Constant of Proportionality Calculator

Enter x and y pairs to compute k = y / x for each pair, estimate the best-fitting constant, and evaluate proportional relationships.

Average k

5.0000

Max deviation

0.000000

Proportional?

Yes (values share a single constant)

Pair-by-pair constants
xyk = y / x
2105.0000
4205.0000
6305.0000

How to Use This Calculator

  1. Enter corresponding x and y values, one pair per line.
  2. Confirm that x ≠ 0 to avoid undefined constants.
  3. Review the constant y/x for each pair and the average constant.
  4. Use the deviation metric to judge how closely data follow y = kx.

Formula

ki = yi / xi

Average k = (Σ ki) / n

Deviation = max |ki − average k|

If all ki are equal, the dataset represents a direct proportionality with constant k.

Full Description

The constant of proportionality links two variables in the relationship y = kx. It is widely used in physics, finance, and algebra to model uniform scaling. This calculator reveals whether the provided data align with a direct proportion and identifies the best-fitting constant.

When measurements contain noise, deviations quantify how far observations stray from perfect proportionality.

Frequently Asked Questions

What happens if x = 0?

The constant is undefined when x = 0. Remove such pairs or adjust data to avoid division by zero.

Can I fit a best k if data aren't proportional?

Yes. The average constant provides a least-squares estimate of k under uniform weighting.

How do I use the deviation value?

Smaller deviations indicate stronger proportional relationships. Use it to assess data quality or measurement error.

Does order of pairs matter?

No. Each pair is treated independently. Ensure x and y values correspond correctly on each line.