Average Percentage Calculator

How to average percentages

Quick answer: add the percentages and divide by how many there are. If the percentages come from groups of different sizes, multiply each by its weight, add the results and divide by the total weight.

The simple average of percentages

1. 1Add all the percentages together.
2. 2Divide the sum by the number of percentages.
3. 3Add the percent sign.

This is the arithmetic mean. It treats every percentage as equally important, which is right when each one comes from a group of the same size, such as four tests marked out of the same total. The percentage average calculator above does this when no weights are given, as does any percent average calculator in its simple mode.

Weighted average of percentages

The weighted average is the sum of each percentage times its weight, divided by the sum of the weights:

Here p is each percentage and w is its weight. The weight can be a sample size, a number of marks or a share of a grade. It only has to be non-negative, and the weights do not need to add up to 100. The weights decide how much each percentage counts.

This is why a simple mean can be wrong. A pass rate of 90% from 50 students should pull the overall figure further than a pass rate of 60% from 20 students, and the simple mean gives them the same pull. Whenever the underlying groups differ in size, switch the calculator above to weighted mode. It works as a weighted percentage calculator and as an average percentage calculator with weights.

How to calculate a weighted average step by step

1. 1Multiply each percentage by its weight.
2. 2Add those products together.
3. 3Add the weights together.
4. 4Divide the sum of the products by the sum of the weights.

Take coursework at 85% with a weight of 40 and an exam at 70% with a weight of 60. The products are 3,400 and 4,200, which add to 7,600. The weights add to 100, so the average is 76%. When the weights are sample sizes, each product is 100 times the number of successes in that group, which is why the weighted average of pass rates equals the combined pass rate.

Adding percentages together

How to add percentages together depends on the whole: you can add them only when they are shares of the same whole. Market shares of 25%, 30% and 12% of one market add up to 67% of that market. When the percentages come from different wholes, the sum means nothing: 50% of 20 people and 25% of 80 people do not make 75% of anyone.

To combine percentages from different groups, turn each into a count, add the counts and divide by the combined total. That is the weighted average with the group sizes as the weights, and it gives the overall percentage. Example 4 below shows it. The calculator above works as a combine percentages calculator when you enter each percentage with its group size as the weight.

Average percentage change over several periods

Growth rates need a different average. If a figure rises 10% and then falls 10%, the simple average is 0%, but the figure ends at 1.1 × 0.9 = 0.99 of its start, a loss of 1%. The average that reproduces the real result is the geometric mean of the multipliers:

For a rise of 10% then a fall of 10%, that is the square root of 0.99, minus 1, which is -0.50% per period. For the change between just two values, use the percentage change calculator, and for a single rise the percentage increase calculator.

Average percentage in Excel and Google Sheets

For a simple average, with the percentages in A2:A5, type =AVERAGE(A2:A5). For a weighted average, with the percentages in A2:A4 and the weights in B2:B4, type =SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4). The percentages in Excel guide covers more formulas.

Averaging percent errors

Average percent error is a different job. Work out each percent error first with the percent error calculator, then average the results as above.

Rounding and checking the result

Round only the final average. Averaging figures that were already rounded passes their rounding error into the result, so keep the exact values where you can. Quote one or two decimal places unless you need more. The calculator shows the sum and the count, or the total weight, beside the average so you can check the division yourself.

Average percentage examples

Average percentage code

Both versions reproduce the examples above (81.25, 81, 76, 76.67 and 19.72), reject non-numeric input, and refuse mismatched or all-zero weights.

