Percentage Calculator: Percent of a Number, Share and Change

About this percentage calculator

This page has one calculator with three modes. The first finds a percentage of a number, such as 15% of 2,400. The second tells you what percent one number is of another, such as 312 out of 400. The third gives the percent change between a starting value and an ending value, up or down. You choose the mode, type two numbers and read the answer.

Almost everyone needs these three questions at some point. Students use them for marks and attendance. Shoppers use them for sale prices and price rises. Anyone reading a payslip, a bill, a news report or a survey meets percentages, and the arithmetic is easy to get wrong when you are in a hurry or dividing by the wrong base.

The three modes cover most of what people ask, and the sections below go further: reverse percentages, percentage points versus percent, successive changes and marks percentage. These are the places where mental maths usually breaks down, so the worked examples and tables are there to help you check yourself.

How to use the Percentage Calculator, step by step

1. Pick the mode. Choose between the three buttons: X% of Y, what percent is A of B, and percent change. The labels on the two input boxes change with the mode, so read them before typing.
2. For percent of a number. Enter the percentage in the Percentage field and the number in Of this number. Typing 15 and 2,400 gives 360. Use this for tips, discounts, interest on a round figure or any share of a total.
3. For what percent one number is of another. Enter the part in This number and the whole in Out of this number. Typing 312 and 400 gives 78%. Put the smaller, partial figure first, unless you want a result above 100%.
4. For percent change. Enter the earlier figure in Starting value (X) and the later one in Ending value (Y). From 2,400 to 2,070 the result is −13.75%. A minus sign means a decrease and a plus means an increase.
5. Read the rounded result. The answer is rounded to two decimals and shown with a percent sign where it applies. In the first mode the result is a plain number, not a percentage, because it is a share of your total.
6. Watch for zero in the base. If the starting value in change mode, or the second number in share mode, is zero, the result shows 0 because dividing by zero has no meaning. Check that you typed the right figure in the right box.

The formula behind the Percentage Calculator

Every percentage question reduces to one of three formulas, plus two useful extensions for reverse and repeated changes.

X% of Y = (X ÷ 100) × Y
Part is what % of Whole = (Part ÷ Whole) × 100
Change % = (New − Old) ÷ Old × 100
Original = Final ÷ (1 ± Rate ÷ 100)
Successive change factor = (1 + r₁ ÷ 100) × (1 + r₂ ÷ 100) − 1

What each symbol means

X

The percentage rate, for example 15 for 15%

Y

The number you are taking the percentage of

Part

The portion you are measuring, such as marks scored

Whole

The total or base, such as full marks

Old / New

The starting and ending values in a change

Final

The amount you have after a rise or fall, used to find the original

r₁, r₂

Percentage rates applied one after the other; use a negative number for a fall

How the formula works

A percent is a fraction with 100 underneath. Fifteen percent means 15 per 100, or 0.15. That is why X% of Y is (X ÷ 100) × Y: you turn the rate into a decimal and scale the number. The mode that asks what percent A is of B simply runs it backwards. Divide the part by the whole to get the fraction, then multiply by 100 to express it per hundred. Both are the same relationship seen from two directions.

Percent change always uses the old value as its base, and that is where most mistakes begin. A rise from 50 to 75 is (75 − 50) ÷ 50 = +50%. A fall from 75 back to 50 is (50 − 75) ÷ 75 = −33.33%. The gap is the same, 25, but the base is different. This is also why a 50% fall needs a 100% rise to recover: you must double what is left. The table below shows the pattern for several falls.

Reverse percentages answer a question like: after a 20% discount the price is 1,600, so what was it before? The tempting step is to add 20% to 1,600, which gives 1,920, but 20% was taken from the original and not from 1,600. Because 1,600 is 80% of the original, divide: 1,600 ÷ 0.80 = 2,000. The same idea works for a price that includes a tax, where the final figure is 100% plus the rate.

Percentages that follow each other multiply; they do not add. A 20% rise and then a 20% fall leaves you at 1.20 × 0.80 = 0.96 of the start, a 4% loss. Percentage points are a separate matter. If an interest rate moves from 8% to 10%, it has risen by 2 percentage points, but by 25% in relative terms. News reports use both, so check which one is meant. For marks, add all scores and all full marks first, then divide.

Worked examples

Three questions with one calculator

Divya is going through three small things in one evening: the interest on a 2,400 balance at 15%, her mock-test score of 312 out of 400, and a monthly bill that fell from 2,400 to 2,070.

