Percentage Calculator — of, increase, decrease and change

How to use

What it's for

Answer the everyday percentage questions — 20% of a price, what percent one number is of another, a figure after a rise or a cut, or how much something changed.

Before you start

Have the two numbers your question is about, such as a price and a discount rate, or an old figure and a new one.

Pick your question
Press the button that matches it: % of for 20% of 1,500, is what % for 300 out of 1,500, increase or decrease to add or take off a percentage, and change for the percent difference between two numbers.
Type the two numbers
The two boxes read like a sentence, such as What is 20 of 1500, or From 100 to 150. Picking a question fills the boxes with example numbers, so type yours after you choose.
Press Calculate
Press Calculate. The answer already updates as you type; the button brings it into view.

Reading the result

Answer: the big number — the amount, for % of. On the other questions the heading above it names the question instead, and an answer that is a percentage ends in %.
The line under it: the sum that gave the answer, written out, such as 20.00 ÷ 100 × 1,500.00. On change, a minus sign means the number went down.
Calculation: each number you typed and the result, step by step, so you can follow how the answer was reached.

If it goes wrong

Both boxes need a number.: a box holds something that is not a plain number — often a comma, as in 1,500, or a % sign. Type 1500 instead.
A percentage change from zero is undefined: change cannot start from 0, because a rise from nothing has no percentage. Compare the two amounts directly instead.
Up 10% and then down 10% does not get back to the start: the second percentage is taken of the bigger number. Work each step separately, using the first answer as the new starting number.

What this is

Most percentage mistakes are not arithmetic mistakes — they are answering a different question from the one asked. "20% of 1,500" and "20 is what percent of 1,500" look almost identical written down, and give 300 and 1.33% respectively.

So the questions are kept apart here, each with its own two fields and its own sentence. Pick the one that matches what you actually want to know.

Questions

If a price goes up 10% and then down 10%, is it back to the original?

No. ₱100 up 10% is ₱110; ₱110 down 10% is ₱99. The second percentage applies to the larger amount, so you end up below where you started. This catches people out constantly, and it is why a 10% discount never quite undoes a 10% price rise.

What is the difference between "20% of 1,500" and "20 is what percent of 1,500"?

They are different questions with different answers. The first gives 300. The second gives 1.33%. They are kept as separate modes here precisely so they cannot be confused.

Why does a change from zero not work?

Because it is undefined. Going from 0 to 50 is an infinite increase — there is nothing to compare against. Returning "100%" would be a made-up answer, so the tool says so instead.

The questions

P% of X

P ÷ 100 × X

X is what percent of Y

X ÷ Y × 100

Increase X by P%

X + (P ÷ 100 × X)

Change from A to B

(B − A) ÷ |A| × 100

The last one divides by the magnitude of A, so a move from −100 to −50 reads as a 50% improvement rather than a 50% fall.

Calculation