How to Calculate a Harmonic Mean with HARMEAN

HARMEAN averages rates and prices correctly when the amount spent each time is fixed — like dollar-cost averaging.

You will learn to

• Find the true average price paid with HARMEAN
• Measure the saving versus a simple average
• Derive total units bought from the harmonic mean

How it works

The harmonic mean is the reciprocal of the average of reciprocals: n ÷ (1/x1 + 1/x2 + …). It is the correct average for rates when the numerator is fixed — the same dollars spent each month at different prices, or the same distance driven at different speeds.

If you invest $500 every month, your average cost per share is HARMEAN of the monthly prices, not AVERAGE. Because you buy more shares when the price is low, the harmonic mean is always at or below the arithmetic mean. HARMEAN requires positive values.

=HARMEAN(B2:B9)