Constant of Proportionality Calculator
Use our constant of proportionality calculator to find k in proportional relationships (y = kx). Compute k from two values, from a table, or from a graph. Includes how to calculate the constant of proportionality, fraction examples, and how to find the constant of proportionality on a graph.
What Does Constant of Proportionality Mean?
The constant of proportionality (often written as k) is the number that relates two proportional quantities. If y is directly proportional to x, the relationship can be written as y = kx.
In a proportional relationship, the ratio y/x is constant for every pair of matching values. That constant ratio is k, which is why you’ll also see this called a “constant of proportionality finder.”
In physics, k shows up anytime one quantity scales directly with another (for example, distance and time at constant speed, or force and extension in Hooke’s law), though the units of k depend on what x and y represent.
Constant of Proportionality Formula
If y = kx, then k is found by dividing y by x. If you’re given a point (x, y), you can compute k directly. On a graph, k is the slope of the line when it passes through the origin.
This is the standard proportional relationship.
Use any matching pair (x, y) where x ≠ 0.
If the relationship is proportional, these ratios should match (within rounding).
k can be a fraction. You can also write k = 1.5.
If the ratios change, the relationship is not proportional (it might be linear but not proportional).
How to Find the Constant of Proportionality
- 1
Pick a matching pair (x, y) from the problem (a table, a point, or a word problem).
- 2
Compute k = y ÷ x (make sure x ≠ 0).
- 3
If you have a table, confirm the ratio y/x is the same for other rows (or very close if values are rounded).
- 4
If you have a graph, use a point on the line and compute k = y/x. For proportional graphs, the line passes through (0, 0) and k is the slope.
Frequently Asked Questions
It’s the constant k in y = kx that stays the same for every pair of proportional values. In a proportional relationship, k = y/x.
Divide y by x: k = y ÷ x (using any valid point where x ≠ 0).
Compute y/x for one row to get k, then check other rows. If it’s proportional, each row’s ratio y/x should match.
Choose a point (x, y) on the line and compute k = y/x. If the line passes through the origin, k is also the slope.
It’s the constant that relates two directly proportional physical quantities. The meaning and units of k depend on the specific relationship (for example, speed relates distance and time).
Then it’s not a proportional relationship of the form y = kx. It may still be linear (y = mx + b), but it doesn’t have a constant of proportionality in the direct-variation sense.