Average Calculator - Arithmetic, Weighted, Geometric, Harmonic

What Does the Average Calculator Do?

Enter a list of numbers and select the type of average - arithmetic, weighted, geometric or harmonic. The calculator returns the result with step-by-step formula breakdown.

Quick start: Type numbers separated by commas (e.g. 10, 20, 30), select "Arithmetic", click Calculate. Result: 20.

Types of Averages

Type	Formula	Best for
Arithmetic	(x1 + x2 + ... + xn) / n	Grades, temperatures, general averages
Weighted	(w1x1 + w2x2 + ...) / (w1 + w2 + ...)	GPA, portfolio returns, survey scores
Geometric	(x1 * x2 * ... * xn)^(1/n)	Growth rates, compound interest, ratios
Harmonic	n / (1/x1 + 1/x2 + ... + 1/xn)	Speeds, rates, price-earnings ratios

Practical Examples

Example 1: Exam grades Numbers: 85, 90, 78, 92, 88 (Arithmetic)
Average: (85+90+78+92+88)/5 = 86.6

Example 2: Weighted GPA Grades: 4, 3, 5 with weights 3, 2, 4 (Weighted)
(4x3+3x2+5x4)/(3+2+4) = 38/9 = 4.22

Example 3: Annual growth rates 10%, 20%, 15% as 1.1, 1.2, 1.15 (Geometric)
(1.1 x 1.2 x 1.15)^(1/3) = 1.149 = 14.9% average growth

Example 4: Average speed 60 km/h and 40 km/h (equal distances) (Harmonic)
2/(1/60+1/40) = 2/(0.0417) = 48 km/h

Example 5: Simple arithmetic Numbers: 10, 20, 30
(10+20+30)/3 = 20

FAQ - Frequently Asked Questions

When should I use weighted average instead of arithmetic?

When not all values have equal importance. For example, a final exam worth 40% of the grade vs homework worth 10% - use weights 4 and 1 to reflect their relative importance.

What is geometric mean used for?

For rates of change and multiplicative data. If your investment grew by 10%, 20% and -5% over 3 years, the geometric mean gives the true average annual return. Arithmetic mean would overestimate it.

Why is harmonic mean always the smallest?

For any set of positive numbers: Harmonic ≤ Geometric ≤ Arithmetic. This is the AM-GM-HM inequality. They are equal only when all numbers are identical.

Can I use negative numbers?

For arithmetic and weighted: yes. For geometric: all numbers must be positive (you cannot take the root of a negative product). For harmonic: all numbers must be non-zero.

How many numbers can I enter?

There is no hard limit. Enter as many comma-separated numbers as you need. The calculator handles hundreds of values efficiently.

What if my weights do not add up to 1 or 100?

The calculator normalizes weights automatically. Weights 2, 3, 5 work the same as 0.2, 0.3, 0.5 or 20, 30, 50. Only the ratios matter.

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