Ratio Calculator
Simplify ratios and find equivalent ratios for any values.
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About
Ratio Calculator
A ratio is a quantitative relationship between two numbers describing how many times one value contains another. The idea is intuitive long before the notation is. Give a child half as many biscuits as his sister and he will not describe the injustice as a ratio, but the protest that follows makes clear he understands he has received 1:2 as many as she has.
Ratios are usually written as two numbers separated by a colon. They can equally be written as "1 to 2" or as the fraction ½. The ratio is the number the denominator has to be multiplied by to produce the numerator, which reads more naturally when the first number is larger: with the ratio 2:1, 2 contains 1 twice. Ratios can also carry more than two terms.
Where ratios come up
Ratios turn up in aspect ratios for screens, in maps and models as scaled-down versions of the real thing, in baking and cooking, in the odds of something happening, and in rates of all kinds in finance.
Say someone wants to bake five cakes, each needing butter, sugar and flour in a 1:2:3 ratio, and wants the totals. Increasing the ratio five times gives 5:10:15, and that can be multiplied by whatever the actual quantities in the recipe are. The proportions never move; only the scale does.
That is the property doing the work in every one of these examples. A 1:200 architectural model, a 16:9 screen and a 1:2:3 cake batter all describe a shape or a balance that stays fixed while the size changes.
Solving A : B = C : D
Two ratios that describe the same relationship form a proportion, and a proportion with one unknown can always be solved. The rule is cross multiplication: the product of the outer pair equals the product of the inner pair.
Rearranging isolates whichever value is missing:
For 3 : 4 = 600 : D, that gives D = 4 × 600 / 3 = 800. The same rearrangement works from any corner: leave A empty instead and A = B × C / D.
The answer will not always be a whole number, and forcing one is usually wrong. For 3 : 5 = 400 : D the exact answer is 666.66666666667, and rounding to 667 is a decision about the situation rather than about the maths. Rounding 667 servings up makes sense; rounding a chemical concentration might not.
Reading a ratio three ways
The same ratio can be normalised to make different comparisons easy.
As 1 : n. Divide both sides by the first number. 3 : 4 becomes 1 : 1.3333333333333, which says the second quantity is about a third larger than the first.
As n : 1. Divide both sides by the second number. 3 : 4 becomes 0.75 : 1, which says the first quantity is three quarters of the second.
As a percentage of the whole. Divide one part by the total of both. Here that is 3 / (3 + 4) = 42.857142857143%, with the remaining 57.142857142857% belonging to the other side.
This last conversion is where ratios most often go wrong, because it crosses between two different kinds of comparison.
Part to part against part to whole
A ratio of 3:4 is a part-to-part comparison. The fraction 3/7 is part-to-whole. They describe the same situation and are not interchangeable.
Read 3:4 as "three sevenths" and every downstream number is wrong, since 3/4 is 75% while 3/7 is 42.86%. The test is what the denominator refers to: in a ratio the second number is the other part, and in a fraction the denominator is everything.
Odds work the same way and trip up the same people. Odds of 3:1 against mean three losing outcomes for every winning one, which is a probability of 1 in 4, not 1 in 3.
Simplifying a ratio
A ratio is in its simplest form when the two numbers share no common factor above 1. Divide both by their greatest common divisor. For 250:280 the greatest common divisor is 10, so the simplified form is 25:28. For 1920:1080 it is 120, which is where 16:9 comes from.
Simplifying changes nothing about the relationship, exactly as scaling does not. 250:280, 25:28 and 125:140 are the same ratio written three ways, and all three normalise to 1 : 1.12.
Scaling a ratio
Enlarging or shrinking multiplies or divides both sides by the same number, which is why the shape survives. Shrink 250:280 by 2.5 and it becomes 100:112. Enlarge the same ratio by 2.5 and it becomes 625:700. Both are still 1 : 1.12.
One thing that does not scale in step is area. Multiply both sides by 2.5 and each side is 2.5 times longer, but the area is 2.5² = 6.25 times larger. Shrinking by 2.5 leaves 0.16 of the area, not 0.4. This catches people out when estimating paint, fabric or paper: halving both dimensions of a poster leaves a quarter of the surface, not half.
Scaling can also produce fractions. Shrink 342:280 by 2.5 and the exact answer is 136.8:112, which rounds to 137:112. The rounded pair is very slightly a different shape, which matters for a print job and not at all for a rough sketch.
