Inverse Proportion Calculator
Calculate a new output when input and output have a constant product.
How to use Inverse Proportion Calculator
1. Enter Known Input, Known Output, New Input in the stated order. 2. Follow nonzero denominator and whole-number requirements where they apply. Keep corresponding quantities on the same unit scale. 3. Select Calculate or press Enter to see new output. 4. Copy result copies the output; Reset clears the inputs and answer.
Why use this tool?
Estimate an inverse relationship, such as ideal time versus rate, when the constant-product assumption applies.
How the calculation works
Constant k = known input × known output; new output = k ÷ new input. Both known and new inputs must be nonzero. Numeric outputs use browser floating-point arithmetic, with six decimal places at most. Smaller nonzero outputs use six significant digits in scientific notation. Unrepresentable intermediate values or numeric outputs beyond the supported magnitude are rejected. Numeric input magnitudes, including each fraction or ratio component, must not exceed 9,007,199,254,740,991. Mathematical references: https://openstax.org/books/prealgebra-2e/pages/4-key-concepts and https://openstax.org/books/prealgebra-2e/pages/6-5-solve-proportions-and-their-applications.
Example
Known Input = 10, Known Output = 25 and New Input = 5 give constant product 250 and New Output = 50.
Practical tip
Check the model before applying it: doubling input halves output only when their product remains constant.
Frequently asked questions
Does this account for fixed overhead or efficiency changes?
No. It uses y = k/x. Real travel, staffing or production problems may have overhead and changing efficiency that invalidate that relationship.
Do signed inputs always have a practical interpretation?
These forms perform the stated arithmetic. Negative values, rates above 100% or a negative baseline can be mathematically valid while being unsuitable for a particular real-world quantity. Check the task and model before applying the result.
Does the tool choose units or round my input first?
Enter corresponding measurements in matching units; the maths forms do not convert units automatically. Exact fraction and ratio text is kept for integer arithmetic. Other numeric operations use browser floating-point values and the display precision stated above.