Plot No. 57 · Education
Ratio Calculator (Simplify and Solve)
Simplify a ratio and solve a proportion in one place. To simplify A to B it divides both terms by their greatest common divisor. To solve A:B equals C:x it rearranges to x equals B times C divided by A, giving the missing term.
The simplifier divides both terms by their greatest common divisor. The proportion solver uses x equals B times C divided by A, so A:B and C:x describe the same ratio. Term A must not be zero to solve. The share line splits the total into A plus B parts and hands each side its number of parts.
The link saves your inputs so you can bookmark or share this exact result.
Common ratios in their simplest form
Reducing a ratio is one step: find the greatest common divisor of the two terms and divide both by it. Six to eight share a divisor of 2, so 6:8 becomes 3 : 4. Sixteen and nine share nothing above 1, which is why 16:9 never gets any shorter. The last two columns are the readings people mix up: the decimal is the first term divided by the second, while the percentage is the first term as a share of both terms added together.
| Ratio | Greatest common divisor | Simplest form | As a decimal (A / B) | As 1 : n | A as % of total |
|---|---|---|---|---|---|
| 16 : 9 | 1 | 16 : 9 | 1.7778 | 1 : 0.563 | 64% |
| 4 : 3 | 1 | 4 : 3 | 1.3333 | 1 : 0.75 | 57.1% |
| 3 : 4 | 1 | 3 : 4 | 0.75 | 1 : 1.333 | 42.9% |
| 2 : 5 | 1 | 2 : 5 | 0.4 | 1 : 2.5 | 28.6% |
| 6 : 8 | 2 | 3 : 4 | 0.75 | 1 : 1.333 | 42.9% |
| 10 : 15 | 5 | 2 : 3 | 0.6667 | 1 : 1.5 | 40% |
| 12 : 18 | 6 | 2 : 3 | 0.6667 | 1 : 1.5 | 40% |
| 20 : 50 | 10 | 2 : 5 | 0.4 | 1 : 2.5 | 28.6% |
| 24 : 36 | 12 | 2 : 3 | 0.6667 | 1 : 1.5 | 40% |
| 45 : 60 | 15 | 3 : 4 | 0.75 | 1 : 1.333 | 42.9% |
| 75 : 100 | 25 | 3 : 4 | 0.75 | 1 : 1.333 | 42.9% |
| 1920 : 1080 | 120 | 16 : 9 | 1.7778 | 1 : 0.563 | 64% |
A ratio and a fraction are not the same object. 3:4 read as a comparison is the fraction 3/4, or 0.75, but read as a share of the whole the first side takes 42.9 percent. To do arithmetic on the fraction itself, the fraction calculator adds, subtracts and reduces them.
Sharing an amount in a ratio
Most ratio questions in real life are splits: a total handed to two sides in a stated ratio. The method never changes. Add the terms to get the number of parts, divide the total by that to get the value of one part, then give each side its own number of parts. A tip jar holding 196 shared in the ratio 9:5 has 14 parts, so one part is 14. The 9 side takes 126 and the 5 side takes 70. The two shares always add back to the total, which is the quickest way to check your answer.
| Total | Ratio | Parts | One part | First share | Second share |
|---|---|---|---|---|---|
| 196 | 9 : 5 | 14 | 14 | 126 | 70 |
| 100 | 1 : 1 | 2 | 50 | 50 | 50 |
| 100 | 3 : 2 | 5 | 20 | 60 | 40 |
| 120 | 2 : 3 | 5 | 24 | 48 | 72 |
| 240 | 5 : 7 | 12 | 20 | 100 | 140 |
| 500 | 2 : 3 | 5 | 100 | 200 | 300 |
| 1,000 | 7 : 3 | 10 | 100 | 700 | 300 |
| 64 | 3 : 5 | 8 | 8 | 24 | 40 |
For a three-part ratio such as 2:3:5 the method is identical: sum all three terms for the part count, then multiply one part by each term. Splitting a bill rather than a plain number is a slightly different job, since tip and rounding come into it, and the tip and bill split calculator handles that case.
