Ratio Calculator Widget
Add one ratio tool that covers the three classroom questions: reduce a ratio to lowest terms, share or scale it to a given total, and find the missing term of a proportion by the rule of three.
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Under the widget on your page: Powered by A2Z Tools
Embed code
<iframe src="https://a2z.tools/embed/w/ratio-calculator" title="Ratio Calculator by A2Z Tools" width="100%" height="520" style="border:0;width:100%" loading="lazy" allow="clipboard-write"></iframe>
A plain iframe. Works everywhere, including site builders that strip scripts. Adjust height if your content needs more room.
<div data-a2z-widget="ratio-calculator" data-height="520"></div> <script async src="https://a2z.tools/embed.js"></script>
Adds a small script (what it does) that sizes the widget to fit its content, loads it lazily and keeps it isolated from your page's CSS.
Works with
How it works
To simplify, the widget first turns both terms into whole numbers by multiplying by the same power of ten - 1.5 : 2.25 becomes 150 : 225 - and then divides by their greatest common divisor, 75, to reach 2 : 3. Working on whole numbers avoids the binary rounding that would otherwise make 0.1 : 0.3 refuse to reduce. The result is also given as 1 : n, n : 1 and as two percentage shares of the whole. Scaling multiplies both terms by one factor chosen so that the first term, the second term or their total hits the target: sharing 700 in the ratio 3 : 4 gives a factor of 100 and parts of 300 and 400. Solving a : b = c : x cross-multiplies to x = b x c / a, the rule of three used in recipe and map-scale problems. Terms must be positive with at most six decimal places.
Calculation method
- Simplify: scale both terms by 10^d to whole numbers, divide by their GCD
- Scale: factor k = target / (a, b or a + b); new ratio = ka : kb
- Solve a : b = c : x: x = b x c / a
Worked examples
Lowest terms
Inputs: 18 : 24
Result: 3 : 4; 1 : 1.333333; shares 42.86% and 57.14%
GCD(18, 24) = 6.
Missing term
Inputs: 2 : 3 = 10 : x
Result: x = 15
x = 3 x 10 / 2.
Limitations
- Two-term ratios only; three-part ratios such as concrete mixes must be split pairwise.
- Terms must be positive and have at most six decimal places.
- Scaled results are shown to four decimals and are not rounded to whole items such as people or eggs.
Where publishers use it
- Maths lessons on ratio and proportion for ages 11 to 14
- Recipe and baking sites resizing ingredient proportions
- Business pages splitting profit between partners in an agreed ratio
- Map and model-making guides converting scales
- Paint, concrete and fertiliser mixing instructions
Questions
How do I share 700 in the ratio 3 : 4?
Choose Scale, set 'a + b (the total)' and type 700. There are 7 parts, each worth 100, so the shares are 300 and 400.
Can I simplify a ratio with decimals such as 1.5 : 2.25?
Yes. Both terms are multiplied by 100 to give 150 : 225, then divided by 75 to give 2 : 3.
What is the rule of three?
If a : b = c : x then x = b x c / a. If 2 cups of flour make 3 dozen biscuits, 10 cups make 3 x 10 / 2 = 15 dozen.
What does 1 : n form mean?
The ratio scaled so the first term is 1. Map scales are written this way: 2 cm to 1 km is 2 : 100,000, which is 1 : 50,000.
Can a ratio have three parts, like 2 : 3 : 5?
Not in this widget, which handles two terms. For three parts, simplify by the GCD of all three or use the LCM and GCD calculator.
What is the difference between direct and inverse proportion?
In direct proportion both quantities rise together, which is what a : b = c : x solves: twice the flour, twice the biscuits. In inverse proportion one falls as the other rises: if 4 workers take 6 days, 8 workers take 3 days, because 4 x 6 = 8 x 3. Inverse problems multiply rather than cross-multiply, so solve them by hand.
How do I dilute squash or a cleaning concentrate 1 : 9?
Choose Scale, set a = 1 and b = 9 and make the total equal your container. For a 2-litre jug that is 0.2 litres of concentrate and 1.8 litres of water.
How do I tell which of two ratios is larger, such as 3 : 5 and 4 : 7?
Turn both into the n : 1 form or a decimal: 3 / 5 = 0.6 and 4 / 7 = 0.571, so 3 : 5 is the larger. Cross-multiplying gives the same verdict without decimals: 3 x 7 = 21 is more than 4 x 5 = 20.
Why is 4 : 6 the same ratio as 2 : 3?
Multiplying or dividing both terms by the same non-zero number leaves the relationship unchanged; such ratios are called equivalent. 4 : 6, 2 : 3, 10 : 15 and 1 : 1.5 all describe two parts of one thing to three of another.
How much water for 300 g of rice at 1 : 1.5?
Solve 1 : 1.5 = 300 : x, so x = 1.5 x 300 / 1 = 450. The same proportion works for cups by volume, which is how most absorption-method recipes for basmati are written.
How long is a 1 : 87 model of a 20-metre railway carriage?
Solve 87 : 1 = 20 : x, giving x = 20 / 87 = 0.23 metres, about 23 cm. HO-gauge railway models use 1 : 87; dolls houses are often 1 : 12 and architects draw floor plans at 1 : 50 or 1 : 100.
Cite or recommend this tool
If you reference this tool in an article, course or documentation, these formats are ready to copy. They are optional - nothing is added to your site unless you paste it.
A2Z Tools Ratio Calculator https://a2z.tools/embed/ratio-calculator
<a href="https://a2z.tools/embed/ratio-calculator">A2Z Tools Ratio Calculator</a>
[A2Z Tools Ratio Calculator](https://a2z.tools/embed/ratio-calculator)
Ratio Calculator by A2Z Tools - https://a2z.tools/embed/ratio-calculator
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