HARMEAN in Google Sheets: Average Rates with the Right Weights

• Introduced: first service launch date is not established by the official history reviewed; no numbered desktop introduction is assigned.
• Availability: documented in the rolling Google Sheets service. Examples target ordinary web-spreadsheet cells; mobile clients and imported file modes are not separately certified.
• Checked: October 14, 2026; official HARMEAN reference. Documentation and independently calculated examples, without native Sheets execution.

=HARMEAN(value1, [value2, ...])

One value or range is required, followed by optional further values or ranges. Google defines the count-over-reciprocal-sum formula. These examples use strictly positive numeric rates so the reciprocal model is well defined.

The selected reference does not establish every nonpositive, text, blank or error-cell outcome. No native error code or type-coercion rule is borrowed from Excel. Use English function names and comma separators for the controls below.

A fictional machine completes 120 units at 20 units per hour, then another 120 units at 60 units per hour. Enter the rates in A2:A3:

=HARMEAN(A2:A3)

Expected average rate: 30 units per hour. The first portion takes 6 hours and the second 2 hours, so total output 240 divided by total time 8 is 30.

The arithmetic mean of the rates is 40, which does not reproduce the total-work/total-time calculation. Equal work means more time is spent at the slower rate; an unweighted arithmetic mean would ignore that difference.

Now suppose each rate operates for two hours. Output is 40 units at rate 20 and 120 units at rate 60. Total output 160 divided by four hours gives 40 units per hour.

=AVERAGE(20,60)

Expected result: 40. The rates are unchanged, but equal time rather than equal work makes the arithmetic mean appropriate. A function name cannot decide what was held equal in the underlying records.

Before reporting an average rate, retain the work and time columns used to derive it. That allows another reader to check the weighting rather than assume every pair of rates has the same interpretation.

For 60 units at rate 20 and 180 units at rate 60, calculate:

=(60+180)/(60/20+180/60)

Expected result: 40 units per hour, from 240 total units divided by 6 hours. The unweighted HARMEAN of 20 and 60 remains 30 and answers the wrong weighting question here.

A small equivalent frequency control is:

=HARMEAN(20,60,60,60)

Expected result: 40. Splitting the 180-unit fast portion into three equal 60-unit portions produces four equal-work contributions. This explains the weighted denominator without inventing a separate weight argument in HARMEAN’s syntax.

For values 3 and 12:

=HARMEAN(3,12)
=GEOMEAN(3,12)
=AVERAGE(3,12)

Expected results are 4.8, 6 and 7.5. The harmonic mean is more influenced by the smaller positive value because that value has a larger reciprocal.

For 5 and 5, all three means equal 5. The mathematical harmonic≤geometric≤arithmetic relationship permits equality; do not describe it as always strictly less. This is a mathematical comparison on positive inputs, not a vendor-specific error rule.

Enter 10, 20 and 40 in C2:C4:

=HARMEAN(C2:C4)

Expected result: 17.142857143, approximately, because the reciprocal sum is 0.1+0.05+0.025=0.175 and 3/0.175=120/7.

The arithmetic mean is 23.333333333. A quick independent control is =3/(1/C2+1/C3+1/C4), which has the same expected harmonic result. Keep the unrounded calculated value for later arithmetic rather than copying a displayed nine-place decimal.

Multiply the original rates by two to obtain 40 and 120. Their harmonic mean is 60, twice the original result 30. Adding 10 instead gives rates 30 and 70 and harmonic mean 42, not 30+10=40.

Scaling a common measurement unit preserves the reciprocal structure differently from adding a fixed amount to every rate. Compare like units and record transformations when combining data sources.

A zero value makes an ordinary reciprocal undefined, and negative values require a separately justified interpretation. The help captured here does not pin the native Sheets error behavior for those cases. The examples stay positive and do not claim a tested extension.

Google’s definition and syntax were retrieved from its indexed official help; the direct capture was partial. No runtime benchmark or complete mixed-type matrix was performed. For a multiplicative-factor question, see GEOMEAN rather than assuming every average of rates uses HARMEAN.

• Google HARMEAN help.
• Editorial testing standards.

Inputs are fictional. Approximate answers are independent mathematical expectations rounded to nine places, not captured native results. Complete type/error matrices, extreme-magnitude accuracy and cross-client behavior remain untested.