Scaling a ratio: solving A : B = C : x
When one term of the new pair is known and the other is not, the problem is a proportion. Cross multiply and rearrange to x equals B times C divided by A. The most common version of this is fitting a 16:9 frame to a known width, so the table gives the height that keeps the ratio exact at each of the widths screens and video use. A width of 1280 gives 720, and 1366 gives 768.38, which is why that particular laptop resolution is 1366 by 768 rather than a clean 16:9.
| Width (C) | Height at 16 : 9 | Height at 4 : 3 | Height at 3 : 2 |
|---|---|---|---|
| 640 | 360 | 480 | 426.67 |
| 720 | 405 | 540 | 480 |
| 1,024 | 576 | 768 | 682.67 |
| 1,280 | 720 | 960 | 853.33 |
| 1,366 | 768.38 | 1,024.5 | 910.67 |
| 1,600 | 900 | 1,200 | 1,066.67 |
| 1,920 | 1,080 | 1,440 | 1,280 |
| 2,560 | 1,440 | 1,920 | 1,706.67 |
| 3,840 | 2,160 | 2,880 | 2,560 |
Heights are shown to two decimal places because a proportion does not have to land on a whole number. Where it does not, the width you chose cannot express that ratio in whole pixels, so rounding either squashes the frame slightly or leaves a thin band. Scaling in the other direction works the same way: to find the width for a known height, swap the terms and solve 9:16 equals C:x instead.
How the ratio is simplified and solved
This does two jobs. To simplify a ratio A to B it finds the greatest common divisor of the two terms and divides both by it, leaving the ratio in its lowest whole-number terms. To solve a proportion, where A:B equals C:x, it cross multiplies and rearranges to x equals B times C divided by A, returning the missing fourth term.
The two halves share the A and B inputs, so a single pair of numbers both reduces and scales. Reducing tells you the simplest form of a ratio; solving tells you what a ratio becomes when one side is scaled up or down to a new first term.
How to use the ratio calculator
- Enter term A and term B, the ratio you want to simplify.
- Read the simplified ratio, both terms divided by their greatest common divisor.
- Enter term C to solve A:B = C:x, and read the missing value x.
Worked examples
A widescreen ratio
Inputs: A 16, B 9, C 32
Result: 16:9 stays 16:9 because 16 and 9 share no common factor above 1. Solving 16:9 = 32:x gives x = 18, since 9 times 32 divided by 16 is 18.
A ratio that reduces
Inputs: A 16, B 8, C 40
Result: 16:8 simplifies to 2:1 (both divide by 8). Solving 16:8 = 40:x gives x = 20.
Limitations and common mistakes
Edge cases and limitations
- Whole-number simplification only runs when both A and B are integers; decimal terms are shown side by side rather than reduced.
- The proportion solver needs term A to be non-zero, because dividing by zero has no answer.
Common mistakes
- Reading x as the simplified second term; x is the answer to the proportion A:B = C:x, not the reduced form of A:B.
- Entering the terms in the wrong order, which swaps the ratio. 16:9 and 9:16 are different ratios and give different results.
Frequently asked questions
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 16 to 9 the greatest common divisor is 1, so 16:9 is already in its lowest terms. For 16 to 8 the divisor is 8, which reduces the ratio to 2:1.
How do I solve a proportion like A:B = C:x?
Cross multiply and rearrange to x equals B times C divided by A. With A as 16, B as 9 and C as 32, x equals 9 times 32 divided by 16, which is 18. So 16:9 is the same ratio as 32:18.
Why does 16:9 stay 16:9?
Because 16 and 9 share no common factor greater than 1, their greatest common divisor is 1. A ratio only reduces when both terms can be divided by the same whole number, so 16:9 is already as simple as it gets.
How do I share an amount in a given ratio?
Add the terms to get the number of parts, divide the total by that, then give each side its share of parts. Splitting 196 in the ratio 9:5 means 14 parts, so one part is 14. The 9 side gets 126 and the 5 side gets 70, and the two shares add back to 196.
What is 3:4 as a fraction, a decimal and a percentage?
As a comparison of the two terms, 3:4 is the fraction 3/4, which is 0.75. As a share of the whole it is different: 3 parts out of 3 plus 4 equals 7 parts, so the first side takes 3/7, which is about 42.9 percent. Ratios trip people up here because both readings are valid and they give different numbers.
How do I scale a ratio up or down?
Multiply or divide both terms by the same number. Doubling 16:9 gives 32:18, which is the same ratio drawn larger. If only one new term is known, that is a proportion: put the known pair on the left, the new term on the right, and solve A:B = C:x with the calculator above.
Can a ratio have three terms?
Yes. A three-part ratio like 2:3:5 works the same way: 10 parts in total, so a 500 total splits into 100, 150 and 250. This calculator handles two terms at a time, so for a three-part split work out one part by dividing the total by the sum of all three terms, then multiply that part by each term.
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