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Ratio Calculator
Simplify ratios, solve for a missing term, scale a recipe up or down, and work out screen aspect ratios with this free ratio calculator. Four tools in one: a ratio simplifier that turns 250:750 into 1:3, an equivalent-ratio scaler, a missing-term solver for proportions like 2:3 = 8:x, and an aspect ratio finder that tells you the height for any 16:9 width. Every answer comes with the working shown.
Both terms are divided by their greatest common divisor to give the smallest whole-number ratio.
Enter a ratio and the new first term you want — the second term is scaled by the same factor, keeping the ratio identical.
Solves a : b = c : x, so with a = 2, b = 3 and c = 8, the missing term x completes the proportion 2 : 3 = 8 : x.
Give the shape (16:9) and one side in pixels — the tool works out the other side and the total pixels.
How to use
- Choose a job from the list at the top: simplify, scale, find a missing term, or aspect ratio.
- Fill in the boxes for that job — each mode has its own short hint underneath.
- Press Calculate (answers also update as you type).
- Read the answer in big type, with the method and extras — fraction, percentage split, or pixel counts — in the line below.
Common aspect ratios
| Aspect ratio | Example size | Used for |
|---|---|---|
| 16:9 | 1920 × 1080 | TVs, monitors, YouTube videos, most phone video |
| 4:3 | 1024 × 768 | Old TVs and monitors, some tablets, presentation slides |
| 21:9 | 2560 × 1080 | Ultrawide monitors and cinema-style video |
| 1:1 | 1080 × 1080 | Square social media posts |
| 9:16 | 1080 × 1920 | Reels, Shorts and Stories — vertical phone video |
| 3:2 | 1500 × 1000 | DSLR photos and printed 6 × 4 inch photographs |
How it works
A ratio compares two quantities of the same kind: 250 ml of syrup to 750 ml of water, 2 boys to 3 girls in a class, 16 units of width to 9 of height on a screen. It is written with a colon, 250:750, and it behaves exactly like the fraction 250/750. That is why the first job of this calculator — simplifying — works exactly like simplifying a fraction: find the greatest common divisor (GCD) of the two terms and divide both by it. The GCD of 250 and 750 is 250, so 250 ÷ 250 = 1 and 750 ÷ 250 = 3, giving 1:3. The comparison is unchanged; only the numbers are smaller and easier to picture.
Scaling keeps the same idea in reverse. If a squash recipe mixes syrup and water in the ratio 1:3 and you want to use 10 measures of syrup, the water must be 10 × 3 = 30 measures — both terms grow by the same factor, so the taste is identical. The missing-term mode solves the formal version of that problem, the proportion a : b = c : x. Cross-multiplying gives x = (b × c) ÷ a. For 2 : 3 = 8 : x, that is x = (3 × 8) ÷ 2 = 12, and indeed 8:12 simplifies back to 2:3. Exam questions about maps, models and mixtures are almost always this one pattern in disguise.
Aspect ratio is a ratio with a special job: it describes the shape of a rectangle without fixing its size. A 16:9 screen can be a 32-inch TV or a phone held sideways; what matters is that for every 16 units of width there are 9 of height. So if the width is 1920 pixels, the height is 1920 × 9 ÷ 16 = 1080 pixels — the familiar Full HD size. Video editors, photographers cropping pictures, and anyone setting a thumbnail size for a Reel (9:16) or a YouTube video (16:9) use this every day. The aspect mode of this tool also reports the total pixel count, which tells you roughly how heavy the image file will be.
Two habits keep ratio work error-free. First, keep the order straight: 1:3 and 3:1 are opposite comparisons — syrup-to-water is not water-to-syrup. Second, keep the units the same before you start: a ratio of 1 m to 50 cm is 100:50 = 2:1, not 1:50. This calculator assumes both terms are already in the same unit. Percentages are just ratios in another dress — the simplify mode shows the percentage split (1:3 is 25%:75%) because shares of a total, from election seats to a 60:40 profit split between partners, are usually easiest to understand that way.
Worked example
A cook makes a big batch of nimbu pani mix using 250 ml of lemon syrup and 750 ml of water. For the recipe card, she wants the ratio in its simplest form.
Step 1: Write the ratio in order — syrup : water = 250 : 750.
Step 2: Find the GCD of 250 and 750 — it is 250.
Step 3: Divide both terms by 250: 250 ÷ 250 = 1 and 750 ÷ 250 = 3.
Step 4: Read the result — 1 : 3, a 25% to 75% split.
The calculator opens with 250 and 750 already filled in and shows exactly this answer. And the same ratio scales without any new thinking: with 10 measures of syrup, the scale mode gives 10:30 — ten times the syrup needs ten times the water to taste the same.
FAQ
How do I simplify a ratio?
Find the greatest common divisor of the two terms and divide both terms by it. For 250:750, the GCD is 250, so dividing gives 1:3. The comparison stays exactly the same — only the numbers get smaller. Decimals are handled too: 0.5:1.5 simplifies to 1:3.
What does 250:750 simplify to?
250:750 simplifies to 1:3. Both terms divide by their greatest common divisor, 250, leaving 1 and 3. As a percentage split that is 25 percent to 75 percent, and as a fraction the first term is 1/3 of the second.
How do I find the missing term in a proportion?
Use cross-multiplication: for a : b = c : x, the missing term is x = (b × c) ÷ a. For 2 : 3 = 8 : x, x = (3 × 8) ÷ 2 = 12. You can check the answer by simplifying both sides — 8:12 simplifies to 2:3, so the proportion holds.
What is the aspect ratio of a 1920 × 1080 screen?
It is 16:9. Divide both sides by their GCD, 120: 1920 ÷ 120 = 16 and 1080 ÷ 120 = 9. 16:9 is the standard shape for TVs, monitors and YouTube videos, which is why 1920 × 1080 (Full HD) and 1280 × 720 (HD) are both 16:9.
Is a ratio the same as a fraction?
Very nearly. The ratio a:b corresponds to the fraction a/b, and simplifying works the same way. The difference is in meaning: a fraction usually compares a part to a whole, while a ratio compares part to part — 1:3 syrup to water means the syrup is 1/4 of the whole mixture, not 1/3.
Can a ratio have more than two terms?
Yes. Three-term ratios like 2:3:5 are common for mixtures such as concrete (cement : sand : aggregate ideas) and profit sharing. This calculator works with two terms at a time; for a three-term ratio, simplify each pair against the first term, dividing all three by their common GCD.