Average calculator

An average calculator for grades and for plain numbers

This average calculator has two tabs. "Grades and weights" is a grade calculator: it works out a weighted average, where each mark counts according to its weight, and it accepts marks out of different totals. "List of numbers" takes any set of values and returns the mean, median and mode, along with the range and the standard deviation.

Results update as you type and are rounded to two decimal places. Your marks stay saved on your device for your next visit.

How to use it

1. Under "Result scale", keep "Percentage (out of 100)" or pick "Out of 20" or "Out of 10".
2. On each row, type the "Mark", what it is "Out of", and its "Weight". Leave the weight alone and it counts as 1. "Subject (optional)" is only there to help you keep track.
3. "Add a mark" creates a new row; the cross at the end of a row deletes it. A row with no mark is ignored.
4. Read the "Weighted average", the "Total weight", the "Highest mark" and the "Lowest mark" under the table, all converted to the scale you chose.
5. "Copy summary" puts the breakdown on your clipboard. "Clear all" empties the rows.

The weighted average formula, step by step

Multiply each mark by its weight, add up the products, then divide by the total weight. Take a module assessed in three parts:

The products add up to 1,700 + 2,100 + 3,100 = 6,900 and the weights to 100, so the weighted average is 6,900 ÷ 100 = 69%. A plain average of the three marks would give (85 + 70 + 62) ÷ 3 = 72.33%, too high because the exam carries half of the grade.

Weights of 2, 3 and 5 give the same 69%: only the proportions matter.

What mark do I need?

The "What mark do I need?" block works backwards. Enter your "Target average" and the "Weight of the next mark". Say your coursework so far averages 68% and is worth 60 of the 100 points, and you want 70% overall with a final exam worth 40. You need (70 × 100 − 68 × 60) ÷ 40 = (7,000 − 4,080) ÷ 40 = 73%. The tool tells you when the target cannot be reached with a single mark, or when it is already secured.

Converting a mark from one scale to another

Divide the mark by its total, then multiply by the scale you want. 18 out of 25 is 18 ÷ 25 × 100 = 72%. 42 out of 60 is 70%. The "Out of" column does this for every row. This is a straight proportional conversion: it does not translate percentages into letter grades or a grade point average, since those rules differ from one school to the next.

Mean, median and mode: three different answers

Take six house prices on one street, in thousands of pounds: 180, 195, 195, 210, 230 and 790. Paste them into "List of numbers".

• The mean is the sum divided by the count: 1,800 ÷ 6 = 300.
• The median is the middle value once the list is sorted. With six values it is halfway between the third and fourth: (195 + 210) ÷ 2 = 202.5.
• The mode is the most common value: 195, which appears twice.

One large house pulls the mean up to £300,000 although five of the six homes sold for less. The median is the better guide to a typical price. The tool also shows the minimum, maximum, range (610 here) and standard deviation, once for a whole population and once for a sample (dividing by n − 1).

A common mistake: averaging averages

Class A has 10 students and a mean score of 80. Class B has 30 students and a mean of 60. Averaging the two means gives 70, but the mean of all 40 students is (80 × 10 + 60 × 30) ÷ 40 = 2,600 ÷ 40 = 65. To combine averages, weight each one by the number of values behind it.

Frequently asked questions

What if I leave the weight empty?

The mark counts with a weight of 1. A weight of 0 leaves it out without deleting the row.

Why is a row outlined in red?

The mark is higher than its total, such as 27 out of 25, or a box holds something that is not a number. The row is ignored until you correct it.

How should I separate the numbers in a list?

Use spaces, commas, line breaks or semicolons. Because a comma separates two values, write large numbers without a thousands separator: 1250, not 1,250.

Which standard deviation should I use?

For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is exactly 2. If those eight values are a sample from a larger group, divide by 7 instead of 8 and you get 2.14.