🧮 Percentage Calculator

Percentage problems are easy to get backwards because the same three numbers can describe two different questions. This calculator splits them into four modes so you always know which quantity is the unknown, and every answer updates as you type — there is no submit button.

The Three Core Problems (Plus Reverse)

Almost every percentage question is one of three types, and the tool also handles the inverse of the first.

1. Find a percent of a number. You know the rate and the base; you want the part. Twenty percent of 150 is the part.
2. Find what percent one number is of another. You know the part and the base; you want the rate. Thirty out of 150 is what percent?
3. Find the percent change between two numbers. You know an old value and a new value; you want the increase or decrease as a rate.
4. Reverse percentage. You know the part and the rate; you want the base. Thirty is 20% of what number?

Worked Examples with Numbers

The tool’s own defaults demonstrate each mode:

Mode	Question	Worked result
Basic	What is 20% of 150?	30
Percent-of	30 is what percent of 150?	20%
Change	100 increases to 150	+50, which is +50%
Reverse	30 is 20% of what?	150

Notice that basic, percent-of, and reverse all use the same trio (150, 20, 30) and simply move the unknown. Change mode is the odd one out: it compares an original to a final value, and its direction sign flips if the new number is lower. Going from 150 down to 100 yields a change of −50 and −33.33%, because the base for a decrease is the original 150, not the final 100.

Formulas Behind Each Mode

• Basic: (percent / 100) * value
• Percent-of: (part / whole) * 100
• Change: ((to - from) / from) * 100, with the absolute change shown alongside
• Reverse: part / (percent / 100)

One practical consequence is that a rise and a fall of the same amount are not symmetric. A 33.33% increase is needed to recover from a 25% decrease, because each percentage is measured against a different base. This is why a stock that falls 50% must double to break even.

Reading the Results and Rounding

The percent-of answer and the change percentage are formatted to two decimal places. The basic answer, the reverse answer, and the absolute change are printed as raw computed values, so a result like 33.33333333333333 can appear. If you are entering the numbers manually, treat the unrounded values as exact and round only your final presentation digit.

Common Mistakes and Edge Cases

• Using the wrong base. A change from 100 to 150 is +50%, but a change from 150 to 100 is −33.33%, not −50%. Always divide by the starting value.
• Dividing by zero. Percent-of when the whole is zero, and reverse when the percent is zero, have no meaningful answer; the tool surfaces an error rather than returning infinity.
• Change from zero. If the original value is zero, there is no percentage to compute, since the denominator is zero. The tool reports a non-finite percentage instead of guessing.
• Confusing the rate with the amount. A 20% discount is not 20 currency units; it is 20% of the price it is applied to.
• Adding percentages directly. Two successive 10% increases do not total 20%; they compound to 21% because the second applies to the already-increased value.
• Reverse with the wrong rate. The percent in reverse mode is the rate applied to the unknown whole, so make sure you are not passing a change rate instead.

Real-World Scenarios

Percentage math shows up in a handful of recurring shapes, and naming the shape makes the mode obvious.

• Sale pricing. A jacket originally 120 is marked 30% off. Basic mode gives 36, the discount, so the sale price is 84. If the tag only shows the sale price and the remaining fraction, reverse mode recovers the original.
• Tips and bills. A 180 dinner bill with an 18% tip adds 32.40, for a total of 212.40. Splitting three ways makes each share 70.80.
• Tax and VAT. A 250 invoice plus 20% tax is 300. To go the other way, a tax-inclusive total of 300 at 20% reverse-calculates to 250, since the tax was applied to the pre-tax amount.
• Growth and decline. Revenue moving from 4.2 million to 5.0 million is a change of 0.8 million, about a 19.05% increase. Falling from 5.0 to 4.2 has the same 0.8 million change but roughly a 16% decrease, because the direction changes the base.
• Grades and scores. A score rising from 60 to 75 is a 25% improvement; the same 15 points from 80 to 95 is only 18.75%.
• Statistics and proportions. If 45 of 300 surveyed people chose an option, that is 15% of respondents.

Two patterns recur across all of these. First, identify whether the unknown is the part, the whole, or the rate before choosing a mode. Second, confirm the base: a percentage change is always measured against the starting value, while a discount or tax is measured against the price it applies to.

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