Percent Calculator: How to Use It

This percent calculator works out any of the three core percentage problems: finding a percentage of a number, finding what percent one number is of another, and finding the original number when a percentage and its result are known. You enter the two or three values you have, and it returns the missing value instantly, along with the formula that produced it. The calculator below handles the first two cases directly; for reverse percentage problems, it shows the steps so you can apply them to your own numbers.

Formula

Three basic formulas cover the standard percentage problems. Let P be the percentage (the number with a % sign), B be the base (the whole or total), and A be the amount (the part of the base).

• Find A when P and B are known: A = (P / 100) × B. This answers “What is P% of B?”
• Find P when A and B are known: P = (A / B) × 100. This answers “A is what percent of B?”
• Find B when P and A are known: B = A / (P / 100). This answers “A is P% of what number?”

All three are rearrangements of the same relationship: A = (P/100) × B. The calculator above uses the first two formulas directly. For the third, you can rearrange the first: B = A × 100 / P.

Worked Example

Using the default values from the calculator: A = 50, B = 20, P = 10.

1. “A is what % of B?” P = (50 / 20) × 100 = 2.5 × 100 = 250%. So 50 is 250% of 20.
2. “P% of B” A = (10 / 100) × 20 = 0.1 × 20 = 2. So 10% of 20 is 2.

These match the calculator’s outputs: 250.00% and 2.00.

When to Use Each Mode

People typically reach for a percent calculator in three everyday situations:

• Sales and discounts: “What is 30% off $80?” You compute 30% of 80 (which is 24) and subtract it from 80 to get $56. Or you can directly compute 70% of 80.
• Grades and scores: “I got 42 out of 50 on a test – what percent is that?” You use the “A is what % of B” mode: (42/50) × 100 = 84%.
• Reverse percentage: “A jacket costs $45 after a 25% discount. What was the original price?” Here $45 is the amount after discount, so it equals 75% of the original. Original = 45 / 0.75 = $60.

The reverse case is the one that confuses most people. If you subtract the discount from 100% first, you get the percentage that the sale price represents. Then divide the sale price by that decimal.

Common Mistakes and How to Avoid Them

Several errors trip up even careful users:

• Mixing up the base and the amount. In “what percent is 20 of 50?”, 50 is the base, 20 is the amount. Swapping them gives 250% instead of 40%.
• Forgetting to convert percent to decimal. In the formula A = (P/100) × B, the division by 100 is essential. Using P directly (e.g., 10 × 20 = 200) gives a wildly wrong answer.
• Adding percentages instead of multiplying. A 10% increase followed by a 10% decrease does not return to the original. It results in 0.9 × 1.1 = 0.99, or 1% less. Percent changes multiply, not add.
• Rounding too early. If you round intermediate values, you can lose accuracy. Round only the final answer.

How to Read the Result

The output “A is what % of B” gives a percentage that can be greater than 100% when A is larger than B. That is correct – for example, 50 is 250% of 20. The output “P% of B” gives a plain number (the amount), not a percentage. If you need the result as a percentage of something else, you must apply a second calculation.

When the result is a monetary value, round to two decimal places (cents). When it is a count or a measurement, round to a sensible precision – you cannot have 3.7 people, but you can have 3.7 kilograms. The calculator gives two decimals by default, which suits most purposes.

Limits of the Formula

Percentage formulas assume a linear relationship. They do not apply to compound growth (like interest or inflation) unless you use the compound formula, which involves exponents. They also assume the base is constant. For example, a “10% increase” followed by a “10% decrease” is not a net zero change because the second percentage applies to a different base. The formulas here are for single-step calculations only.

Another limit: the calculator cannot know which of the three values is the unknown. You must choose the correct mode. If you are unsure, write down what you know and what you are looking for, then match it to one of the three formulas above.

Frequently Asked Questions

How do I calculate a percentage increase or decrease?

Subtract the original value from the new value, divide by the original value, then multiply by 100. For example, if a price goes from $50 to $60, the increase is (60-50)/50 × 100 = 20%. If it goes from $60 to $50, the decrease is (50-60)/60 × 100 = -16.67% (a 16.67% decrease).

What is the difference between percentage and percentage points?

A percentage point is the arithmetic difference between two percentages. If an interest rate rises from 5% to 7%, it increased by 2 percentage points. In relative terms, it increased by 40% (since 2/5 = 0.4). The two numbers are often confused in news reports.

How do I find the original number before a percentage was added?

If you know the final number and the percentage that was added, divide the final number by (1 + percentage/100). For example, if a price includes a 20% tax and the final price is $120, the pre-tax price is 120 / 1.20 = $100. This is the reverse of the “P% of B” formula.

Can a percentage be more than 100?

Yes. A percentage is just a ratio multiplied by 100. If the part is larger than the whole, the percentage exceeds 100. For instance, if a company’s revenue this year is $150,000 and last year it was $100,000, this year’s revenue is 150% of last year’s.

Why do I get different results when I calculate a discount in two steps?

Because the order matters when percentages are applied to different bases. A 20% discount followed by a 10% discount is not the same as a 30% discount. The first reduces the price to 80%, then the second reduces that to 72% of the original (0.8 × 0.9 = 0.72). Always apply discounts sequentially, not by adding the percentages.

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in a | Value A | - | 50 | 0
in b | Value B | - | 20 | 0
in p | Percent | % | 10 | 0
out pct_of | A is what % of B | % | (a / b) * 100 | 2
out pct_of_b | P% of B | - | (p / 100) * b | 2