Average Calculator
Free, with no sign up. Calculations run on your device; your entries stay in this browser.
Enter 1–1,000 values separated by commas, spaces or newlines, each between −1,000,000,000,000 and 1,000,000,000,000 (±10¹²). Optionally enter one weight per value, each from 0 to 1,000,000,000 (10⁹), with at least one positive weight. Values text is capped at 24,000 characters and weights at 14,000. Decimal and scientific notation are accepted. Values must share the same unit: mean, median, mode, range and standard deviation use that unit, sum uses its total, and count is unitless. Weights are relative, unitless amounts.
Your result
mean = Σx/n; weighted mean = Σ(wx)/Σw; population SD = √(Σ(x − mean)²/n); sample SD = √(Σ(x − mean)²/(n − 1)); median = middle sorted value or mean of the middle pair.
Primary source: OpenStax Introductory Statistics 2e, measures of center; OpenStax Introductory Statistics 2e, population and sample standard deviation.
All ordinary statistics use the unweighted list; optional weights affect only the separately labelled weighted average. Modes include every repeated value tied for highest frequency; if all values occur once, there is no mode. For a single value, population SD is zero and sample SD is undefined. Floating-point results display up to 12 significant digits and may be approximate.
Worked example
For 2, 4, 4, 6, sum = 16, count = 4, mean = 4, median = 4, mode = 4 and range = 4. Population SD = √2 ≈ 1.41421356237; sample SD = √(8/3) ≈ 1.63299316186. Weights 1, 1, 1, 3 give a weighted average of 28/6 ≈ 4.66666666667.
How to use this tool
Enter your measured values and select Calculate to see the result, formula and details below.
Frequently asked questions
What is the difference between mean and median?
The mean divides the sum by the count. The median is the middle value after sorting, or the mean of the two middle values for an even count.
Do weights change the standard deviation?
No. Weights affect only the separate weighted average. The median, mode and both standard deviations are calculated from the original unweighted values.
Can there be more than one mode?
Yes. Every repeated value tied for the highest frequency is listed. When no value repeats, the calculator reports no mode.