Proportionality Calculator
Proportionality calculator works out Answer and Constant of variation k from Relationship, Exponent n (power variation) and Known x. The default figures on this page give answer of 28; 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
- Substitute the known pair into y = kx:
- 12 = k x 3^1, so k = 12 / 3 = 4
- Equation of variation: y = 4x
- Substitute x = 7: y = 4 x 7^1 = 28
Its 10 worked examples are re-run on every release, last on 15 September 2026. What changed
What the proportionality 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 proportionality calculator
Enter Relationship, Exponent n (power variation), Known x and Known y. Answer updates as you type, and “Use a worked example” loads checked figures you can adjust. 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.
Direct: y = 12 when x = 3, find y when x = 7 example
With Relationship: direct, Known x: 3, Known y: 12, New x: 7, the calculator returns Constant of variation k: 4, Answer: 28, y in the second situation: 28. This example is checked against an independent source in the test suite.
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 Relationship, Exponent n (power variation), Known x, Known y, Known z (joint variation) and Constant of variation k (if already known).
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 do you calculate proportionality?
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 information do I need for the proportionality calculator?
You need Relationship, Exponent n (power variation), Known x, Known y, Known z (joint variation), Constant of variation k (if already known), New x and New y. The page opens with default figures that give answer of 28, so you can see the scale before entering your own.
What does this proportionality 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 proportionality 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.