Rule of three calculator
Three values in, the fourth out — with the working shown.
Examples temporarily replace the input and settings. You can restore your previous work.
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Example
Example: 310 miles on 12.4 gallons — how much gas for a 450-mile drive?
On the last road trip the car went 310 miles on 12.4 gallons. The next drive is 450 miles. More miles take more gas in the same proportion, so this is a direct rule of three.
- Enter A = 310 (miles), B = 12.4 (gallons) and C = 450 (miles), and leave Proportion on Direct.
- Multiply across and divide by the third value: X = 12.4 × 450 ÷ 310 = 18.
- The check divides both sides: 310 ÷ 12.4 = 450 ÷ 18 = 25, the car’s 25 miles per gallon.
| Problem | A → B | C → X | Kind | X |
|---|---|---|---|---|
| Gas for a trip | 310 mi → 12.4 gal | 450 mi → X | direct | 18 gal |
| Miles on a tank | 12.4 gal → 310 mi | 9 gal → X | direct | 225 mi |
| Recipe for more people | 4 servings → 3/4 cup | 6 servings → X | direct | 1.125 cups |
| What percent is it | 1200 → 100 % | 186 → X | direct | 15.5 % |
| Painters and hours | 3 painters → 8 h | 5 painters → X | inverse | 4.8 h |
| Speed and time | 60 mph → 3.5 h | 75 mph → X | inverse | 2.8 h |
The 450-mile drive takes 18 gallons. In the inverse ones the pair you know is multiplied and divided by the new value: at 75 mph instead of 60, 60 × 3.5 ÷ 75 = 2.8 hours.
How it works
- Enter A and the value B that goes with it (e.g. 4 kg cost 10).
- Enter the new value C (e.g. 6 kg).
- Choose direct if the two grow together, inverse if one grows as the other shrinks.
- X appears with the cross-multiplication and a check.
Frequently asked questions
- How does the rule of three work?
- A is to B as C is to X, so X = B × C ÷ A: if 4 kg cost 10, 6 kg cost 10 × 6 ÷ 4 = 15.
- When is it inverse?
- When one quantity grows as the other shrinks: 6 workers take 12 days, so 9 take 6 × 12 ÷ 9 = 8. Then X = A × B ÷ C.
- Can I type fractions like 3/4?
- Yes. 3/4 is read as 0.75, so a recipe for 4 that takes 3/4 cup of sugar takes 0.75 × 6 ÷ 4 = 1.125 cups for 6 — a cup and an eighth.
- How should I type large numbers?
- Either way: 1200 and 1,200 are both read as twelve hundred, and 1,234.5 works too. A comma followed by exactly three digits is a thousands separator; any other lone comma is taken as a decimal comma, as many countries write 4,5 for 4.5. A decimal point (12.4) is always read as one.
- What is the rule of three used for?
- Any time three values are known and two quantities change in step: gas and miles, ingredients and servings, a part and its percentage, a map scale, a currency rate. If one goes up as the other goes down — workers and days, speed and time — choose Inverse.
- Is anything uploaded?
- No. It is worked out in your browser.
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