Calculators
Combined Variation Calculator
Find the combined variation constant and a new y value for y = kx/z from a known triple and new x and z values.
For combined 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.
Combine direct and inverse proportionality.
Combined variation follows y = kx/z: y varies directly with x and inversely with z. Find k = y₁z₁/x₁, then y₂ = kx₂/z₂. For x₁ = 4, y₁ = 12 and z₁ = 2, k = 6. New x₂ = 6 and z₂ = 3 give y₂ = 12. Doubling x doubles y; doubling z halves y; doubling both leaves y unchanged. Use this model only when the relationship is established; it does not infer proportionality from data or include an offset. Enter five positive values from 1e-12 to 1e12 inclusive. Decimals and scientific notation are supported. Keep units consistent for each variable; k has units of y times z divided by x. Zero and negative inputs are excluded. Results use browser floating-point arithmetic rounded to 12 significant digits. Inputs stay in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do I calculate combined variation?
For y = kx/z, find k = y₁z₁/x₁. Then calculate y₂ = kx₂/z₂. A known triple (4, 12, 2) gives k = 6; new x = 6 and z = 3 give y = 12.
How does combined variation differ from joint variation?
Joint variation y = kxz multiplies both independent variables. This combined variation model y = kx/z is directly proportional to x and inversely proportional to z.
Which inputs are supported?
Enter five positive numbers from 1e-12 to 1e12 inclusive, using decimals or scientific notation. Keep units consistent for each variable. Zero and negative inputs are excluded.
Are results exact and private?
Calculations run locally in your browser. Results use floating-point arithmetic rounded to 12 significant digits.