Rule of Three Calculator
The rule of three is the classic method for solving proportions: given three known values, it finds the fourth unknown value. This calculator handles both the direct rule of three, where two quantities grow or shrink together, and the inverse rule of three, where one quantity rises as the other falls. Just type your three values and the unknown X is worked out instantly, along with the exact formula used. It is perfect for scaling recipes, converting units, working out prices, speeds, and any everyday proportion problem.
Result (X)
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How it works
A proportion links two ratios that are equal. In the direct rule of three you know that A corresponds to B, and you want the value X that corresponds to C. Because the quantities are directly proportional, the ratio stays constant, so X = (B × C) ÷ A. In the inverse rule of three the two quantities move in opposite directions — more of one means less of the other — so the product stays constant and X = (A × B) ÷ C. The calculator applies the correct formula for the mode you select and updates the result as soon as you change any value, dividing safely so a zero never breaks the output.
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Preguntas frecuentes
- What is the rule of three?
- The rule of three is a simple method to solve a proportion when three of its four values are known. You set two ratios equal to each other and solve for the missing value, called X. For example, if 2 apples cost 6 dollars, the rule of three tells you what 5 apples cost by keeping the price-per-apple ratio constant.
- What is the difference between the direct and inverse rule of three?
- In the direct rule of three the two quantities change in the same direction: more of one means more of the other, so X = (B × C) ÷ A. In the inverse rule of three they change in opposite directions: more of one means less of the other, so X = (A × B) ÷ C. Use direct for prices or quantities that scale together, and inverse for things like speed and time or workers and duration.
- How do I know whether to use the direct or inverse rule?
- Ask yourself what happens to the second quantity when the first one increases. If it also increases (more hours worked, more pay), the relationship is direct. If it decreases (more workers, less time to finish), the relationship is inverse. Choosing the wrong mode gives a result that goes the wrong way, so this check is important.
- Can you give an example of the direct rule of three?
- If 3 litres of paint cover 12 square metres, how many square metres do 5 litres cover? Here A = 3, B = 12 and C = 5, and because more paint covers more area the relationship is direct: X = (12 × 5) ÷ 3 = 20 square metres.
- Can you give an example of the inverse rule of three?
- If 4 workers build a wall in 6 days, how long do 8 workers take? Here A = 4, B = 6 and C = 8, and because more workers means less time the relationship is inverse: X = (4 × 6) ÷ 8 = 3 days.