What is a Ratio?
A ratio is a comparison between two or more quantities of the same kind. It tells you how many times one value contains another or how the values relate in size. Ratios are written with a colon (2:1), as a fraction (2/1), or with the word "to" ("two to one") — these three forms all mean the same thing. A ratio of 2:1 means "twice as much of the first as of the second."
Ratios can be simplified the same way fractions are: divide both sides by their greatest common divisor. The ratio 20:10 has GCD 10, so it simplifies to 2:1. The ratio 1920:1080 has GCD 120, so it simplifies to 16:9 — which is why a 1920×1080 screen is called "16:9 aspect ratio." A simplified ratio loses no information; it is the most compact way to express the same relationship.
Example: a bag with 20 red and 10 blue marbles has a red:blue ratio of 20:10, or simplified, 2:1 — meaning there are twice as many red as blue. The same situation can be described as fractions of the total (2/3 red, 1/3 blue) or as percentages (66.67% red, 33.33% blue). Choosing one form over another depends on the audience: ratios feel natural for recipes and mixing; percentages feel natural for surveys; fractions feel natural for math homework.
Ratios are used everywhere there is a fixed proportion to preserve — paint mixing, fertilizer dosage, photographic exposure (f-numbers are ratios), mortgages (loan-to-value), business analysis (price-to-earnings, debt-to-equity), and recipes. Most of these problems reduce to "if A:B is fixed and I know one quantity, what is the other?" — which is exactly what the second form on this page solves.
What is Aspect Ratio?
Aspect ratio is the ratio of width to height of a rectangular image, video, or screen. It is written as width:height — so 16:9 means the width is 16 units for every 9 units of height. The actual size does not matter, only the shape: a 1280×720 image and a 1920×1080 image both have 16:9 aspect ratio, because 1280/720 and 1920/1080 both simplify to 16/9 ≈ 1.778.
Common aspect ratios you will encounter: 16:9 (HDTV, YouTube, most modern displays, ratio ≈ 1.778); 4:3 (older CRT TVs, classic computer monitors, ratio ≈ 1.333); 1:1 (Instagram square posts); 9:16 (vertical phone video, TikTok, Reels); 21:9 (ultrawide monitors and cinema-style displays, ratio ≈ 2.333); 2.39:1 (theatrical cinema); 3:2 (DSLR photo sensors, full-frame and APS-C). The third form on this page lets you compute the missing dimension when you know one — for example, if you want a 16:9 video at 1440 pixels wide, enter 16:9 = 1440:? and the tool returns 810.
Aspect ratio also affects how content is displayed when source and screen mismatch. A 16:9 video on a 4:3 screen either gets letterboxed (black bars top/bottom, preserving the original shape) or cropped (the sides cut off). A 9:16 vertical phone video on a 16:9 YouTube player gets pillarboxed (black bars left/right). Streaming platforms automatically pick one strategy based on the aspect ratio they detect; for professional output, you usually choose the mode explicitly.
Popular aspect ratios and sizes of videos and Screens
| Name | Aspect ratio | Width (pixel) | Height (pixel) |
|---|
| 480p | 3:2 | 720 | 480 |
| 576p | 5:4 | 720 | 576 |
| 720p | 16:9 | 1280 | 720 |
| 1080p | 16:9 | 1920 | 1080 |
| 2160p (4K UHD) | 16:9 | 3840 | 2160 |
| 4320p (8K UHD) | 16:9 | 7680 | 4320 |
| 8640p | 16:9 | 15360 | 8640 |
| SVGA | 4:3 | 800 | 600 |
| WSVGA | ~17:10 | 1024 | 600 |
| XGA | 4:3 | 1024 | 768 |
| XGA+ | 4:3 | 1152 | 864 |
| WXGA | 16:9 | 1280 | 720 |
| WXGA | 5:3 | 1280 | 768 |
| WXGA | 16:10 | 1280 | 800 |
| SXGA (UVGA) | 4:3 | 1280 | 960 |
| SXGA | 5:4 | 1280 | 1024 |
| HD | ~16:9 | 1360 | 768 |
| HD | ~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 |
Frequently Asked Questions
Find the greatest common divisor (GCD) of the two numbers and divide both by it. GCD(1920, 1080) is 120, so 1920÷120 : 1080÷120 = 16:9. For ratios with three or more terms (12:18:24), find the GCD of all three (6) and divide each: 2:3:4. By hand, the Euclidean algorithm is the fastest way — repeatedly replace the larger number with the remainder of dividing it by the smaller, until you hit zero; the previous value is the GCD. This calculator does the simplification automatically when you enter a single ratio on the top form.
