Ratio Calculator
1 What exactly is a ratio?
A ratio tells how many times one quantity fits inside another. It’s the mathematical shorthand behind everyday fairness fights (“You gave my sister twice as many cookies!”), recipe scaling, betting odds, and cinematic widescreens.
1.1 Three common notations
| Notation | Example | How to read it |
|---|---|---|
| Colon | 1 : 2 | “1 to 2” |
| Word | 1 to 2 | “1 two” |
| Fraction | ½ | “One-half” |
All three communicate the same truth: multiply the second number by ½ to get the first. In reverse, multiply the first by 2 to reach the second.
2 Core vocabulary
Part-to-part ratio – compares two components within a whole (flour : sugar).
Part-to-whole ratio – compares one component to the total (sugar : mixture).
Equivalent ratios – 1 : 2 = 2 : 4 = 50 : 100; they scale by the same factor.
Proportion – an equation stating that two ratios are equal (1 / 2 = 3 / 6).
3 Why ratios feel so intuitive
Humans (and even toddlers) grasp multiplication by repeated addition. When the smaller number “fits” a certain number of times inside a larger one, the brain smells pattern and quickly learns to shout “Unfair!” or “Double!”.
Example: cookie justice
| Child | Cookies | Ratio to sibling |
|---|---|---|
| Big sister | 6 | – |
| Little brother | 3 | 1 : 2 (half as many) |
No calculator required—just counting slots in the cookie jar.
4 How to manipulate ratios
4.1 Simplifying
Divide both terms by their greatest common divisor (GCD).
24 : 60 → divide by 12 → 2 : 5.
4.2 Scaling up or down
Multiply (or divide) every term by the same factor.
A 1 : 2 : 3 cake batter (butter : sugar : flour) × 5 → 5 : 10 : 15 for five cakes.
4.3 Converting to fractions or percentages
3 : 7 as part-to-whole → 3/(3 + 7) = 3/10 = 0.30 = 30 %.
5 Applications across real life
| Domain | Typical ratio | Meaning |
|---|---|---|
| Cooking | 1 : 2 : 3 (butter : sugar : flour) | Classic pound-cake baseline |
| Map scale | 1 : 50 000 | 1 cm on paper = 50 000 cm (0.5 km) on Earth |
| Finance | 0.4 : 1 debt-to-equity | Firm owes $0.40 for every $1 of equity |
| Photography | 3 : 2 frame | 35 mm film proportions |
| Gearbox | 4 : 1 | Motor shaft turns four times per wheel rotation |
| Sports odds | 5 : 1 against | Five losses for every win in long-run trials |
6 Aspect ratios – the screens we stare at
An aspect ratio is simply width : height. When engineers standardized TVs and phones, they turned “rectangle shape” into a ratio.
6.1 Complete Aspect-Ratio Cheat-Sheet
| Name / Label | Aspect Ratio | Width (px) | Height (px) |
|---|---|---|---|
| 480p | 3 : 2 | 720 | 480 |
| 576p | 5 : 4 | 720 | 576 |
| 720p (HD) | 16 : 9 | 1280 | 720 |
| 1080p (Full HD) | 16 : 9 | 1920 | 1080 |
| 2160p (4 K UHD) | 16 : 9 | 3840 | 2160 |
| 4320p (8 K UHD) | 16 : 9 | 7680 | 4320 |
| 8640p | 16 : 9 | 15 360 | 8640 |
| Legacy / Computer-monitor formats | |||
| SVGA | 4 : 3 | 800 | 600 |
| WSVGA | ≈ 17 : 10 | 1024 | 600 |
| XGA | 4 : 3 | 1024 | 768 |
| XGA+ | 4 : 3 | 1152 | 864 |
| WXGA (variant 1) | 16 : 9 | 1280 | 720 |
| WXGA (variant 2) | 5 : 3 | 1280 | 768 |
| WXGA (variant 3) | 16 : 10 | 1280 | 800 |
| SXGA (UVGA) | 4 : 3 | 1280 | 960 |
| SXGA | 5 : 4 | 1280 | 1024 |
| HD 1360 | ≈ 16 : 9 | 1360 | 768 |
| HD 1366 | ≈ 16 : 9 | 1366 | 768 |
| SXGA+ | 4 : 3 | 1400 | 1050 |
| WXGA+ | 16 : 10 | 1440 | 900 |
| HD+ | 16 : 9 | 1600 | 900 |
| UXGA | 4 : 3 | 1600 | 1200 |
| WSXGA+ | 16 : 10 | 1680 | 1050 |
| FHD | 16 : 9 | 1920 | 1080 |
| WUXGA | 16 : 10 | 1920 | 1200 |
| QWXGA | 16 : 9 | 2048 | 1152 |
| WQHD | 16 : 9 | 2560 | 1440 |
| WQXGA | 16 : 10 | 2560 | 1600 |
6.2 Visualizing the landscape (see Figure 1)
The scatter chart plots each canonical resolution in the width–height plane. Points cluster along distinct slope “rails”:
4 : 3 rail – old CRT monitors and iPads.
