Solve
Pick the type of proportion and fill in A, B and C: X is the missing cell.
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Quick guide
Understand the calculation
Calculate the unknown value X from three known values using a direct or inverse rule of three. The tool accepts integers, decimals with a point or comma, and scientific notation such as 3.16e-10, and can display the result with 4 or 10 significant figures.
When to use this tool
Choose Direct when both quantities change in the same direction: if one doubles, the other doubles too. This is useful for scaling mixtures, recipes, conversions, and laboratory quantities. Choose Inverse when they change in opposite directions: if one doubles, the other is halved, as when relating the number of people to working time or speed to duration.
How to choose a mode and calculate X
Each row of the grid is one case and the two columns are the two related quantities. Direct mode keeps the ratio between columns constant, A/B = C/X, which gives X = (B×C)/A. Inverse mode keeps the product of each row constant, A·B = C·X, which gives X = (A×B)/C. Choosing a mode means deciding which of those two equalities describes the phenomenon, not memorising two formulas. The unknown always sits in the fourth position: if the missing value belongs somewhere else, reorder the known values while preserving the correspondence between rows. Switching modes does not clear the fields, so the same three numbers can be read both ways for comparison.
A cannot be 0 in Direct mode, nor C in Inverse mode: they are the divisors of the solved formula. A zero written as zero remains a valid value in the other positions. Incomplete or ambiguous entries such as “1e” or “1.2.3” are rejected instead of being partially interpreted, and so are values and results that fall outside the representable numeric range. The tool solves generic algebra: it does not validate clinical or dosing decisions.
Examples
- Direct · 2 L require 50 g; for 5 L
(50 × 5) / 2 = 125 g - Inverse · 4 people take 6 h; for 8 people
(4 × 6) / 8 = 3 h - Direct in scientific notation · 2e-3 mol yield 5 g; for 8e-3 mol
(5 × 8e-3) / 2e-3 = 20 g
Frequently asked questions
How do I know whether the proportion is direct or inverse?
Ask what happens to the second quantity when the first one doubles. If it doubles as well —litres and grams of the same reagent— the proportion is direct. If it is halved —people and working time, speed and duration— it is inverse. If the relationship is not proportional at all, neither mode applies: adding a constant or growing with the square is not a rule of three.
Can I put the unknown in another position?
The grid always solves for X in the fourth cell. If the missing value belongs somewhere else, reorder the known values while preserving the correspondence between rows: the complete case on top and the case with the gap below.
Does it work for percentages or unit conversions?
Yes, because both are direct proportions: 15 out of 100 is the same as X out of 200. Even so, the percentage calculator is the better fit for percentages and the converters for units, since they already carry the factors and save you from typing them.