ratio
- C
- the term of the second ratio that corresponds to A
- ?
- the missing term that corresponds to B
What a ratio describes
A ratio compares two quantities by how many times one contains the other. A drink mixed at 1 : 4 uses one part concentrate for every four parts water. The proportion stays the same for a single glass or a whole jug. Ratios are written with a colon, read as “to”, and the order of the terms matters: 1 : 4 and 4 : 1 are very different drinks.
Solving a proportion
A proportion states that two ratios are equal: A : B = C : D. If you know three of the terms, you can find the fourth. Cross-multiplying gives A × D = B × C, so the missing term is D = (B × C) ÷ A.
For example, if 2 cups of rice need 3 cups of water, 10 cups of rice need (3 × 10) ÷ 2 = 15 cups of water.
The result isn’t rounded to a whole number, because many real quantities aren’t whole. Round it yourself to whatever precision makes sense, such as the nearest gram.
Solving a proportion by hand
Suppose 3 boxes of tile cover 8 square yards and you want to know how much 12 boxes cover. Write it as 3 : 8 = 12 : ?.
- Cross-multiply the known diagonal: 8 × 12 = 96.
- Divide by the remaining known term: 96 ÷ 3 = 32.
- Check that the ratios match: 3 ÷ 8 = 0.375 and 12 ÷ 32 = 0.375.
So 12 boxes cover 32 square yards. A quicker route when the numbers are friendly is to spot the scale factor: 12 is 4 times 3, so the answer is 4 times 8.
Simplifying the ratio of two numbers
Simplifying divides both terms by their greatest common divisor until no whole number greater than 1 divides both. 18 : 12 has a GCD of 6, so it reduces to 3 : 2. The simplified ratio describes exactly the same proportion in the smallest whole numbers.
To simplify 45 : 60 by hand, list the factors or divide step by step. Both are divisible by 5, giving 9 : 12, and both of those are divisible by 3, giving 3 : 4. Dividing by 15 in one go, the GCD, gets the same result.
Alongside the simplified ratio, the ratio calculator shows:
- As a fraction: the simplified ratio written as A/B.
- A ÷ B: the ratio as a single number, useful for comparing several ratios at a glance.
- A as a share of the total: the percentage of the combined amount that A makes up. For 3 : 2, that’s 3 out of 5 parts, or 60%.
Aspect ratios in pixels
An aspect ratio is width to height. Simplifying the pixel dimensions shows the true shape, which doesn’t always match the name it’s sold under.
| Resolution (W × H) | Simplified ratio | Width ÷ height | Usually called |
|---|---|---|---|
| 1280 × 720 | 16 : 9 | 1.7778 | HD, 720p |
| 2560 × 1440 | 16 : 9 | 1.7778 | QHD, 1440p |
| 3840 × 2160 | 16 : 9 | 1.7778 | 4K UHD |
| 1366 × 768 | 683 : 384 | 1.7786 | 16:9 (approximately) |
| 1024 × 768 | 4 : 3 | 1.3333 | 4:3 |
| 1920 × 1200 | 8 : 5 | 1.6 | 16:10 |
| 2560 × 1080 | 64 : 27 | 2.3704 | 21:9 ultrawide |
| 3440 × 1440 | 43 : 18 | 2.3889 | 21:9 ultrawide |
| 4096 × 2160 | 256 : 135 | 1.8963 | DCI 4K (cinema) |
| 6000 × 4000 | 3 : 2 | 1.5 | 35 mm photo |
| 1080 × 1350 | 4 : 5 | 0.8 | Portrait social post |
| 1080 × 1920 | 9 : 16 | 0.5625 | Vertical video |
To resize an image without stretching it, keep the ratio fixed and solve for the missing side. A 16 : 9 video that needs to be 1,200 pixels wide should be 16 : 9 = 1200 : ?, which is 675 pixels tall.
Real-life uses
Scaling recipes for cooking and baking
Scaling a recipe is a proportion between servings and each ingredient. If a recipe for 4 uses 250 g of flour, you can solve for any other number of servings, as in the first worked example below. Bakers often go further and express every ingredient as a ratio to the flour weight, which makes recipes easy to scale to any batch size.
Maps, plans and models
A map scale is a ratio between distance on paper and distance on the ground. On a 1 : 24 scale model car, a 4.5 m long car becomes 450 ÷ 24 = 18.75 cm. Architects and engineers use the same idea with floor plans, where 1/4 inch on the drawing commonly represents 1 foot.
Mixing fuel, paint and cleaners
Two-stroke engines often take fuel mixed at 50 : 1, meaning 50 parts gasoline to 1 part oil. A U.S. gallon is 128 fluid ounces, so one gallon of gas needs 128 ÷ 50 = 2.56 oz of oil. Concentrated cleaners and fertilizers list dilution ratios the same way. Follow the label’s ratio and solve for the amount of water in your container.
Unit pricing
Ratios also compare prices. A 12 oz jar for $3.60 costs $0.30 per ounce, and an 18 oz jar for $5.04 costs $0.28 per ounce, so the larger jar is cheaper per ounce. To find the price of 7 items when 3 cost $4.50, solve 3 : 4.50 = 7 : ?, which gives $10.50.
