Ratio Calculator
Simplify, scale, share an amount out, or work an aspect ratio
Decimals are fine: 1.5 : 2 is scaled up to 15 : 20 first, then reduced to 3 : 4.
Scaling a recipe: enter the ratio you have, then set the term you are changing. A mix for 4 people scaled to 7 keeps every ingredient in proportion.
Splitting profits, rent, an inheritance or a bag of sweets: the amount is unit-free, so it works for pounds, dollars, grams or anything else.
Fill in one dimension and leave the other blank to solve it. Enter both and the calculator tells you what aspect ratio you actually have.
How to Use
- 1Pick the job: simplify, scale, share out an amount, or aspect ratio.
- 2Enter two terms, or three for a three-way ratio.
- 3Read the answer, then the tiles for the decimal, fraction and percentage forms.
- 4The working underneath shows every step, ready to copy into homework.
The Rules
- SimplifyDivide every term by the GCD
- ScaleMultiply every term by k
- Share outOne part = total ÷ Σ terms
- Aspectheight = width × h ÷ w
- As a percentterm ÷ total × 100
Quick Examples
Tap an example to load it above.
Everything about the Ratio Calculator
Four things people mean by "work out the ratio", and how each one is done.
A ratio compares quantities of the same kind, so 3 : 5 says that for every three of the first thing there are five of the second. This ratio calculator handles the four jobs that actually come up: simplifying a ratio, scaling one, sharing an amount out in one, and working an aspect ratio.
Every mode also shows the ratio as a decimal, a fraction, a percentage split and in 1 : n form, because those are usually what the question is really asking for once you get past the colon.
Which calculator do I need? If you have two ratios and one missing number (something shaped like 3 : 4 = 9 : ?), that is a proportion, so use the proportion calculator. This page is for working with one ratio: tidying it up, resizing it, or splitting something with it.
Simplifying a ratio
Divide every term by their greatest common divisor. For 12 : 16 the GCD is 4, so the ratio reduces to 3 : 4. The relationship is unchanged, and you have only written it in the smallest whole numbers that say the same thing.
Decimals need one extra step first. A GCD only exists for whole numbers, so 1.5 : 2 is multiplied by 10 to give 15 : 20, and only then divided by its GCD of 5 to reach 3 : 4. The calculator does this automatically and shows both steps.
Sharing an amount out in a ratio
This is the most common real ratio task and the one most calculators skip. Add the terms to get the number of parts, divide the amount by that, then give each side its number of parts.
| Step | Working | Result |
|---|---|---|
| Add the parts | 3 + 5 | 8 parts |
| Value of one part | 2,400 ÷ 8 | 300 |
| First share | 3 × 300 | 900 |
| Second share | 5 × 300 | 1,500 |
| Check | 900 + 1,500 | 2,400 ✓ |
Three-way splits work the same way: 120 sweets in 2 : 3 : 7 is 12 parts of 10, giving 20, 30 and 70.
Scaling a ratio
- 1Multiply every term by the same number
That is the whole rule. 2 : 3 doubled is 4 : 6, a different pair of numbers describing exactly the same relationship.
- 2Scaling from a known new value
A mix for 4 people needs to feed 7. The factor is 7 ÷ 4 = 1.75, so every ingredient is multiplied by 1.75. Set "Scale by → the first term" and enter 7.
- 3Never add instead of multiplying
Adding 2 to both sides of 2 : 3 gives 4 : 5, which is a completely different relationship. Ratios scale multiplicatively, and this is the single most common mistake.
Aspect ratios
An aspect ratio is width : height. Give the calculator one dimension and it returns the other, so "what height do I need for a 1920-pixel-wide 16:9 image" is answered instantly: 1080. Enter both dimensions and it tells you what ratio you actually have, which is useful for checking whether an image will letterbox.
| Ratio | Where it is used | Common sizes |
|---|---|---|
| 16 : 9 | HD video, YouTube, most monitors | 1280×720, 1920×1080, 3840×2160 |
| 9 : 16 | Reels, Shorts, TikTok, Stories | 1080×1920 |
| 4 : 3 | Older TVs, iPad, many projectors | 1024×768, 1600×1200 |
| 3 : 2 | DSLR and mirrorless photos | 3000×2000, 6000×4000 |
| 21 : 9 | Ultrawide monitors, cinema | 2560×1080, 3440×1440 |
| 1 : 1 | Square social posts, avatars | 1080×1080 |
Ratios, fractions and percentages
They are three ways of saying the same thing, and the confusion between them costs marks in exams. In a 3 : 5 ratio the first quantity is 3/5 of the second, but 3/8 of the total, which is 37.5%. The calculator prints all of these so you never have to pick the wrong denominator. To work with the fractions themselves, use the fraction calculator; for straight percentage questions the percentage calculator is the quicker route.
Frequently Asked Questions
How do I simplify a ratio?
Divide every term by their greatest common divisor. For 12 : 16 the GCD is 4, so the ratio simplifies to 3 : 4. The relationship is identical. You have just written it with the smallest whole numbers possible. The calculator shows the GCD it used so you can check the working.
How do I divide an amount in a given ratio?
Add the ratio terms to find the total number of parts, divide the amount by that to get the value of one part, then multiply each term by it. Sharing 2,400 in 3 : 5 gives 8 parts of 300, so the shares are 900 and 1,500. The Divide an amount tab does this for two or three-way splits.
Can I simplify a ratio with decimals in it?
Yes. A greatest common divisor only exists for whole numbers, so the calculator multiplies every term by the power of ten needed to clear the decimals first. 1.5 : 2 becomes 15 : 20, which then reduces to 3 : 4. Both steps are shown in the working.
What is the difference between a ratio and a proportion?
A ratio compares two or more quantities, such as 3 : 5. A proportion is a statement that two ratios are equal, such as 3 : 5 = 9 : 15. Use this page to work with a single ratio; use the proportion calculator when you have two ratios and need to find a missing term.
How do I scale a recipe using a ratio?
Multiply every ingredient by the same factor. If a mix serves 4 and you need it to serve 7, the factor is 7 ÷ 4 = 1.75. In the Scale tab, choose "Setting the first term" and enter your new number, and the calculator works out the factor and applies it to every term at once.
What height do I need for a 1920-pixel-wide 16:9 image?
1080 pixels. In the Aspect ratio tab, pick 16:9, enter 1920 as the width and leave the height blank. The formula is height = width × 9 ÷ 16. Leave the width blank instead to solve the other way round, or fill both in to see what ratio your existing dimensions really are.
In a 3 : 5 ratio, what fraction is the first part?
It depends what you are comparing it to, which is where most mistakes happen. The first part is 3/5 of the second part, but only 3/8 of the total, which is 37.5%. The calculator shows the fraction, the decimal and the percentage split at the same time so you can pick the right one.
Why can a ratio term not be zero or negative?
A ratio compares how large quantities are relative to each other, and a zero or negative share has no meaning in that comparison, because a zero term would also make the decimal and percentage forms undefined. The calculator says so plainly rather than returning NaN or a misleading number.