Statistics

Harmonic Mean Calculator

Calculate the harmonic mean of a list of positive numbers. The tool divides the count of values by the sum of their reciprocals, which is the standard average for rates such as speeds. It also shows how many values were used.

What this calculator does

The Harmonic Mean Calculator estimates your result instantly from the values you enter, using standard statistics formulas. Calculate the harmonic mean of a list of positive numbers. The tool divides the count of values by the sum of their reciprocals, which is the standard average for rates such as speeds. It also shows how many values were used. Calculations run in your browser, so nothing you type is sent to a server, and the output is an estimate rather than a certified or official figure.

Harmonic Mean Calculator

Result

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Harmonic Mean
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Count

About Harmonic Mean Calculator

The harmonic mean is the right average when your values are rates, such as speeds over equal distances. This calculator takes a comma-separated list of positive numbers and computes n / (Σ 1/x), the number of values divided by the sum of their reciprocals.

Every value must be greater than zero. The result is shown to four decimals along with the count of numbers used.

Formula & Mathematical Calculation

Harmonic Mean = f(Values (comma-separated, all > 0))

Calculated according to standard stats formulas implemented in the calculator core.

Calculation Example

Enter the values 1, 2, 4:

  • Sum of reciprocals = 1/1 + 1/2 + 1/4 = 1.75
  • Harmonic mean = 3 / 1.75 ≈ 1.7143

The result panel shows a Harmonic Mean of 1.7143 and a Count of 3.

Key Benefits

  • Computes n divided by the sum of reciprocals, the correct average for rates and ratios
  • Handles a list of any length and reports the harmonic mean to four decimals
  • Confirms the number of values parsed in the Count box
  • Rejects zero or negative entries, since reciprocals require positive values; free and in-browser

How to Use this Calculator

  1. Enter your values
    Type your positive numbers into the Values field, separated by commas, for example 1, 2, 4.
  2. Calculate
    Press Calculate to compute the harmonic mean.
  3. Read the results
    Check the Harmonic Mean box for the answer and the Count box for how many values were used.

Assumptions & Limitations

What the calculation assumes

  • Every value you enter is treated as an exact, known amount.
  • Any rate or interval you enter is assumed to hold for the whole period unless the form asks for it separately.
  • Results use standard published formulas and account only for the values entered above.
  • Rounding is applied for display; the underlying calculation uses your full precision.
  • Results are returned in the same units you enter, unless the tool states the output unit.

What it does not cover

  • Harmonic Mean Calculator produces a calculated result for reference and learning, not a certified or official measurement.
  • Real-world outcomes differ when tolerances, rounding rules or local standards apply.
  • Definitions and standards vary by region and change over time; verify the convention that applies to your case.
  • Figures are only as accurate as the inputs you supply — check them before acting on the result.
  • For work where the result carries real consequences, confirm it against an authoritative source.

Frequently Asked Questions

It suits rates and ratios, such as averaging speeds over equal distances, where the reciprocal relationship matters; it is always less than or equal to the arithmetic mean of the same positive numbers.

The calculation sums the reciprocals of the values, and a zero would make a reciprocal undefined, so the tool requires every entry to be greater than 0.

It divides the count of values, n, by the sum of their reciprocals, giving n / (1/x1 + 1/x2 + ... + 1/xn).

It shows how many valid numbers were read from your list, so you can confirm none were dropped.

Free to use, no account needed. Calculations run in your browser, so nothing you type is sent to a server. Results are estimates — how we build and check our calculators.