Calculators
Contraharmonic Mean Calculator
Calculate the contraharmonic mean of non-negative numbers with an arithmetic mean comparison, privately in your browser.
Calculate a mean weighted by the observations themselves.
The contraharmonic mean is C = Σx² / Σx. It is an arithmetic mean weighted by the values themselves, so larger observations receive more weight and zero values do not change C. For 1, 2, 3, C = 14 / 6 ≈ 2.33333333333, compared with an arithmetic mean of 2. For non-negative data with a positive sum, C lies between the arithmetic mean and the maximum. Identical positive values return that value. All-zero data is undefined because the denominator is zero. Enter 1 to 10000 finite non-negative numbers separated by commas, semicolons, spaces or newlines. Scientific notation is supported; omit thousands separators. Use consistent units; the result has the same units as the inputs. Normalized arithmetic avoids overflow when squaring large values. Results use browser floating-point arithmetic displayed to 12 significant digits; extremely small contributions relative to the maximum can round to zero. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How is the contraharmonic mean calculated?
Divide the sum of squared values by the sum of values: C = Σx² / Σx. For 1, 2, 3, the result is 14 / 6, approximately 2.33333333333.
How does it compare with the arithmetic mean?
For non-negative values with a positive sum, the contraharmonic mean is at least the arithmetic mean and at most the largest value. Larger values receive greater weight.
Can I enter zeros or negative values?
Zeros are accepted alongside positive values and do not change the contraharmonic mean. All-zero data is undefined. This calculator restricts inputs to non-negative numbers; negative values are not supported.
What precision does this calculator use?
The calculator normalizes values before squaring to avoid overflow and displays up to 12 significant digits. Browser floating-point arithmetic may lose extremely small contributions. Inputs stay in your browser.