How to use the Proportion Calculator
- Choose which of a, b, c or d you want to find.
- Enter the three known values.
- Read the missing value and the completed proportion.
- Check the result by cross multiplying: a × d should equal b × c.
Formula used
a ÷ b = c ÷ d means a × d = b × c. So a = b × c ÷ d, b = a × d ÷ c, c = a × d ÷ b and d = b × c ÷ a.
Worked example
Here is the Proportion Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Find | d |
| a | 2 |
| b | 5 |
| c | 6 |
| d | 15 |
| Result | |
| Missing value | 15 |
| Proportion | 2 : 5 = 6 : 15 |
Cross multiplication
If a ÷ b = c ÷ d, then a × d = b × c. To find d, rearrange to d = b × c ÷ a. With a = 2, b = 5 and c = 6, d = 5 × 6 ÷ 2 = 15, so the proportion is 2 : 5 = 6 : 15.
The same idea finds any term. With b = 4, c = 9 and d = 6, a = b × c ÷ d = 6, giving 6 : 4 = 9 : 6.
A practical example
A recipe uses 250 g of flour for 4 people. For 10 people you need d where 4 : 250 = 10 : d, so d = 625 g. In words: people and flour change in the same ratio.
The key is to keep the order consistent. If a and c are both numbers of people, b and d must both be amounts of flour.
Where proportions appear
Maps use proportions: if 1 cm on the map is 5 km on the ground, 7.5 cm is 37.5 km. Currency and unit conversions are proportional, as is mixing paint or concrete in set ratios, and working out similar triangles in geometry.
Percentages are proportions too: "what is 15% of 80" is the same as solving 15 : 100 = x : 80.
Direct and inverse
This calculator handles direct proportion, where both quantities rise together. In an inverse proportion, one quantity falls as the other rises, such as speed and travel time for a fixed distance. For inverse problems, use the fact that the products are equal: speed × time = constant.
If a value in the denominator is zero, the proportion cannot be solved, and the calculator tells you.
Setting a proportion up correctly
Write the quantities in matching positions. If the first ratio is "people : flour", the second must also be "people : flour". Swapping one pair is the most common mistake, and it gives an answer that looks reasonable but is wrong. A quick check: if more people should need more flour, the answer should be bigger than the starting amount.
Units must also match across the ratio. Convert minutes to hours or centimetres to metres before you enter the numbers, or the answer will be out by that factor. The result is only as good as the assumption that the two quantities really are proportional, which is not true for everything, such as cooking times, which do not usually scale with quantity.
Frequently asked questions
What is a proportion?
An equation stating that two ratios are equal, like 2/5 = 6/15.
How do I solve a proportion?
Cross multiply and divide: to find d in a/b = c/d, d = b × c ÷ a.
What if I get a decimal answer?
That is fine. Proportions do not need whole numbers.
How is a ratio different from a proportion?
A ratio compares two quantities. A proportion says two ratios are equal.
Can I use it for percentages?
Yes. Treat a percentage as a ratio to 100, such as 15 : 100 = x : 80.
Does the order of the terms matter?
Yes. a and c must be the same kind of quantity, and so must b and d.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.