Harmonic Mean Calculator

How to use the Harmonic Mean Calculator

1. 1Enter your numbers, separated by commas, spaces or lines.
2. 2Pick the units or options from the menus if the harmonic mean tool offers them.
3. 3Read the harmonic mean in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the harmonic mean

Whenever you average a rate over equal distances or equal amounts, the harmonic mean gives the true figure. Finance people use it for price-to-earnings ratios of a portfolio, and scientists use it in parallel resistors and in the F1 score of machine learning.

The tool also shows the arithmetic and geometric means, so you can see how far apart they are. The more the numbers vary, the bigger the gap between the three.

How the harmonic mean is worked out

Harmonic mean = n ÷ (1/x1 + 1/x2 + … + 1/xn). It is always the smallest of the three common means: harmonic ≤ geometric ≤ arithmetic. The harmonic mean of 2, 4 and 8 is 3 ÷ (0.5 + 0.25 + 0.125) = 3.4286, below the geometric mean of 4 and the arithmetic mean of 4.667. If you drive 40 km/h one way and 60 km/h back, your average speed is not 50 but the harmonic mean, 48 km/h.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Compares three means
• Any number of values
• Clear errors for zero or negative values

Mistakes to avoid with harmonic mean

Do not use the harmonic mean when a value is zero or negative; the calculator asks for positive numbers. Also, use it only for rates over equal amounts of the denominator; if the times, not the distances, are equal, the ordinary average is correct.

On phone and computer

On a phone, type into the boxes one after another and read the harmonic mean underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the harmonic mean move. The harmonic mean calculator works the same on both. The other averages are close by. Use Geometric Mean Calculator for growth rates, Average Calculator for the plain mean, Weighted Average Calculator when values count differently, and Speed Calculator for a single trip.

Features

• Use for rates
• Smaller than the arithmetic mean
• Positive numbers only
• Clear messages when the harmonic mean inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions