Calculators
Joint Variation Calculator
Find the joint variation constant and a new y value for y = kxz from a known triple and new x and z values.
For joint variation, y = k × x × z. Enter a known triple and new x and z values to find y₂ = k × x₂ × z₂. Use positive values from 1e-12 to 1e12. Calculations stay in your browser.
Solve a relationship proportional to two variables.
Joint variation follows y = kxz. Find k = y₁/(x₁z₁), then calculate y₂ = kx₂z₂. For x₁ = 4, y₁ = 24 and z₁ = 2, k = 3. New x₂ = 6 and z₂ = 3 give y₂ = 54. Doubling either independent variable doubles y; doubling both multiplies y by four. Use this model only when joint proportionality is established; it does not fit data or include an offset. Enter positive decimals or scientific notation from 1e-12 to 1e12 inclusive. Keep units consistent between old and new values of each variable; k has units of y divided by the product of x and z units. Results use browser floating-point arithmetic rounded to 12 significant digits. Inputs are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I calculate joint variation?
Divide the known y by the product of the known x and z to find k. Multiply k by the new x and z to find the new y. For (4, 24, 2), k = 3; new x = 6 and z = 3 give y = 54.
How does joint variation differ from direct variation?
Direct variation y = kx has one independent variable. Joint variation y = kxz is directly proportional to each of two variables while the other is held constant.
Which inputs are supported?
Enter five positive numbers from 1e-12 to 1e12 inclusive. Decimals and scientific notation are accepted. Zero and negative inputs are outside this calculator’s scope. Keep units consistent for each variable.
Are results exact and private?
Results use floating-point arithmetic rounded to 12 significant digits. All calculations run in your browser without uploading or storing inputs.