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A proportion says two ratios are equal: a / b = c / d. If you know any three of the four values, the fourth is fixed. This is the "rule of three", the everyday tool for scaling recipes, converting units, reading maps and adjusting prices.
Choose which value is unknown, enter the other three, and get the answer.
Proportion Calculator: step-by-step worked example
A recipe for 4 uses 300 g of flour. How much for 10?
- Solve for
- d (default)
- a
- 4
- b
- 300
- c
- 10
- 1
Set up the proportion
a ÷ b = c ÷ d
= 4 / 300 = 10 / d
- 2
Cross-multiply
a × d = b × c
300 × 10 = 3,000
- 3
Isolate the unknown
d = (c × b) ÷ a
3,000 ÷ 4 = 750
- 4
Check with the unit rate
b ÷ a = d ÷ c
300 ÷ 4 = 750 ÷ 10 = 75
- b (a = 4)300
- d (c = 10)750
Good to know: This is a direct proportion (both grow together). For inverse relations — more workers, less time — use a × b = c × d instead; mixing them up is the most common mistake.
Proportion Calculator — how it works
Cross-multiplication
A proportion a / b = c / d is solved by cross-multiplying: a × d = b × c. Rearranged, each value is:
| Unknown | Formula |
|---|---|
| a | c × b ÷ d |
| b | a × d ÷ c |
| c | a × d ÷ b |
| d | c × b ÷ a |
The rule of three in practice
Most real problems are "if b gives c, what does a give?" — line them up as a / b = x / c... but keep the pairs consistent. Set the same kind of quantity on top on both sides (e.g. amount over price on both), enter the three knowns, and solve.
Direct vs inverse proportion
This calculator handles direct proportion, where doubling one side doubles the other (more litres cost more money). Some problems are inverse — more workers means less time — where the product a × b stays constant instead. For those, multiply rather than cross-divide.
Where it helps
Scaling a recipe up or down, currency and unit conversion, map scale to real distance, mixing ratios, and percentage problems. It's the single most useful piece of everyday arithmetic after the four operations.
Worked example
A recipe for 4 people needs 300 g of flour; how much for 6 people? Set it up as 4 / 300 = 6 / d and solve for d: d = 6 × 300 ÷ 4 = 450 g. The same structure covers "if 3 apples cost 2.40, what do 5 cost?": 3 / 2.40 = 5 / d gives d = 5 × 2.40 ÷ 3 = 4.00.
Frequently asked questions
What is the rule of three?+
It is a method to find an unknown value in a proportion a / b = c / d when the other three are known, by cross-multiplying: the unknown equals the product of the diagonal divided by the remaining value.
How do I solve a proportion?+
Cross-multiply so a × d = b × c, then divide to isolate the unknown. To find d in a / b = c / d, compute d = c × b ÷ a.
What is the difference between direct and inverse proportion?+
In direct proportion both quantities grow together (more items, more cost). In inverse proportion one grows as the other shrinks (more workers, less time), and the product stays constant instead.
Can I use this to scale a recipe?+
Yes. Put the known people-to-ingredient ratio on one side and the new number of people on the other, then solve for the ingredient amount.
Does the order of the values matter?+
The two ratios must be arranged consistently — the same kind of quantity in the numerator on both sides. As long as the pairs line up, cross-multiplication gives the right answer.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
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