Solve direct and inverse proportions with step-by-step equations.
The rule of three solves proportions: it is the quick method for finding a fourth value when you already know three and understand how two quantities relate. This calculator covers both simple cases, the direct proportion, where the quantities grow together (A/B = C/X, so X = B × C / A), and the inverse proportion, where one rises while the other falls (A × B = C × X, so X = A × B / C). You pick the type, enter values A, B and C, and the tool computes X, showing the assembled equation and every step of the arithmetic so you can check or study it. It accepts a period or a comma as the decimal separator and warns you when a divisor would be zero. It is the right calculation for converting units, scaling recipes, working out proportional prices, estimating work time and solving everyday math exercises.
The rule of three starts from a proportion: four values where three are known and one, the X, is unknown. In the direct version you set up A/B = C/X, where A and B form a known pair and C corresponds to the unknown X; cross-multiplying and isolating X gives X = B × C / A. Two directly proportional quantities grow together, doubling one doubles the other.
In the inverse version the relationship flips: when one quantity increases, the other decreases by the same measure, so the product A × B stays constant. From that comes A × B = C × X, and isolating X: X = A × B / C. The tool shows the assembled equation and each step of the arithmetic, for both the direct and the inverse proportion, and accepts a period or a comma as the decimal separator.
Example 1, direct: if 4 kg of flour cost $20, how much do 7 kg cost? Price is directly proportional to quantity, so A = 4, B = 20 and C = 7. Applying X = B × C / A = 20 × 7 / 4 = 140 / 4 = 35. So 7 kg cost $35, which checks out, since each kilo is $5 and 5 × 7 = 35.
Example 2, inverse: if 3 painters finish a wall in 8 hours, how long do 6 painters take? More painters means less time, so it is inverse: A = 3, B = 8 and C = 6. Applying X = A × B / C = 3 × 8 / 6 = 24 / 6 = 4. So 6 painters take 4 hours, consistent with the total of 24 painter-hours of work divided by 6 people.
The rule of three is one of the most useful everyday calculations: converting units at a fixed rate, scaling recipe amounts, working out proportional prices and discounts, estimating team work time and solving scale problems on maps and blueprints. The direct rule fits when the quantities move together; the inverse, when one offsets the other. For problems with three or more quantities at once there is the compound rule of three, which combines several columns.
The main thing to watch is choosing the right type: treating an inverse relationship as direct (or vice versa) flips the result. It also helps to remember that not every relationship is proportional, doubling the amount does not always double the effect, especially in non-linear phenomena. The tool uses 64-bit floating-point arithmetic and displays up to 10 decimal places, plenty of precision for everyday use.
Paste the code into your HTML and the tool shows up on your page, without J-Kit's navigation and ads. It still runs in the browser of whoever visits your site.
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></iframe>These references help contextualize formulas, standards, APIs and limitations used on this page. They do not replace professional validation when a result has legal, financial, medical or operational impact.
In a direct proportion, two quantities grow or shrink together: doubling one doubles the other. You set up A/B = C/X and isolate the unknown with X = B × C / A. For example, if 3 workers produce 6 items per day, 5 workers produce X = 6 × 5 / 3 = 10 items, because more labor yields more output in the same proportion.
All calculations stay in your browser. No data is sent to any server.