Joint Variation Calculator

Joint Variation Calculator calculator can be used to find a value that varies directly with the product of two other values.

Input Parameters

If you're finding k, leave this at 1 and calculate first.

Calculation Results

Calculation Formula

z = k × x × y

Where:
z = dependent variable
k = constant of variation
x = first independent variable
y = second independent variable

Joint variation occurs when a variable (z) is proportional to the product of two other variables (x and y). This means if x doubles and y stays constant, z will also double.

Joint Variation Calculator Calculator Usage Guide

Learn how to use the Joint Variation Calculator and understand the concept of joint variation.

What is Joint Variation?

Joint variation is a relationship between variables where one variable varies directly with the product of two or more other variables. The general form is:

z = k × x × y

Where z is the dependent variable, x and y are independent variables, and k is the constant of variation.

How to Use This Calculator

  1. Enter the values for x and y.
  2. Enter the constant of variation (k). If you're trying to find k, you can leave this at 1 and calculate z first, then use the result to find k.
  3. Click the "Calculate" button to find the value of z.
  4. The calculator will display the formula and the result.

Example

Suppose z varies jointly with x and y, and when x = 3 and y = 4, z = 24. Find z when x = 5 and y = 6.

First, find k:

24 = k × 3 × 4

k = 2

Now calculate z for x = 5 and y = 6:

z = 2 × 5 × 6 = 60

Applications

Joint variation appears in many real-world situations:

  • Area of a rectangle (A = l × w)
  • Work done (Work = Force × Distance)
  • Volume of a cylinder (V = π × r² × h)