Average Calculator

What the Average Calculator does

This average calculator finds the mean, median, mode and range of a list of numbers, and a weighted average if you give each number a weight - with every step of the working written out so you can follow it, check it or copy it into homework. Paste numbers separated by commas, spaces or new lines, straight from a spreadsheet column if you like.

"Average" usually means the mean: add everything up and divide by how many there are. But the median and the mode are averages too, and each one answers a slightly different question, so the calculator shows all three side by side. It runs entirely in your browser; nothing you paste is sent anywhere.

How to use it

1. Type or paste your numbers into the first box. Commas, spaces, semicolons and new lines all separate numbers; use a dot for decimals (2.5).
2. For a weighted average - grades with different credits, or prices bought in different quantities - put one weight per number in the second box, in the same order.
3. Choose how many decimal places you want. Rounding happens only at the end, so it never changes the result.
4. Read the headline average, the mean, median, mode and range tiles, and open the step-by-step working to see exactly how each was found.
5. Copy the results or the working, download a CSV, or print the page.

Reading the results

The mean uses every value, so one very large or very small number pulls it. The median is the middle value once the list is sorted and ignores how extreme the ends are, which is why house prices and incomes are usually quoted as medians. The mode is the value that occurs most often; a list can have one, several, or none.

When the mean and the median are close, the numbers are roughly symmetrical. When the mean is well above the median, a few high values are stretching it; well below, a few low ones are.

The range is the gap between the largest and smallest value - the simplest measure of spread. "More statistics" adds the standard deviation, which measures the typical distance from the mean, and the geometric and harmonic means for growth rates and speeds.

Worked example: nine test marks: 72, 85, 91, 68, 85, 77, 94, 85, 60

Formulas and scoring rules

Mean

mean = (x1 + x2 + ... + xn) / n

Median

sort the values; odd n: the value at position (n + 1) / 2; even n: the mean of the values at positions n / 2 and n / 2 + 1

Mode

the value or values with the highest count; none if every value appears once

Range

range = largest - smallest

Weighted average

weighted = (w1 x1 + w2 x2 + ... + wn xn) / (w1 + w2 + ... + wn)Weights cannot be negative and must not add up to zero.

Standard deviation

population: sqrt( sum (x - mean)^2 / n ); sample: sqrt( sum (x - mean)^2 / (n - 1) )

Geometric and harmonic mean

geometric = (x1 x x2 x ... x xn)^(1/n); harmonic = n / (1/x1 + 1/x2 + ... + 1/xn)Only defined here when every value is above zero. Sums use compensated summation; results are rounded half away from zero to the decimal places you choose.

Mean, median or mode - which average should you use?

Use the mean when every value matters equally and there are no wild outliers: marks in a test, daily temperatures, the average spend per order. Use the median when a few extreme values would mislead: incomes, house prices, journey times with the occasional traffic jam. Use the mode for the most typical choice or category: the most common shoe size sold, or the score most students got.

For rates and ratios there are two specialist averages. The geometric mean is the right average for growth over several periods - returns of +50% and -50% have a geometric mean change of about -13%, not 0%. The harmonic mean is the right average for speeds over equal distances: 60 km/h out and 40 km/h back averages 48 km/h, not 50.

How a weighted average works

A weighted average lets some values count more than others. Multiply each value by its weight, add the products, then divide by the total of the weights. University grade point averages weight each grade by course credits; a portfolio's average return weights each holding by the amount invested; a frequency table weights each value by how many times it occurs.

Weights do not need to add up to 1 or 100. Credits of 4, 3, 3 and 2 work exactly as well as 33.3%, 25%, 25% and 16.7%, because the calculation divides by the total either way.

Limitations: what the result does not prove

• Commas always separate numbers, so 1,234 is read as two numbers, 1 and 234. Remove thousands separators before pasting, and use a dot for decimals.
• A grade point average on a 4.0 or 10-point scale depends on your institution's conversion table; enter the grade points you have been given, not percentages, if that is what your school averages.
• Averages summarise a list; they say nothing about why values differ. Two lists can share a mean and median and look completely different - check the range and standard deviation too.
• At most 10,000 numbers at a time, so the page stays responsive.

Privacy: where your data goes

Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.

Standards and sources

• NIST/SEMATECH e-Handbook of Statistical Methods - Measures of location
• NIST/SEMATECH e-Handbook - Measures of scale (standard deviation)
• Khan Academy - Summarizing quantitative data (mean, median, mode)

Frequently asked questions

Last reviewed 20 October 2026 by the A2Z.Tools team against the sources listed above.