16 : 10 rail – productivity-oriented laptops.
16 : 9 super-rail – the video era’s king, stretching from 720p to 8K.
Lone high-flyers (4320p, 8640p) simply extend the same 16 : 9 line—proof that aspect ratio stays constant while pixel density skyrockets.
7 Worked examples
7.1 Baking for a crowd
A brownie recipe calls for a 2 : 3 cocoa-to-sugar ratio and produces an 8-serving pan. You need 60 servings.
Scale factor: 60 ÷ 8 = 7.5×.
Cocoa and sugar amounts each multiply by 7.5.
New ratio unchanged: still 2 : 3, just larger piles.
7.2 Mixing antifreeze
Desired antifreeze strength: 60 % coolant, 40 % water ⇒ 3 : 2 ratio.
For a 5-liter radiator: 5 × (3/5) = 3 L coolant, 2 L water.
7.3 Evaluating camera sensor shape
Sensor measures 24 mm × 36 mm. 24 : 36 simplifies to 2 : 3 (same as 35 mm film). That’s why 24 MP full-frame JPEGs default to 6000 × 4000 pixels.
8 Ratios vs. rates vs. percentages
Ratio – pure comparison (3 : 5).
Rate – ratio with units (miles per hour, dollars per ounce).
Percentage – part-to-whole ratio scaled to 100 (30 %).
Remember: 30 % protein in granola is 3 : 7 part-to-whole, not 3 : 7 part-to-part.
9 The golden ratio (φ ≈ 1 .618 : 1)
History’s most famous ratio arises from splitting a segment so that the whole : long = long : short. From the Parthenon façade to modern UI cards, φ appeals to our pattern-hungry brains. While debated, designers still use 1 : 1.618 rectangles for pleasing balance.
10 Common pitfalls
| Misstep | Fix |
|---|---|
| Mixing units (cups : ounces) | Convert first |
| Reversing order (salt : water vs. water : salt) | Label clearly |
| Forgetting the whole (part-to-part ≠ part-to-whole) | Specify type |
| Leaving ratio unsimplified (100 : 250) | Reduce to 2 : 5 |
11 Mini-infographic idea (description)
Left panel: Cartoon sibling cookie plates (3 cookies vs. 6) with “1 : 2” caption.
Center panel: Color-coded measuring cups showing 1 : 2 : 3 cake ingredients.
Right panel: Nested rectangles (4 : 3, 16 : 10, 16 : 9) overlaying a monitor outline.
FAQ
Q : Is 0.75 the same as a 3 : 4 ratio?
A : Yes—3 ÷ 4 = 0.75. Ratios, fractions, decimals, and percents are interchangeable languages.
Q : Do ratios need integers?
A : No, but reducing to whole numbers aids intuition; multiply both sides by a common denominator if needed.
Key takeaways
A ratio compares; a proportion equates ratios.
Notation is flexible—colon, word, or fraction form.
Equivalent ratios scale every term equally.
Aspect ratios determine modern media shapes; 16 : 9 rules 4K and beyond.
Understanding ratios avoids recipe disasters, gear misalignments, and spreadsheet errors.
Figure 1 above illustrates the pixel playground of today’s most popular displays. Keep this map handy the next time you wonder why your 1920 × 1080 smartphone video looks letter-boxed on a 4 : 3 projector—the culprit is an underlying, stubborn little ratio.