Splitting costs and profits
Business partners who invest $6,000 and $9,000 might split profits 2 : 3. With the percentage calculator you can then check each partner’s share: 2 parts out of 5 is 40%.
Tips and common mistakes
- Keep the units matched. In A : B = C : ?, A and C must be the same kind of quantity in the same units. Mixing grams and ounces, or centimeters and meters, gives a wrong answer that looks plausible.
- Don’t add the same amount to both terms. 2 : 3 is not the same as 4 : 5. Ratios stay equal only when you multiply or divide both terms by the same number.
- Remember the total. In a 1 : 4 mix, the concentrate is 1/5 of the total, not 1/4. Use the share-of-total figure if you need the fraction of the whole.
- Check the direction. “Water to rice” and “rice to water” are reciprocals. Say the ratio out loud with its units before entering it.
Ratios as fractions and percentages
Ratios, fractions and percentages are three views of the same idea. A 3 : 1 mix means the first ingredient is 3/4 of the total, or 75%. Once you’ve simplified a ratio, the fraction calculator can combine the parts exactly, and the percentage calculator can turn shares into amounts of a real total. The guide to fractions, decimals and percentages shows how to move between all three forms.
- Proportion: a statement that two ratios are equal, such as 2 : 3 = 8 : 12.
- Scale factor: the number you multiply every term by to scale a ratio up or down.
- Unit rate: a ratio with a second term of 1, such as $0.28 per ounce.
Worked examples
Scaling a recipe
A recipe uses 250 g of flour for 4 servings. How much flour for 6 servings?
Inputs (Solve A : B = C : ?): A = 4; B = 250; C = 6
? = (250 × 6) ÷ 4 = 375
Answer: 4 : 250 = 6 : 375
Simplifying a screen aspect ratio
Simplify a 1920 × 1080 resolution to its aspect ratio.
Inputs (Simplify A : B): A = 1920; B = 1080
Answer: 1,920 : 1,080 simplifies to 16 : 9.
Reading a map scale
On a map, 2 cm represents 5 km. How far is a route that measures 7.5 cm?
Inputs (Solve A : B = C : ?): A = 2; B = 5; C = 7.5
? = (5 × 7.5) ÷ 2 = 18.75
Answer: 2 : 5 = 7.5 : 18.75
Simplifying a ratio with decimals
A cleaning concentrate is mixed as 2.5 oz to 10 oz of water.
Inputs (Simplify A : B): A = 2.5; B = 10
Answer: 2.5 : 10 simplifies to 1 : 4.
Assumptions and limitations
- In the solve mode, A can't be 0. B and C can be any number, including zero, negatives and decimals.
- The missing value is shown to up to 6 decimal places and isn't rounded to a whole number.
- The simplify mode accepts positive numbers up to 1,000,000,000,000. Zero and negative values aren't accepted.
- Decimals in the simplify mode are scaled to whole numbers before reducing, using up to 10 decimal places.
- In the simplify mode, A ÷ B is shown to up to 6 decimal places and A's share of the total to up to 4.
- Both modes work with two-term ratios. For three or more terms, such as 1 : 2 : 3, work with two terms at a time.
Frequently asked questions
How do I simplify a ratio that contains decimals?
Multiply both terms by the same power of 10 until they are whole numbers, then divide both by their greatest common divisor. 1.5 : 2.5 becomes 15 : 25, which simplifies to 3 : 5. The ratio calculator does both steps for you.
Is a ratio the same as a fraction?
Not quite. The ratio 3 : 5 compares two parts with each other. The matching fractions of the whole are 3/8 and 5/8, because the total is 3 + 5 = 8 parts. That's why the calculator also shows A as a share of the total.
Which way round should I enter the terms?
Keep the same order on both sides. If A is the number of servings and B is grams of flour, then C must also be servings, and the answer will be grams of flour.
How do I split an amount in a given ratio?
Add the terms to get the number of parts, divide the amount by that number, then multiply by each term. To split $900 in the ratio 2 : 3, there are 5 parts of $180, so the shares are $360 and $540.
Why is a 3440 × 1440 monitor called 21:9 when it simplifies to 43:18?
21:9 is a marketing label rather than an exact ratio. 3440 ÷ 1440 is about 2.39, while 21 ÷ 9 is about 2.33. The same applies to 1366 × 768 laptop screens, which are sold as 16:9 but reduce exactly to 683 : 384.
How do you calculate a ratio of 3 numbers?
Divide all three terms by their greatest common divisor, just as with two terms, so 6 : 9 : 15 simplifies to 2 : 3 : 5. To scale a three-part mix such as concrete at 1 : 2 : 3 (cement, sand, gravel), multiply every term by the same number. This calculator handles two terms at a time, so solve each pair against the first term separately.
How do you calculate a ratio as a percentage?
Add the terms to get the total number of parts, then divide each term by the total and multiply by 100. In a 3 : 2 ratio, the first part is 3 ÷ 5 × 100 = 60% of the total and the second is 40%. The Simplify mode shows A's share of the total for you.