Median Calculator

How to find the median of your numbers

1. Enter one observation per number. Paste a spreadsheet column or type a list; keep repeated values when they represent separate observations.
2. Choose decimal point or decimal comma to match the text. In point mode, commas can separate values. In comma mode, use semicolons, spaces, tabs or line breaks between values.
3. Read the median and count, then check the displayed middle position or pair. The short interpreted preview shows how the beginning of your list was read.
4. Open Calculation and sorted preview to check the ordering, or copy the result. Clear starts a new blank list and restores this page language's default decimal mark.

What the calculator shows

• One exact numerical median with the number of observations.
• The middle position and value for an odd count, or the two middle positions, values and their average for an even count.
• An explicit decimal-format choice and a short interpreted preview, without guessing thousands separators.
• A sorted preview: all values for lists of up to 20, or the first and last 10 values for longer lists.
• A copyable summary that keeps the result, count, middle-value explanation and input-format context together.

When this is useful

• Check a numerical median for a lesson, exercise or small research list.
• Summarize comparable observed prices, waiting times or measurements in a shared unit, including a list with a few extreme values.
• Verify a reported middle value against the underlying individual observations, rather than guessing it from a mean or from group medians.

How the median is calculated

The calculator orders every valid observation numerically from smallest to largest. Your pasted text is not reordered, and equal values remain separate observations.

With an odd number of values, the central observation is the median. With an even number, the calculator adds the two central observations and divides by two. Positions shown beside the answer start at 1.

An even-count median does not have to appear in the original list. With repeated values, several observations can equal the median; it is not necessary for exactly half the values to be strictly smaller and half strictly larger.

The arithmetic mean uses the sum of all values divided by their count. The median is based on ordering. They answer different questions; neither is automatically the right summary for every list. Use the separate Average Calculator when you need the arithmetic mean.

Decimals entered with up to four places are handled exactly. Averaging two such values needs at most five decimal places, so this tool does not round the median or use About wording. Zeros display as zero, not negative zero.

Choose the decimal mark deliberately. The text 1,5 means the two numbers 1 and 5 in point mode, giving median 3; in comma mode it means the single number 1.5. Grouping separators are never inferred or stripped.

Median examples

Odd count: 12; 4; 9; 7; 20 sorts to 4; 7; 9; 12; 20. The third value is 9, so the median is 9.

Even count: 2; 10; 4; 8 sorts to 2; 4; 8; 10. The middle values are 4 and 8, so the median is (4 + 8) ÷ 2 = 6.

Repeated values: 2; 2; 2; 9; 100 has median 2. The repeats are kept, not replaced by a list of unique values.

Small decimals: 0; 0.0001 in point mode has median 0.00005. The extra fifth place is exact, not an approximation.

An extreme observation: 8; 9; 10; 11; 200 has median 10. This one-number summary does not describe the spread of the list or establish whether the observations are a useful sample.

Input rules and limits

Use one list of individual numerical observations. Do not enter frequency columns, interval bins, weights, units, currency symbols, dates, clock times, fractions or formulas.

Accepted values use ASCII digits 0–9, an optional leading + or - sign, and up to four decimal places. A digit is required before the decimal mark. Thousands separators, exponent notation and non-ASCII minus signs are unsupported.

The limits are 5,000 values, 100,000 UTF-16 text units, 32 characters per number and values between -1,000,000,000 and 1,000,000,000. Repeated separators do not create zero observations. Invalid or oversized lists are not silently shortened or partly calculated.

This is not a weighted median, grouped-data estimate, percentile-method selector, mode, quartile or full statistics tool. Do not combine group medians by taking their median and assume it is the median of all original observations.

Your list and copied result

This calculator processes the list in your browser. It does not add an upload, saved history or a share URL containing your numbers. Inputs and calculated output use the site's existing private-content markers.

Copying sends the requested summary to your clipboard when the browser permits it. If not, a selected read-only field lets you copy it manually. This tool-specific behavior is not a guarantee about every third-party script or the whole website.