Rule of Three Calculator
Direct and inverse – with calculation method and step-by-step explanation
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If stands for – what does stand for? Relationship:
Proportional: double the amount, double the value – e.g. price and quantity.
Unknown value x
2.5
2.5If 3 stands for 1.5, then 5 stands for 2.5.
How this was calculated
First reduce to 1 (1 → 0.5), then multiply by c.
RZ-26 · headon.pro
Rule of three: method and application
Understanding direct and inverse proportions
The rule of three is one of the most fundamental calculation methods in mathematics and indispensable every day – when shopping, cooking, in technical fields, and at work. The principle: a fourth unknown value is calculated from three known values. The method works because two quantities are related to each other in a fixed ratio.
The direct rule of three applies wherever more of one quantity also means more of the other. If 1 kg of flour costs €1.20, 3 kg costs exactly €3.60. The price grows in the same ratio as the quantity. Formula: x = c × b ÷ a. You first calculate the unit value (b ÷ a) and then multiply by the desired quantity c.
The inverse rule of three is used when an increase in one quantity causes a decrease in the other. If 4 workers need 6 days for a task, 12 workers complete the same task in just 2 days. Formula: x = a × b ÷ c. Memory aid: the product of both value pairs is always equal (a × b = c × x).
In everyday life and at work you encounter the rule of three constantly: scale calculations for maps and building plans, recipe quantities for different numbers of people, currency conversions, speed-distance-time calculations, and material calculations. Our calculator shows you not only the result but also the complete calculation method.
Calculation examples
- Known pair
- 3 kg → €1.50
- Unit value
- 1 kg → €0.50
- Desired quantity
- 5 kg
- Result x
- €2.50
- a × b
- 4 × 6 = 24
- New quantity c
- 12 workers
- Formula
- 24 ÷ 12
- Result x
- 2 days
Frequently asked questions about the rule of three calculator
Everything about direct and inverse rule of three
What is the rule of three and what is it used for?
The rule of three (also called cross-multiplication) is a calculation method that lets you determine an unknown fourth value from three known values. It is used whenever two quantities are related in a fixed ratio. Typical applications: price calculations for quantities, travel times, recipe quantities, or scale conversions.
What is the difference between direct and inverse rule of three?
With the direct rule of three, one quantity grows in the same ratio as the other: if you buy twice as many apples, you pay twice as much. With the inverse rule of three, the opposite applies: if twice as many workers complete a task, the time needed is halved. The formula for the direct rule of three is x = c × b ÷ a, for the inverse rule of three x = a × b ÷ c.
How do I calculate the direct rule of three step by step?
Step 1: Set up the known values (e.g. 3 kg costs €1.50). Step 2: Reduce to 1 (1 kg costs 1.50 ÷ 3 = €0.50). Step 3: Multiply by the desired quantity (5 kg costs 0.50 × 5 = €2.50). Our calculator performs all steps automatically and shows the calculation method.
When do I use the inverse rule of three?
You use the inverse rule of three when two quantities behave inversely to each other. Classic situations: machines and production time (more machines = shorter time), workers and construction time, speed and travel time. If a × b = c × x holds, the rule of three is inverse.
What is the formula for the rule of three?
Direct: x = (b × c) ÷ a. Inverse: x = (a × b) ÷ c. Here a and b are the known pair of values, c is the new quantity, and x is the desired value. Memory aid: for the inverse rule of three, you invert the second ratio – instead of multiplying, you divide.