Harmonic Mean Calculator

What is the Harmonic Mean Calculator?

Calculate the harmonic mean — the right average for rates and speeds. The harmonic mean is the correct average for rates such as speeds or prices per unit, where the ordinary average gives the wrong answer.

How to use the Harmonic Mean Calculator

1. Paste or type your numbers into the box (a sample is pre-filled so you can see how it works).
2. Results update automatically as you type; you can also press Calculate.
3. Read the output: harmonic mean, arithmetic mean.
4. Use the 📊 chart to see the result visually, then copy or share it.

Formula and method

Worked example

With the sample input, the Harmonic Mean Calculator returns harmonic mean: 48; arithmetic mean: 50.

Where the Harmonic Mean Calculator helps in real life

You drive 60 miles to a meeting at 30 mph and 60 miles back at 60 mph. The harmonic mean shows your average speed was 40 mph, not the 45 mph a simple average suggests.

You buy $100 of fuel each week at different prices per gallon. The harmonic mean of those prices gives the true average price you paid per gallon.

Common mistakes to avoid

• Using the arithmetic mean for speeds over equal distances.
• Including a zero, which makes the harmonic mean undefined.
• Applying it when the time spent, not the distance, is equal.
• Mixing miles per hour with kilometers per hour.

💡 Practical tip: The harmonic mean is always less than or equal to the arithmetic mean of the same positive numbers.

Tips for better results

• Use the harmonic mean when the amount (distance or spending) is fixed.
• Use the arithmetic mean when the time at each rate is fixed.
• Check the answer is lower than the ordinary average, as it always should be.

Related tools