Average Calculator
Enter any list of numbers to instantly calculate mean, median, mode, range, sum, standard deviation, and more. Add numbers as chips or paste a comma-separated list.
How to Calculate the Average — And What the Other Stats Mean
When most people say "average," they mean the arithmetic mean — the sum of all numbers divided by the count. But in statistics, there are several types of averages, and each one tells you something different about your data. This calculator computes all of them at once, plus spread metrics like standard deviation and variance. For deeper statistical analysis, pair this with our Standard Deviation Calculator.
All 10 Statistics — Explained
| Statistic | What It Measures | Best Used For |
|---|---|---|
| Mean | Sum ÷ Count | General central tendency; test scores, temperatures |
| Median | Middle value when sorted | Skewed data; income, house prices (outlier-resistant) |
| Mode | Most frequently appearing value | Categorical data; which size sells most |
| Range | Max − Min | Data spread at a glance |
| Sum | Total of all values | Totalling expenses, scores, quantities |
| Std Deviation σ | Average distance from the mean | Measuring consistency, risk, variability |
| Variance σ² | Std deviation squared | Statistical modeling, probability theory |
| Geometric Mean | nth root of the product of all values | Growth rates, investment returns, ratios |
| Min | Smallest value | Finding the lowest score, temperature, price |
| Max | Largest value | Finding the highest in a dataset |
Mean vs. Median — When to Use Which
The mean is sensitive to outliers. If you have data like 10, 12, 11, 13, 200, the mean is 49.2 — which doesn't represent the typical value at all. The median for that same set is 12 — a much better description of the "centre" of the data. This is why economists use median household income rather than mean income: a handful of billionaires would skew the mean far above what most families actually earn. Use the Income Tax Calculator alongside median income data to get a realistic picture of tax impact.
Formulas Used in This Calculator
x̄ = (x₁ + x₂ + … + xₙ) / n
σ = √[ Σ(xᵢ − x̄)² / n ]
This calculator uses population std dev (÷n). For sample std dev, use ÷(n−1) — available in our Standard Deviation Calculator.
GM = (x₁ × x₂ × … × xₙ)^(1/n)
Only valid when all values are positive. Useful for compound growth rates and ratios.
x̄w = Σ(wᵢ × xᵢ) / Σ(wᵢ)
Each value xᵢ is multiplied by its weight wᵢ before summing. Enable "Weighted Average" in the options above.
Common Uses for an Average Calculator
Student Grades
Calculate your class average or GPA. Use with our Grade Calculator and GPA Calculator.
Finance & Investing
Average returns, portfolio costs, moving averages. Pair with our Investment Calculator.
Sports & Fitness
Average pace, score per game, workout stats. See our Pace Calculator for running.
Science & Research
Average experimental readings, temperature logs, survey responses, error analysis.
Frequently Asked Questions
Common questions about averages, statistics, and how this calculator works
2, 3, 3, 5, 100: mean = 22.6, median = 3, mode = 3. The mean is misleading here; median and mode tell the real story. For further stats, try our Standard Deviation Calculator.
Σ(value × weight) / Σ(weights). For example, if your exam counts 60% and your assignment 40%: exam score 80 × 0.6 = 48, assignment 70 × 0.4 = 28, weighted average = 76. Toggle "Weighted Average" in the options above, enter your numbers, then enter corresponding weights in the same order. This is commonly used for GPA calculations, financial portfolio returns, and survey data where some responses matter more than others.
78, 79, 80, 81, 82 have a mean of 80 and a very low std dev (~1.4). Scores of 10, 50, 80, 95, 100 also average 67 but have a std dev of ~34 — the class is highly inconsistent. In finance, high std dev means higher volatility/risk — pair this with our Investment Calculator. For sample standard deviation (÷n−1) instead of population (÷n), use our dedicated Standard Deviation Calculator.
(x₁ × x₂ × … × xₙ)^(1/n). Unlike the arithmetic mean, it's the correct average for multiplicative processes — things that compound or grow by percentages. If an investment grows 10% in year 1, −5% in year 2, and 15% in year 3, the geometric mean return is (1.10 × 0.95 × 1.15)^(1/3) − 1 ≈ 6.5% per year — not the arithmetic mean of 6.67%. It only works with positive numbers. Use it for investment returns, population growth, and ratio comparisons. Our Compound Interest Calculator uses similar compounding logic.
3, 7, 12, 18 (4 numbers), the two middle values are 7 and 12, so the median is (7 + 12) / 2 = 9.5. This calculator handles even and odd counts automatically. The sorted values panel highlights which value(s) contribute to the median.
−5). The geometric mean is the exception: it is only defined for strictly positive numbers. If your dataset includes zero or negative values, the geometric mean field will show "N/A". Negative number averages are common in finance (losses, temperature below zero, elevation below sea level).
2, 2, 3, 5, 5, both 2 and 5 appear twice — both are modes. In 1, 2, 3, 4, 5, no value repeats — no mode exists.