JavaScript

1function finite(name, v) {2  if (typeof v !== "number" || !Number.isFinite(v)) throw new TypeError(`${name} must be a finite number`);3}4​5function places(decimals) {6  if (!Number.isInteger(decimals) || decimals < 0 || decimals > 10) throw new RangeError("decimals must be a whole number from 0 to 10");7  return decimals;8}9​10function list(name, values) {11  if (!Array.isArray(values) || values.length < 1) throw new TypeError(`${name} must be a non-empty array of numbers`);12  values.forEach((v) => finite(name, v));13}14​15// Simple average: [80, 90, 70, 85] -> 81.2516export function averagePercent(values, decimals = 2) {17  list("values", values);18  const d = places(decimals);19  return Number((values.reduce((a, b) => a + b, 0) / values.length).toFixed(d));20}21​22// Weighted average: weights can be sample sizes, marks or any non-negative numbers23export function weightedAveragePercent(values, weights, decimals = 2) {24  list("values", values);25  list("weights", weights);26  if (values.length !== weights.length) throw new RangeError("values and weights must be the same length");27  if (weights.some((w) => w < 0)) throw new RangeError("weights must not be negative");28  const d = places(decimals);29  const total = weights.reduce((a, b) => a + b, 0);30  if (total === 0) throw new RangeError("the weights must not all be 0");31  const sum = values.reduce((acc, v, i) => acc + v * weights[i], 0);32  return Number((sum / total).toFixed(d));33}34​35// Average percentage change per period over several periods (geometric mean)36export function averageGrowth(ratesPercent, decimals = 2) {37  list("rates", ratesPercent);38  const d = places(decimals);39  let product = 1;40  for (const r of ratesPercent) {41    if (r <= -100) throw new RangeError("a rate of -100% or less cannot be averaged this way");42    product *= 1 + r / 100;43  }44  return Number(((Math.pow(product, 1 / ratesPercent.length) - 1) * 100).toFixed(d));45}

Python

1from decimal import Decimal, ROUND_HALF_UP2from math import isfinite3​4​5def _num(name, v):6    if isinstance(v, bool) or not isinstance(v, (int, float, Decimal)) or not isfinite(float(v)):7        raise ValueError(f"{name} must be a finite number")8    return Decimal(str(v))9​10​11def _round(x, decimals):12    if not isinstance(decimals, int) or isinstance(decimals, bool) or not 0 <= decimals <= 10:13        raise ValueError("decimals must be a whole number from 0 to 10")14    return x.quantize(Decimal(1).scaleb(-decimals), rounding=ROUND_HALF_UP)15​16​17def _list(name, values):18    if not isinstance(values, (list, tuple)) or len(values) < 1:19        raise ValueError(f"{name} must be a non-empty list of numbers")20    return [_num(name, v) for v in values]21​22​23def average_percent(values, decimals=2):24    nums = _list("values", values)25    return _round(sum(nums) / len(nums), decimals)26​27​28def weighted_average_percent(values, weights, decimals=2):29    nums = _list("values", values)30    w = _list("weights", weights)31    if len(nums) != len(w):32        raise ValueError("values and weights must be the same length")33    if any(x < 0 for x in w):34        raise ValueError("weights must not be negative")35    total = sum(w)36    if total == 0:37        raise ValueError("the weights must not all be 0")38    return _round(sum(n * x for n, x in zip(nums, w)) / total, decimals)39​40​41def average_growth(rates_percent, decimals=2):42    rates = _list("rates", rates_percent)43    product = Decimal(1)44    for r in rates:45        if r <= -100:46            raise ValueError("a rate of -100% or less cannot be averaged this way")47        product *= 1 + r / 10048    return _round((product ** (Decimal(1) / len(rates)) - 1) * 100, decimals)

weightedAveragePercent([60, 80, 90], [20, 30, 50]) returns 81, the group-size example, and averageGrowth([10, 20, 30]) returns 19.72. Round only for display. The Python version rounds half up, which is the usual school convention, and returns Decimal values, so 81 prints as 81.00.

Privacy and input safety

• Values are calculated in your browser. The numbers you enter are not sent to a server or stored.
• Fields accept numbers only, with an optional trailing % sign on a percentage. Text, empty fields, NaN and Infinity are rejected with a message, and nothing you type is ever evaluated as code.
• A row with a percentage but no weight is read as a weight of 1 in weighted mode. A completely empty row is ignored.
• Weights must not be negative. If every weight is 0 the calculator asks for at least one positive weight, because the total would be zero.
• Percentages above 100 or below 0 are accepted in the simple and weighted modes, because some data has them. Average growth refuses a rate of -100% or lower, which would wipe out the whole figure.
• Decimal places are limited to a whole number from 0 to 10.
• A comma followed by exactly three digits is read as a thousands separator, so 1,200 is 1200. Any other comma is a decimal point, so 12,50 is 12.50, and a number starting with 0, such as 0,500, is read as a decimal. Mixed formats such as 1.234,5 and ambiguous entries such as 1,2,3 are refused instead of guessed. Spaces, including no-break spaces, between digit groups are ignored.
• A very long paste cannot freeze the page.

Common average percentage mistakes

Which average to use