Ratio Calculator
Simplify A:B or A:B:C, solve a proportion for x, split a total in a ratio, scale a ratio, or size an image to 16:9 and other aspect ratios.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Ratio Calculator?
A ratio says how much of one thing there is for each amount of another. This calculator handles the five jobs people most often need: reducing a ratio to its simplest whole numbers, solving A : B = C : D when one value is missing, sharing a total in a given ratio, scaling a ratio by a factor, and finding a width or height for an aspect ratio such as 16:9.
Pick a task, type the numbers you know, and the answer updates as you type. Decimal and fraction terms are allowed: 1.5 : 2.25 simplifies to 2 : 3. The step list shows the GCF used to reduce the ratio, the cross-multiplication used to solve a proportion, and the size of one part when a total is shared.
The aspect-ratio mode has presets for screens, photos and film, draws a small preview of the shape, and warns when a size will not come out as whole pixels.
- Five ratio tasks in one tool
- Two- or three-term ratios with decimal or fraction terms
- Proportion solver for any one missing value
- Share-of-total breakdown with a proportional bar
- Aspect ratio presets and a shape preview
How to use the Ratio Calculator
- Choose the task: Simplify, Solve A:B = C:D, Share a total, Scale, or Aspect ratio.
- Enter the ratio terms. The third term is optional for three-part ratios such as concrete mixes.
- For a proportion, fill three boxes and leave the unknown one empty.
- For sharing, type the total; for scaling, type the factor; for aspect ratio, type either the width or the height.
- Read the result cards and the steps, then copy the result or share the link.
Worked examples
Simplify
Input
24 : 36
Output
2 : 3
The GCF of 24 and 36 is 12, so each term is divided by 12. As parts of a whole that is 40% and 60%.
Solve a proportion
Input
3 : 4 = 9 : x
Output
x = 12
Cross-multiplying gives 3x = 36, so x = 12. Check: 3/4 and 9/12 are both 0.75.
Share a total
Input
500 in the ratio 2 : 3
Output
200 and 300
There are 5 parts, so one part is 100. The first share gets 2 parts and the second 3.
Size a video frame
Input
16 : 9 at width 1920
Output
1920 × 1080
Height = 1920 × 9 / 16 = 1080. At width 1366 the height would be 768.375, which is why that screen is not exactly 16 : 9.
Background and insight
Two ratios are equivalent when you can multiply every term of one by the same number to get the other. That is why 24 : 36, 12 : 18 and 2 : 3 describe the same mix, and why dividing every term by the greatest common factor gives the simplest form. With decimal terms, first multiply by a power of ten to clear the decimals, then reduce.
A proportion is an equation between two ratios, A : B = C : D, which is the same as A / B = C / D. Cross-multiplying gives A × D = B × C, so any one unknown can be found from the other three. This is the rule of three taught in schools and used daily in dosing, scaling recipes and converting map distances.
Aspect ratios are ratios of width to height. A display of 1920 × 1080 is 16 : 9 because both sides divide by 120. Some popular resolutions are only close: 1366 × 768 reduces to 683 : 384, about 1.779 : 1, not exactly 16 : 9 (1.778 : 1).
Common use cases
Mixing and recipes
Scale a 1 : 2 : 3 cement, sand and gravel mix, or a 3 : 1 rice-to-water ratio, to the batch size you need.
Splitting money
Divide a bill, profit or inheritance between people in agreed proportions, with each share and percentage shown.
Design and video
Resize images and video to 16:9, 4:5, 9:16 or 2.39:1 without stretching, and find the matching side.
Maps and models
Use a proportion to turn a 1 : 25,000 map distance into metres or to size a scale model.
Tips and limitations
- Ratios compare amounts in the same unit. Convert grams and kilograms, or minutes and hours, before simplifying.
- Order matters: 2 : 3 is not 3 : 2. Keep the terms in the same order on both sides of a proportion.
- A ratio of 2 : 3 means 2 parts out of 5, which is 40%, not 2/3. The calculator shows both views.
- When sharing a total of people or items, the shares may not be whole numbers; decide how to round and who gets the remainder.
- For aspect ratio, sizes that divide evenly (multiples of 16 by 9, for example) avoid half-pixel rounding.
Frequently asked questions
How do you simplify a ratio?
Divide every term by their greatest common factor. 24 : 36 has GCF 12, so it simplifies to 2 : 3. If the terms are decimals, multiply them all by 10, 100 or 1000 first so they are whole numbers.
How do I solve a proportion for x?
Write it as A / B = C / D and cross-multiply: A × D = B × C. For 3 : 4 = 9 : x, 3x = 36 and x = 12. Leave the unknown box empty and the calculator does the same.
How do I divide an amount in a ratio?
Add the ratio terms to get the number of parts, divide the total by that to get one part, then multiply. 500 in the ratio 2 : 3 is 5 parts of 100, so 200 and 300.
How do I calculate height from width for 16:9?
Multiply the width by 9 and divide by 16. A width of 1280 gives a height of 720; 3840 gives 2160. For other ratios use width × second term / first term.
Is a ratio the same as a fraction?
They are closely related but not identical. The ratio 2 : 3 compares two parts, while the fraction of the whole for the first part is 2/5. The fraction 2/3 is the ratio of the first part to the second.
Can a ratio have three or more parts?
Yes. A concrete mix of 1 : 2 : 3 or a budget split of 50 : 30 : 20 are three-part ratios. They simplify and scale the same way, by dividing or multiplying every term by the same number.
Is there an in-depth guide to the Ratio Calculator?
Yes. “Percentages, Fractions and Ratios: How the Arithmetic Fits Together” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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