Find the constant of proportionality (k) for two directly proportional quantities.
How it works
For a direct variation relationship y = kx, the constant is k = y ÷ x. If y = 12 when x = 4, then k = 3.
What this does not include
This handles direct variation (y = kx) only. Inverse variation (y = k/x) uses a different formula (k = xy), not covered here.
How to use this calculator
- Enter a known x value.
- Enter its corresponding y value.
A worked example
y = 12 when x = 4: constant of proportionality k = y/x = 12 ÷ 4 = 3.
y = 7.5 when x = 2.5: k = 3 — the same constant, confirming both pairs follow the same direct proportional relationship.
What the variables mean
| Variable | Meaning |
|---|---|
| x | The independent variable |
| y | The dependent variable |
| k | The constant relating them, where y = kx |
Edge cases worth knowing
A constant of proportionality only applies to direct (linear-through-origin) relationships. If y doesn’t scale cleanly with x, there’s no single k that fits every data pair — this calculator finds k from one pair at a time.
An x value of zero makes k undefined — dividing y by zero has no meaningful result.
What does the constant of proportionality actually represent?
It’s the fixed rate at which y changes relative to x — once you know k, you can predict y for any new x value just by multiplying by k.
Why is x = 0 not allowed?
Dividing by zero is undefined, and more fundamentally, direct variation is meaningless at x = 0 unless y is also 0 — there’s no way to determine a rate of change from a single point at the origin.
Is the constant of proportionality always positive?
No — a negative k describes an inverse relationship where y decreases as x increases, still a valid direct variation, just with a negative rate.