1. Mode 1, X% of Y: (15 ÷ 100) × 2,400 = 0.15 × 2,400 = 360.
2. Mode 2, what percent is A of B: (312 ÷ 400) × 100 = 0.78 × 100 = 78%.
3. Mode 3, change: (2,070 − 2,400) ÷ 2,400 × 100 = −330 ÷ 2,400 × 100 = −13.75%.
4. The negative sign in mode 3 means a decrease, so the bill is 13.75% lower than before.
5. Check mode 3 backwards: 2,400 × (1 − 0.1375) = 2,400 × 0.8625 = 2,070.

Result: 360, 78% and −13.75%, one from each mode.

Finding the original price

A pair of headphones costs 1,600 after a 20% discount. Separately, an invoice total of 11,800 includes 18% tax added on top of the base amount. In both cases you need the starting figure.

1. The discounted price is 100% − 20% = 80% of the original, so original = 1,600 ÷ 0.80 = 2,000.
2. Check: 20% of 2,000 is 400, and 2,000 − 400 = 1,600.
3. The wrong shortcut, 1,600 + 20% = 1,920, does not match the original price of 2,000.
4. For the invoice, the total is 118% of the base, so base = 11,800 ÷ 1.18 = 10,000.
5. Check: 18% of 10,000 is 1,800, and 10,000 + 1,800 = 11,800.

Result: The original price was 2,000 and the base amount was 10,000.

Raises in a row and a change in rate

A salary of 45,000 gets a 10% raise and then an 8% raise a year later. Separately, a savings rate moves from 8% to 10%. Which numbers can be added and which cannot?

1. After the first raise: 45,000 × 1.10 = 49,500.
2. After the second raise: 49,500 × 1.08 = 53,460.
3. Combined change: 53,460 ÷ 45,000 = 1.188, so the total rise is 18.8%, not 18%.
4. Rate change in percentage points: 10 − 8 = 2 percentage points.
5. Rate change in percent: (10 − 8) ÷ 8 × 100 = 25% relative increase.

Result: Two raises combine to 18.8%, and an 8% to 10% move is 2 points or 25%.

Reference tables

Quick reference: common percentages of common amounts

Each cell is the percentage multiplied by the amount at the top, computed exactly. Use it to sanity-check mental estimates.

Rise needed to recover from a fall

After a fall, the base is smaller, so recovering takes a larger percentage rise. The rise is 1 ÷ (1 − fall) − 1.

Common mistakes and tips

Check which number is the base

In share mode the base is the second number, and in change mode it is the starting value. Swapping them gives a different answer. A quick test: the base is the figure that stands for 100% in the question.

Do not add successive percentages

Two changes in a row multiply. A 10% rise then 8% is 18.8%, not 18%. A 20% rise then 20% fall is a 4% loss. Convert each rate to a factor like 1.10 or 0.80, multiply the factors, then subtract 1.

Percent and percentage points are not the same

A rise from 8% to 10% is 2 percentage points and 25% in relative terms. When you read a report, check which one is meant. If you are writing one, say points when you mean the simple difference.

Use total marks over total full marks

For an overall marks percentage, add every score and every maximum, then divide. Averaging the individual percentages is only equal when each paper has the same maximum. With 78/100, 64/80, 41/50 and 88/120 the totals give 271 ÷ 350 = 77.43%, while the average of percentages is 78.33%.

Reverse a discount by dividing

To find the price before a 20% discount, divide by 0.80. Adding 20% to the sale price gives a figure that is too low. The same rule applies to any rate you want to undo: divide by 1 minus the rate for a fall, or 1 plus the rate for a rise.

Do not compare percent changes from different bases

A 50% rise on a small amount can be less than a 5% rise on a large one. Look at the actual quantities as well as the percentages before drawing a conclusion, especially in news figures.

Where people use this calculator

Marks, attendance and cut-offs

Convert scores into a percentage, check attendance against a minimum such as 75%, and find out how many marks you still need. For example, with 205 of 350 so far, you need 95 of the last 150 to finish at 60% overall.

Sale prices and price rises

Work out the amount off and compare two offers. A 35% reduction on a 850 item takes off 297.50, leaving 552.50. Use change mode to see how much a price has risen between two visits to the shop.

Pay, bills and budgets

Find what percent of your pay goes to rent, or how much a bill rose from last month. Percent change turns two raw figures into one number you can compare across months or against inflation reports.

Reading statistics and reports

Survey results, election shares and company figures are all quoted in percent. Share mode lets you check whether a quoted share matches the raw counts, and change mode checks a headline growth figure.

Recipes, mixes and measures

Scaling a recipe by 150%, working out a 12.5% extra of an ingredient, or checking a concentration all use the percent-of mode. It keeps the arithmetic clean when you are working with awkward quantities.

Frequently asked questions

Related calculators

Results are estimates for general information. See our disclaimer and about page for how we build and check these tools.

Last reviewed: October 2026. Spotted a mistake? Tell us on the contact page.