How this calculator works
A direct relationship has a fixed ratio y/x and passes through the origin. An inverse relationship has a fixed product xy and excludes zero x. The solve-for selector rearranges that same equation. Enter consistent units: direct k has units of y per x, while inverse k has units of y times x. One pair determines a candidate constant but cannot establish proportionality across a data set.
Formula
Direct: k = y/x, x = y/k, y = kx. Inverse: k = xy, x = k/y, y = k/x.
Worked example
If y = 20 when x = 8 in a direct relationship, k = 20/8 = 2.5. For inverse values x = 3 and y = 4, k = 12.
Advertisement
Frequently asked questions
Can k be negative?
Yes. A negative constant makes the signs opposite for positive x in either equation.
Why reject a zero pair when finding k?
The point (0,0) does not determine a direct constant, and an inverse relationship excludes zeros. This tool uses nonzero proportionality constants.
How do I check several observations?
Compute k for each pair with consistent units. Large differences show that exact proportionality does not hold.