Orpheus

Percentage Calculator

Four different percentage questions, without guessing which formula.

Inputs
15% of 200
30
Remaining
170
As a fraction
15⁄100
of: X÷100·Y · isWhat: X÷Y·100 · change: (Y−X)÷|X|·100

Multiplication commutes, so 15% of 200 equals 200% of 15. That often makes mental arithmetic easier.

Every tool runs entirely in your browser. Your files are never uploaded to a server.

Percentage questions come in a few distinct shapes and each needs a different formula. Pick the one you are asking — a percentage of a number, one number as a percentage of another, or a change between two — and enter the values.

How to use the Percentage Calculator

  1. Choose the question. Four modes: X% of Y, X as a percent of Y, percentage change, and increase or decrease.
  2. Enter the two numbers. Negative values are accepted where they make sense.
  3. Read the result. With the related figures beneath, since percentage questions usually come in pairs.

About percentage calculations

Most percentage mistakes are not arithmetic errors but the wrong question being answered, which is why this offers the four shapes separately rather than one box. The commonest trap is assuming percentage changes are reversible. They are not, because each is measured against whatever the value is at that moment: a stock that falls fifty percent must rise one hundred percent to recover, and a price marked up twenty percent then discounted twenty percent ends below where it started. The second trap is confusing percent with percentage points. An interest rate moving from four to six percent has risen two percentage points and fifty percent, and both statements are true, which is precisely why careful reporting always says which it means. The third is the base: fifteen percent of a bill calculated before tax is not the same tip as fifteen percent after. None of this is difficult once the question is stated precisely, and stating it precisely is most of the work. Everything here is computed in your browser and nothing you type is transmitted.

Frequently asked questions

Why is +10% then −10% not back to where I started?
Because each percentage is taken from a different base. 100 rises to 110, then 10% of 110 is 11, leaving 99. Percentage change always measures against the current value, not the original.
What is the difference between percent and percentage points?
A rise from 4% to 6% is two percentage points, but a fifty percent increase. Financial and polling reporting uses points precisely to avoid that ambiguity.
Why can I not calculate percentage change from zero?
Any increase from zero is infinite in percentage terms, so the result is undefined. Report the absolute change instead.
Is there a trick for mental arithmetic?
Yes — percentages commute. 15% of 200 is the same as 200% of 15, which is 30 and far easier to do in your head. Swap them whenever one side is friendlier.

Last updated