Percentage Calculator
Use one calculator for the three percentage questions that are easy to mix up: find a percentage of an amount, find what percentage a part represents of a whole, or measure the increase or decrease between two values. The result shows the formula as well as the answer, so you can check whether the inputs have the meaning you intended. Everything runs in this browser tab without sending your numbers to a server.
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Add to Chrome — freeWhat it does
- Percentage of an amount calculation
- Part-to-whole percentage calculation
- Percentage increase and decrease
- Visible formula for checking the result
- Local browser-only processing
How to use Percentage Calculator
- 1
Choose the question
Select whether you want a percentage of an amount, a part as a percentage of a whole, or the percentage change from an original value to a new value. Picking the question first gives each input an unambiguous label.
- 2
Enter the two values
Fill in the labeled fields. For a percentage of an amount, enter the rate and amount. For a ratio, enter the part and whole. For change, enter the old value first and the new value second.
- 3
Read the working
The answer updates immediately and the line underneath shows the operation used. A negative change means the new value is lower than the original one. A zero whole or original value cannot produce a meaningful percentage.
- 4
Copy or reset
Use Copy result to put both the question and the working on your clipboard. Clear removes the two values so you can start another calculation quickly.
How it works
The calculator keeps three related formulas separate because the denominator is different in each one. That small distinction is the source of most percentage mistakes.
For a percentage of an amount, the first value is a rate. The tool divides it
by 100 and multiplies by the amount: rate ÷ 100 × amount. Thus 12 percent of
250 is 30. If you need the price after a 12 percent discount, 30 is only the
discount; subtract it from 250 to get 220.
For a part as a percentage of a whole, the tool divides the part by the whole and multiplies by 100. This can produce a result below 100 percent when the part is smaller than the total, exactly 100 percent when they match, or above 100 percent when the measured part exceeds the chosen reference.
For percentage change, the calculator subtracts the original value from the new value, then divides by the absolute original value. Multiplying by 100 turns that ratio into a percentage. A positive answer indicates growth and a negative answer indicates decline. Using the original value as the baseline is important: using the new value instead would describe a different comparison.
Reading the result
The visible working is deliberately part of the answer. Before using a result in a budget, report, or spreadsheet, check that the field labels match the sentence you are trying to answer. “15 percent of 240” is not the same as “240 is what percent of 15.” The tool also leaves full precision in the calculation and formats the display to a readable number of decimal places, which is useful for rates that do not divide evenly.
When to use it
The percentage-of mode is useful for discounts, tax estimates, commissions, tips, and allocating a fixed amount. The part-to-whole mode suits completion rates, survey responses, pass rates, and progress reporting. Percentage change is the right view for comparing a current measurement with its prior baseline, such as monthly revenue, response time, or inventory. For financial decisions, keep the unrounded result until the final currency display so intermediate rounding does not accumulate.
A rise and an equal fall do not cancel
This is the arithmetic that surprises people most often, and it is worth internalising because it appears everywhere prices and metrics are discussed.
Take 100, add 20 percent, and you have 120. Now take 20 percent off, and you get 96 — not back to 100. The two moves are the same number of percent and different amounts of money, because the second is calculated against a larger base.
The gap widens fast. A 50 percent fall needs a 100 percent rise to recover. A 90 percent fall needs a 900 percent rise. This is why a portfolio down 50 percent in one year and up 50 percent the next is not level; it is down 25 percent.
The same asymmetry runs through discounts. Two successive 20 percent reductions are not 40 percent off — they are 36 percent, because the second applies to the already-reduced price. A shop advertising "20% off, then 20% off at the till" is offering less than one 40 percent discount, and the difference is real money.
When you need to reverse a change rather than repeat it, work from the original base. Going from 120 back to 100 is a fall of 16.67 percent, which the percentage-change mode will tell you if you enter the two numbers in that order.
Percentage points are not percent
Two words that get used interchangeably in writing and mean different things in arithmetic.
If an interest rate moves from 4 percent to 5 percent, that is a rise of one percentage point — and a rise of 25 percent, because one is a quarter of four. Both statements are true and they describe the same event with numbers that differ by a factor of twenty-five.
The ambiguity is exploitable, and it is exploited. "Support rose 50 percent" sounds dramatic and may mean a move from 2 percent to 3 percent. "Fees increased by only 2 percent" may mean a rise from 1 percent to 3 percent, which is a tripling.
The habit that protects you: whenever a change is described in percent and the underlying quantity is itself a percentage, ask for both numbers. When writing your own figures, say "percentage points" for the difference and "percent" for the relative change, and give the two raw values so a reader can check.
The percentage-change mode computes the relative change. For percentage points, subtract the two figures directly.
Examples
Finding a sale price discount
This is the discount amount, not the final price. Subtracting 17 from 85 gives 68, which is the amount a customer pays after the 20 percent discount. Keeping those two steps separate prevents a discount calculation from being mistaken for the discounted total.
Comparing completed applications
The part-to-whole question answers how much of the total has been completed. Because 42 is three quarters of 56, the result is 75 percent. The order of the fields matters; reversing them would answer a different question.
Frequently asked questions
What is the difference between percentage of and percentage change?
Percentage of multiplies a rate by an amount, such as finding 15 percent of 240. Percentage change compares an old value with a new value and divides their difference by the original value. They use different inputs and answer different questions, even when both results are displayed with a percent sign.
How do I calculate what percent one number is of another?
Choose the part-to-whole mode, put the smaller measured amount in Part and the reference total in Whole, then read the result. The calculation is part divided by whole multiplied by 100. For example, 18 out of 24 is 75 percent, because 18 divided by 24 equals three quarters.
Can percentage change be negative?
Yes. A negative result means the new value is below the original value, so it represents a decrease rather than an increase. For example, changing from 80 to 60 gives negative 25 percent because the loss of 20 is one quarter of the original 80. The sign carries useful direction information.
Why does the calculator reject a zero original value?
Percentage change uses the original value as its denominator. Dividing by zero is undefined, so there is no mathematically valid baseline against which to measure the change. If a process moved from zero to a positive result, report the absolute change and describe the new process separately instead of inventing a percentage.