Typical aspect ratios of screens and video
An aspect ratio is the ratio between a shape's dimensions. For a rectangle it is width to height. Aspect ratios appear in tyre sizing, paper sizing and photographic print sizes, but the most frequently met examples are screens and video.
| Name | Aspect ratio | Width (px) | Height (px) |
|---|---|---|---|
| 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 |
| SVGA | 4:3 | 800 | 600 |
| WSVGA | ~17:10 | 1024 | 600 |
| XGA | 4:3 | 1024 | 768 |
| XGA+ | 4:3 | 1152 | 864 |
| WXGA | 5:3 | 1280 | 768 |
| WXGA | 16:10 | 1280 | 800 |
| SXGA (UVGA) | 4:3 | 1280 | 960 |
| SXGA | 5:4 | 1280 | 1024 |
| 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 |
16:9 dominates because it stacks: 1280×720, 1920×1080, 3840×2160 and 7680×4320 are the same shape at four sizes, so content made for one fits all of them. 4:3 was the old television and monitor standard, and 16:10 keeps a foothold on laptops because the extra vertical space suits documents and code.
Two entries in the table are marked with a tilde because they are not exact. 1366×768 works out at 1.7786 rather than the 1.7778 of true 16:9, and 1024×600 is 1.7067 against 1.7 for 17:10. Both are close enough for a panel specification and not close enough for arithmetic.
Reading the three pictures
The calculator draws the same ratio three ways, because each one answers a different question and all three redraw as the numbers change.
The pie shows the split as parts of a whole, which is the view that matches the percentage line. With 3:4 the smaller wedge is 42.86% of the circle.
The split bar makes the same comparison easier to judge by eye. People read length far more accurately than angle, so a bar is the better picture when two ratios are close enough that the pies look alike.
The rectangle is the aspect-ratio view: width takes the second number and height the first, so 3:4 draws a box four wide and three tall. This is the one to look at when the ratio describes a shape rather than a share, such as a screen, a photograph or a sheet of paper.
Common mistakes
The first is treating a ratio as a fraction of the whole, which turns 3:4 into 75% when the first part is really 42.86% of the total.
The second is adding ratios. Two classes with boy-to-girl ratios of 2:3 and 3:2 do not combine to 5:5 unless both classes are the same size. Ratios have to be converted back to actual counts before they can be added.
The third is forgetting that area and volume scale by the square and the cube of a length factor. Doubling the sides of a box multiplies its surface by 4 and its capacity by 8.
The fourth is rounding too early. Round at the end, once, and keep the exact value while the arithmetic is still running.
Common questions
Frequently asked questions
Cross multiply, so A times D equals B times C, then divide to isolate the unknown. For 3 : 4 = 600 : D that is D = 4 x 600 / 3 = 800. The same rearrangement works from any of the four positions.
For every 3 of the first thing there are 4 of the second. It is a part-to-part comparison, so the first part is 3 out of a total of 7, which is 42.857142857143% of the whole, not 75%.
A ratio compares one part with another part; a fraction compares a part with the whole. The ratio 3:4 corresponds to the fraction 3/7, not 3/4. Check what the second number refers to: the other part, or everything.
Divide both sides by their greatest common divisor. For 250:280 that is 10, giving 25:28. For 1920:1080 it is 120, which is where the familiar 16:9 comes from.
Multiply or divide both sides by the same number. Shrinking 250:280 by 2.5 gives 100:112 and enlarging it by 2.5 gives 625:700. Both keep the same shape, since only the size changed.
No, it quadruples. Length scales by the factor, area by its square and volume by its cube. Shrinking a ratio 2.5 times leaves 0.16 of the area, not 0.4, which is why halving a poster leaves a quarter of the surface.
Keep the exact value and round once at the end, if at all. For 3 : 5 = 400 : D the exact answer is 666.66666666667, and whether 667 is right depends on whether the quantity has to be whole.
Yes. A cake recipe using butter, sugar and flour in 1:2:3 has three terms, and scaling works the same way: five times the recipe gives 5:10:15.
Odds are a part-to-part ratio of losing to winning outcomes. Odds of 3:1 against mean three losses for every win, so the probability of winning is 1 in 4, not 1 in 3.
Because it stacks cleanly. 1280x720, 1920x1080, 3840x2160 and 7680x4320 are all the same shape, so material made for one resolution fits the others without cropping or bars.