Set up the cross-multiplication: 3 × ? = 4 × 600, so ? = 2400 / 3 = 800. The rule is "product of the extremes equals product of the means" — in A:B = C:D, that is A × D = B × C, so any missing one of the four can be solved if the other three are known. The second form on this page does the cross-multiplication for you: enter three of the four values (A, B, C, D) and leave one blank. Useful for: cooking (scaling a recipe up), maps ("if 1 cm = 5 km on the legend, how many km is 14 cm?"), pharmacy ("if 5 mL of solution contains 250 mg, how much for 400 mg?").
16:9 was chosen as the international HDTV standard in 1988 partly as a mathematical compromise: it sits roughly halfway between the old 4:3 (1.333) and the widescreen cinema 2.39:1, so neither legacy TV content nor modern movies would be excessively distorted on a 16:9 screen. It also matches the human visual field reasonably well — peripheral vision is wider than tall. After HD broadcasting standardized on it, monitors, laptops, and smartphones followed, making 16:9 the dominant landscape aspect ratio for the past two decades. Modern phones in landscape are creeping toward 19.5:9 or 20:9 because tall phones held vertically need vertical-leaning aspect ratios, but the 16:9 ecosystem (Netflix, YouTube, broadcast) is locked in.
Divide width by height. 1920 / 1080 ≈ 1.778, which matches 16/9 ≈ 1.778 — so it's 16:9. 3840 / 2160 = 1.778 too — also 16:9 (just 4K). Some non-obvious ones: a Galaxy S phone screen at 2340×1080 has aspect ratio 2340/1080 ≈ 2.167, which is approximately 19.5:9 — not a clean simplification, but the marketing name. The math version is to find GCD(2340, 1080) = 540, giving 4.33:2 — but tall-phone aspect ratios are usually quoted as :9 for marketing convenience. The calculator above also handles non-integer ratios by floating-point arithmetic.
The golden ratio (φ ≈ 1.618) is a specific mathematical constant where the ratio of (a+b) to a equals a to b. It shows up in art, architecture, and nature (sunflower spirals, nautilus shells) because the human eye seems to find it aesthetically pleasing. It is in the same family as aspect ratios — both express "shape" of a rectangle — but "aspect ratio" is the generic term for width:height. A rectangle with aspect ratio φ:1 is called a "golden rectangle" and is approximately 1.618:1. For comparison, 16:9 is ≈ 1.778:1, slightly wider than golden; 4:3 is 1.333:1, narrower. Some designers deliberately use golden ratio in layouts (a 21:13 layout is very close), but it is not standard for screens.
Treat the recipe as a ratio of ingredients and multiply everything by the same scaling factor. A pancake recipe for 2 people uses 1 cup flour : 1 egg : 1 cup milk : 2 tbsp sugar. To make pancakes for 5 people, multiply each ingredient by 5/2 = 2.5: 2.5 cups flour, 2.5 eggs (round to 3 in practice), 2.5 cups milk, 5 tbsp sugar. The proportion form on this page handles the scaling: enter "original servings : scaled servings" on top and "original quantity : ?" on the right, and the tool gives you the scaled quantity. Caveat for baking: some ratios (like yeast or baking powder) do not scale linearly past a certain point — at very large or very small batches you need a baking calculator that knows about leavening agents.
Mathematically, ratios are usually defined for positive numbers, since they express "how much of one compared to the other." A ratio of 0:5 technically simplifies to 0:1 and means "none of the first, five units of the second" — it is meaningful in some contexts (a 0:1 dilution means no solute, just solvent). Negative ratios are uncommon and usually mean the underlying quantities have direction or sign (like vectors or financial gains/losses), in which case people usually use signed numbers directly rather than ratio notation. The calculator on this page assumes positive values and will warn if you enter zero in the denominator (since you cannot divide by zero).
A ratio compares two quantities of the same kind (apples to apples — both in count, or both in mass). A rate compares two quantities of different kinds, usually divided by time (miles per hour, dollars per item, beats per minute). 60 mph is a rate (distance to time), not a ratio. 60 cm to 30 cm is a ratio (both lengths). In everyday speech the words are often interchanged — "the conversion ratio" and "the conversion rate" are sometimes the same metric — but in math and physics they are kept distinct. Ratios are dimensionless after simplification (16:9 is just numbers, no units), while rates carry units (mph, $/lb).
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