Average Percentage Calculator

Which average describes the whole group?

A small class reports an 80% pass rate and a larger class reports 50%. Taking the midpoint gives 65%, but that does not tell you what share of all students passed. You also need the number of students in each class.

This calculator shows both answers. The Simple average treats each group as one equally important entry. The Weighted average by group size gives each person or unit in the combined base equal influence. Choose the result that matches what you are reporting: the average of the group rates, or the rate across all observations.

Choose the right percentages and sizes

You can enter 1–20 groups. Rates must be between 0 and 100, and sizes must be greater than zero and no more than 1,000,000,000,000. Both fields accept up to four decimal places. Use a decimal point without commas, signs, percent symbols or exponent notation. A blank field hides both averages until the row is complete.

How the two formulas work

The simple mean divides the sum of the percentages by the number of groups. The weighted mean first multiplies each percentage by the size it represents, then divides the sum of those products by the total size.

Here, p is an entered percentage such as 80, n is its group size, and k is the number of groups. The result of each average is already in percent. The implied matching amount converts each percentage back into the number or quantity that meets the condition.

Example: 10 students and 90 students

The first class has 10 students and an 80% pass rate. The second has 90 students and a 50% pass rate. First reconstruct how many students passed in each class.

Across both classes, 53 of 100 students passed, so 53% is the combined pass rate. The 65% figure describes the average of two class rates when the classes receive equal influence. The larger class contains nine times as many students, which is why the combined result sits closer to its 50% rate.

Why the denominator is the total size

Each class rate starts as its passing count divided by its class size, multiplied by 100. Multiplying that rate by the size reverses the division. Adding the products therefore combines the passing counts on a percentage scale; dividing by all students puts the result back on the same scale.

The denominator is 100 students in this example, rather than two classes. That choice gives each student equal influence in the overall rate. When the entered percentages are exact, this is the same arithmetic as adding the original passing counts and dividing by the total tested. When the percentages are rounded, the reconstructed count and combined rate inherit that rounding.

When the results match

If both classes instead contain 10 students, the passing counts are 8 and 5. Together, 13 out of 20 pass, giving 65%. Both means now agree because the group sizes are equal. They also agree when every entered percentage is the same, whatever the sizes.

With positive sizes, each average stays between the smallest and largest entered percentage. A single group produces its own percentage as both results. These are useful checks when reviewing a report.

Adding a third group

The same rule works beyond two rows. Consider rates of 20%, 40% and 80% applied to sizes of 1, 2 and 3 units. The implied matching amounts are 0.2, 0.8 and 2.4 units. These are divisible quantities for this example, so fractional amounts are meaningful.

The highest rate belongs to the largest group, so weighting raises the result in this example. Weighting does not always raise an average: the two-class example lowers it because the larger class has the lower rate. The result depends on which rates belong to which sizes.

Decimal sizes and rounded rates

A group size can represent a divisible quantity as well as a count. If 12.5% of 2.5 kg and 37.5% of 7.5 kg meet the same condition, the matching amounts are 0.3125 kg and 2.8125 kg. Together that is 3.125 kg out of 10 kg, or 31.25%. The simple average is 25%. Use the same unit for both quantities.

For people or whole items, use whole-number sizes. An entered rate of 33.3333% for 3 people implies 0.999999 people before display rounding. That does not establish a fractional observed person; it reflects the rounded rate. If you have the original matching counts and totals, adding those counts and dividing by the combined total gives the more dependable rate.

The calculator uses the entered decimals without intermediate rounding, then rounds displayed results to up to four decimal places. Halfway values round up and trailing zeros are omitted. Positive results below 0.0001 use a less-than sign; rates just below 100% use a greater-than sign above 99.9999%. Extra display digits cannot recover precision lost in the original records.

Check the records before reporting a combined rate

• Use the original denominator for each rate. A response rate based on invitations must be weighted by invitations, not replies.
• Use compatible definitions, reporting periods and units. A percentage symbol alone does not make two measures comparable.
• Avoid counting the same observation twice. Overlapping groups can produce a rate across records without describing unique people.
• Remove groups with no base. A zero percent rate for a positive group is valid; a zero-size group has no defined proportion.
• Keep successive changes separate. Averaging percentage increases does not calculate their compounded effect.

Choose the observation you intend to count. A person taking two different tests contributes two test attempts if attempts are your reporting unit. Counting both attempts is appropriate for an attempt-based rate, but it does not tell you the percentage of unique people who passed. This calculator cannot identify repeated people or merge overlapping records.

Before copying a result into a report, record what the rate measures, which groups it includes, and whether the source percentages were rounded. Keep the original denominators with the report so another reader can reproduce the weighting. Do not change group sizes simply to obtain a preferred answer.

Formula reference

The NIST Dataplot reference for the weighted mean (PDF) gives the sum-of-products divided by sum-of-weights formula. Here the weights are the group sizes. The examples on this page reconstruct the matching amounts to check the combined rates independently.

Frequently asked questions

Related calculators

• Average Calculator — find the simple mean of a list when no group weighting is needed.
• Percentage Calculator — turn an original matching amount and its total into a percentage.
• Percentage Point Calculator — describe the gap between two rates in percentage points.