Calculate direct proportion between two quantities
Enter a known pair of values and a new x value. The calculator finds the matching y value when the ratio between the quantities is constant.
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Worked example
- x₁: 2
- y₁: 10
- x₂: 5
Result
y₂
25
Working
- y₂ = y₁ × x₂ / x₁
10 × 5 / 2 = 25
What does direct proportion mean?
Two quantities are directly proportional when their ratio stays the same throughout the calculation. If one quantity is multiplied by a factor, the other must be multiplied by the same factor. The calculator uses the known ratio to find a new matching value.
This can be useful when you scale a recipe or calculate a quantity with a fixed consumption per unit. The relationship must actually be proportional. A calculation with a fixed starting amount or a volume discount cannot simply be treated the same way.
How the values are used in the formula
The known pair consists of x₁ and y₁. You also enter x₂, which is the new value, and get y₂ as the result. The formula is y₂ = y₁ × x₂ / x₁.
Dividing by x₁ keeps the known relationship. x₁ must not be zero, because the calculation would otherwise require dividing by zero. Keep the same kind of quantity on each side: x₁ and x₂ must belong together, just as y₁ and y₂ must.
Example with a known ratio
The known pair is x₁ = 2 and y₁ = 10. You want to find y₂ when x₂ = 5. The working is 10 × 5 / 2 = 50 / 2 = 25. The result is therefore y₂ = 25. The ratio is kept, because 10 / 2 = 5 and 25 / 5 = 5.