Constant of Proportionality Calculator — Direct Variation k
Enter a known (x, y) pair and the calculator finds the constant of proportionality k so that y = kx for every point on the relationship — then predict y for any new x.
k = y ÷ x so that y = k · x
Direct proportion: y increases (or decreases) by 4 for every 1-unit increase in x.
- 1
Constant of proportionality
k = 12 ÷ 3 = 4Divide the known y by the known x to find k. - 2
Find y for new x
y = 4 × 7 = 28
How does this calculator work?
The constant of proportionality k = y/x defines the direct variation y = kx — all points lie on a straight line through the origin. Enter a known (x, y) pair to find k and predict y for any other x value.
Formula
How this is calculated
Two quantities x and y are in direct proportion when y = k·x for a fixed constant k. The ratio y/x is the same for every pair of values on the relationship, and k measures how much y changes for each unit change in x. To find k, simply divide: k = y/x.
Once k is known you can predict the output for any input. If the "find y" field is filled in, the calculator computes y = k·x_new immediately. The line y = kx always passes through the origin (0, 0) because when x is zero, y must also be zero in a true direct proportion — this is what distinguishes it from a general linear relationship y = kx + b.
Common examples include unit price (total cost = price per unit × quantity), speed (distance = speed × time), and unit conversions (miles = 1.609 × km). Proportionality breaks down when a non-zero offset applies, so verify that your data passes through the origin before relying on this model.
Frequently asked questions
It is the fixed ratio k = y/x that describes how fast y grows relative to x. A k > 1 means y grows faster than x; a k between 0 and 1 means y grows slower; a negative k means y decreases as x increases.
A direct proportion y = kx passes through the origin — when x = 0, y = 0. A general linear function y = kx + b has a y-intercept b. If the data points do not pass through (0, 0), use a linear regression calculator instead.
If all points satisfy y = kx exactly, any single point gives the same k. If there is scatter in the data, average the individual k values (y₁/x₁, y₂/x₂, …) or fit a forced-through-origin regression for a best estimate.
Also known as
TG we-Calculate Editorial Team. (2026). Constant of Proportionality Calculator — Direct Variation k [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/constant-of-proportionality-calculator
TG we-Calculate Editorial Team. "Constant of Proportionality Calculator — Direct Variation k." TG we-Calculate. 2026. https://we-calculate.com/calculator/constant-of-proportionality-calculator.
TG we-Calculate Editorial Team, "Constant of Proportionality Calculator — Direct Variation k," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/constant-of-proportionality-calculator
@misc{wecalculate_constant_of_proportionality_calculator, title = {Constant of Proportionality Calculator — Direct Variation k}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/constant-of-proportionality-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?