Proportions Calculator
Proportions Calculator works out Answer and Constant of variation k from Known x, Known y and New x. The default figures on this page give answer of 6; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
4 steps
- Write the proportion: 1 / 2 = c / x
- Cross multiply: 1 · x = 2 · c, so x = 2 · c / 1
- Substitute x = 3: y = 2 x 3^1 = 6
- Completed proportion: 1 / 2 = 3 / 6
Its 10 worked examples are re-run on every release, last on 15 September 2026. What changed
What the Proportions Calculator calculates
Finds the constant of variation from a known pair and uses it to predict the other variable for direct, inverse, joint and power (including inverse-square) relationships, solves a proportion a/b = c/x by cross multiplication, and reduces a ratio a : b to its lowest whole-number terms.
How to use this Proportions Calculator
Enter Known x, Known y and New x. Answer updates as you type. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Answer, Constant of variation k and x in the second situation.
The method follows OpenStax, College Algebra 2e §5.8 "Modeling Using Variation" — direct variation y = kx^n, inverse variation y = k/x^n and joint variation.
What you can compare
Change one input at a time to see how it affects Answer, Constant of variation k and x in the second situation. The inputs you can vary are Known x, Known y and New x.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How can I calculate proportions?
Finds the constant of variation from a known pair and uses it to predict the other variable for direct, inverse, joint and power (including inverse-square) relationships. Open “How this is worked out” beside the result to see each step for your own figures.
What is the formula for calculating proportions?
Finds the constant of variation from a known pair and uses it to predict the other variable for direct, inverse, joint and power (including inverse-square) relationships. On this page it is computed from Known x, Known y and New x and shown as Answer, Constant of variation k and x in the second situation.
How to solve proportions calculator?
It needs Known x, Known y and New x. Nothing else is required, and the figures stay in your browser.
What information do I need for the Proportions Calculator?
You need Known x, Known y and New x. The page opens with default figures that give answer of 6, so you can see the scale before entering your own.
What does this Proportions Calculator show?
It shows Answer, Constant of variation k, x in the second situation, y in the second situation, Equation of variation, What the relationship means, Ratio a / b as a decimal and Ratio in lowest terms, with the working and any warnings for your entries.
Can I check how the Proportions Calculator result was calculated?
Yes. The “How this is worked out” section shows the calculation steps, and the sources section identifies the references used for the method.