Percentage Calculator

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This is one of several utilities. For the full list of utilities, see All tools.

Percentage calculations are fundamental to everyday numeracy, but they are easy to get wrong under pressure, especially when working with percentage change versus percentage of a total, or when trying to work backwards from a discounted price to the original. The formula varies depending on exactly what question you are asking, and mixing up the formulas produces confidently wrong answers.

The ToolzPedia Percentage Calculator solves four distinct percentage problems with separate clearly-labelled calculators: What is X% of Y (basic percentage of a number), X is what percent of Y (percentage expressed as a fraction), percentage change from X to Y (increase or decrease), and what original value produces X after a Y% change (reverse percentage). Each section shows the formula used alongside the result so you can verify the logic and adapt it.

All calculations run in your browser with no data transmitted anywhere.

Use the tool edit

How to use Percentage Calculator edit

Follow these steps to use the tool:

  1. Choose a mode

    Pick what you want to calculate: a percentage of a number, percent change, add/remove percentage, etc.

  2. Enter values

    Fill in the two numbers and click Calculate.

  3. Get the result

    See the exact answer along with the formula used.

Frequently asked questions edit

A percentage point is the arithmetic difference between two percentages. If the interest rate rises from 3% to 5%, it rises by 2 percentage points. The percentage change in the rate is 66.7% (2 divided by 3). Confusing these two is one of the most common statistical errors in media reporting.
Compound percentage changes multiply the result of each period's change rather than adding them. To apply a 10% increase followed by a 5% increase: 100 × 1.10 × 1.05 = 115.5, not 100 + 10 + 5 = 115. The difference grows significant over many periods or large percentages.
Divide the first number by the second and multiply by 100. If sales this month are 340 and last month were 400, then 340 / 400 × 100 = 85%. This month's sales are 85% of last month's (a 15% decrease).

Use cases edit

Retail discounts

Calculate the sale price when an item is 35% off, or work backwards to find the original price when you know the discounted price and the discount percentage.

Financial analysis

Calculate month-on-month percentage change in revenue, cost, or user counts. The percentage change formula (new minus old, divided by old, times 100) is the same calculation used in financial reports and dashboards.

Grade and score calculation

If you scored 68 out of 85 on an exam, what is your percentage? The "X is what percent of Y" calculator answers this in one step.

Tax calculations

Calculate 20% VAT on a price, or find the pre-tax amount when you only know the tax-inclusive total. The reverse percentage mode handles the latter.

Tip calculation

Calculate a 15%, 18%, or 20% tip on any restaurant bill amount.

Nutrient and composition analysis

If a food item contains 12g of protein and has 250g total weight, what percentage is protein? Use the fraction percentage mode.

How it works edit

What is X% of Y: result = (X / 100) × Y. This is the most fundamental percentage calculation.

X is what percent of Y: result = (X / Y) × 100. This finds what fraction X is of Y, expressed as a percentage.

Percentage change from X to Y: result = ((Y - X) / X) × 100. A positive result is an increase; a negative result is a decrease.

Reverse percentage (what was the original if Y is X% of it): original = Y / (X / 100), which simplifies to original = Y × (100 / X). For finding pre-discount prices: original = discounted price / (1 - discount percentage/100).

Tips and best practices edit

  • Percentage change and percentage of are different calculations. A common mistake is using the wrong formula when asked "by what percentage did sales increase?" (percentage change) versus "what percentage of target did we achieve?" (fraction percentage).
  • When calculating a tip, round the result to the nearest convenient number. A tip of $8.37 is mathematically exact but practically awkward. Round up to $9 or $10 for simplicity.
  • Percentage decreases have a lower absolute bound than percentage increases. You cannot decrease something by more than 100%, but you can increase it by any positive percentage. A 50% decrease followed by a 50% increase does not return to the original value; it returns to 75% of it.

Common mistakes edit

Calculating a percentage increase on the new value instead of the old

Percentage change is always calculated relative to the starting (old) value, not the ending (new) value. Going from 100 to 120 is a 20% increase (20/100). Going from 120 to 100 is a 16.7% decrease (20/120), not a 20% decrease.

Forgetting that percentage changes do not reverse symmetrically

A 25% decrease followed by a 25% increase does not return to the original. It returns to 93.75% of the original. To reverse a 25% decrease, you need a 33.3% increase.

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See also edit