What is a ratio?
A ratio compares two quantities and shows their relative sizes. 3:2 means “for every 3 of one thing, there are 2 of another.” Ratios are unit-agnostic — they work for cups, litres, pixels, or dollars equally well.
How simplification works
Both numbers are divided by their Greatest Common Divisor (GCD). The ratio 12:8 simplifies to 3:2 because GCD(12,8) = 4. The result is the same proportion in the smallest whole numbers possible.
Solving for a missing value
If A:B = C:D and you know three values, cross-multiplication finds the fourth.
Common real-world uses
| Context | Example |
|---|---|
| Concrete mix | 1:2:3 cement:sand:gravel |
| Recipe scaling | 2:1 flour:sugar |
| Screen aspect | 16:9 (1920:1080) |
| Map scale | 1:50,000 |
| Bill split | 3:2 shares |
Frequently asked questions
What’s the difference between a ratio and a proportion?
A ratio (3:2) compares two quantities. A proportion states that two ratios are equal: 3:2 = 6:4. Use Simplify for ratios, use Solve when you have a proportion with one missing term.
Can I use decimals?
Yes. Enter 1.5:2 or 0.75:1 — the calculator converts to whole-number equivalents internally before simplifying, so results are always clean integers.
What does the Scale mode do?
Scale multiplies both sides of a ratio by the same factor. Useful for scaling a recipe (×4 batches), a larger concrete pour, or resizing an image at a fixed aspect ratio.
What is the GCD?
The Greatest Common Divisor is the largest number that divides evenly into both values. Dividing by it gives the lowest-terms form of the ratio.
Why ratios matter in cooking
A ratio is the backbone of any recipe. Once you know the ratio, you can scale to any batch size — just multiply both sides by the same factor. The classic vinaigrette is 3:1 oil to vinegar.
How to scale a recipe
Switch to Scale mode, enter your base ratio, and drag the slider. Every ingredient stays in proportion automatically.
Classic cooking ratios
| Recipe | Ratio |
|---|---|
| Vinaigrette | 3:1 (oil:vinegar) |
| Pancake batter | 2:1 (flour:liquid) |
| Bread dough | 5:3 (flour:water) |
| Pie crust | 3:2 (flour:fat) |
| Béchamel | 1:1 (butter:flour) |
| Cookie dough | 3:2 (flour:butter) |
My recipe doesn’t use round numbers — will this work?
Yes. Enter decimals like 1.5:1 or 2.25:1. The calculator gives you the simplified whole-number form plus all scaled equivalents.
How do I scale a 3-ingredient recipe?
Use Simplify for any two ingredients at a time, or use Scale mode and apply the same factor to all three components.
Mix ratios in construction
Concrete, mortar, grout, and render are all defined by ratios. The proportions of cement, sand, and aggregate determine final strength and workability.
How to use this for a mix
Enter two main components (e.g. cement:sand as 1:3). Use Scale mode to find exact quantities for your batch size.
Standard mix ratios
| Application | Cement:Sand(:Gravel) |
|---|---|
| General concrete | 1:2:3 |
| Strong concrete | 1:1.5:3 |
| Mortar (brickwork) | 1:4 |
| Mortar (pointing) | 1:3 |
| Render (base coat) | 1:4 |
| Screed | 1:3 |
| Grout (floor tiles) | 1:2 |
My mix ratio has 3 parts — how do I use this calculator?
Work with two components at a time. For a 1:2:3 mix, check cement:sand (1:2) and cement:gravel (1:3) separately.
How do I find how much of each material I need?
Simplify your ratio, then use Scale mode. If you need 60 units total at a 1:2 ratio, that’s 20 of part A and 40 of part B.
Aspect ratios explained
An aspect ratio is the relationship between width and height. A 1920×1080 screen has a 16:9 ratio — both values divided by their GCD of 120.
Finding your ratio
Enter width and height in Simplify mode — you get the simplified aspect ratio instantly, plus the decimal (e.g. 1.78 for 16:9) useful for CSS.
Common screen aspect ratios
| Format | Resolution → Ratio |
|---|---|
| HD / Full HD | 1920×1080 → 16:9 |
| 4K UHD | 3840×2160 → 16:9 |
| Old monitor | 1024×768 → 4:3 |
| Ultrawide | 3440×1440 → 43:18 |
| Square (Instagram) | 1080×1080 → 1:1 |
| Portrait (Reels/TikTok) | 1080×1920 → 9:16 |
How do I resize an image while keeping the ratio?
Use Scale mode. Enter your original width:height, then drag the slider. Both dimensions scale together so the aspect ratio stays identical.
What’s the decimal value of 16:9?
16÷9 = 1.777… This is shown in the result panel as the decimal. CSS uses it in the aspect-ratio property: aspect-ratio: 16/9.
Splitting costs by ratio
When two people share a cost in proportion — by income, usage, or agreement — a ratio defines each person’s fair share. A 3:2 ratio means one person pays 60%, the other 40%.
Use Simplify to find the base ratio, then read the percentage cards in the result panel — those are the exact shares.
Common split scenarios
| Scenario | Ratio → shares |
|---|---|
| Equal split (2 people) | 1:1 → 50% / 50% |
| 2:1 income split | 2:1 → 67% / 33% |
| 3:2 income split | 3:2 → 60% / 40% |
| Business profit split | Equity % → simplify |
How do I split between 3 people?
Work in pairs. For a 3:2:1 split, check 3:2 for persons A and B, then 3:1 for A vs C.
Can I enter dollar amounts directly?
Yes — enter $3,500 : $2,100 and simplify to get the ratio, then read the percentage split from the result panel.
Map scales as ratios
A map scale of 1:50,000 means 1 unit on the map equals 50,000 units in reality. 1 cm on the map = 500 metres on the ground.
Use Solve mode: set A=1, B=scale denominator, C=your measured map distance. D gives the real-world distance in the same unit.
Common map scales
| Scale | 1 cm = real distance |
|---|---|
| 1:1,000 | 10 metres |
| 1:10,000 | 100 metres |
| 1:25,000 | 250 metres (OS Explorer) |
| 1:50,000 | 500 metres (OS Landranger) |
| 1:100,000 | 1 kilometre |
| 1:250,000 | 2.5 kilometres |
How do I use Solve mode for map distances?
Enter A=1, B=50000, C=your measured map distance in cm. D gives the real-world distance in cm — divide by 100,000 to get kilometres.
What’s the difference between 1:25,000 and 1:50,000?
A 1:25,000 map shows more detail — 1 cm covers 250 m, good for hiking. A 1:50,000 map covers more area — 1 cm covers 500 m, better for longer route planning.