# Percentage calculations: the four formulas

> There are four distinct percentage calculations and each needs a different formula. X% of Y is Y x (X/100). X as a percent of Y is (X/Y) x 100. Percentage change is (new - old) / old x 100, always dividing by the old value. Removing a percentage means dividing, not subtracting.

Source: https://rankcert.com/blog/percentage-calculations-explained
Published: 2026-09-02 · Updated: 2026-09-02

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Almost every percentage mistake is a mismatch between four calculations that look similar and are not. Getting them straight takes about five minutes and stops a whole category of quiet spreadsheet errors.

## The four calculations

**What is X% of Y?** Multiply. 15% of 240 is 240 x 0.15 = 36. Converting the percentage to a decimal first is the whole trick.

**X is what percent of Y?** Divide, then multiply by 100. 36 out of 240 is (36 / 240) x 100 = 15%.

**Percentage change from old to new.** (new - old) / old x 100. From 240 to 300 is (60 / 240) x 100 = 25%.

**Removing a percentage from a total.** Divide. To strip 20% VAT from a gross figure of 120, divide by 1.2 to get 100. Subtracting 20% of 120 gives 96, which is wrong by four.

Free tool: [Percentage Calculator](https://rankcert.com/tools/percentage-calculator) - Work out X% of Y, what percentage one number is of another, and percentage increase or decrease between two values.

## The trap in percentage change

The denominator is always the original value. Using the new one gives a different number, and it is a plausible-looking different number, which is what makes it dangerous.

From 240 to 300 is a 25% increase. From 300 to 240 is a 20% decrease. Same two numbers, same absolute gap, different percentages, because the base changed.

This also explains why a 50% fall does not undo a 50% rise. 100 rises to 150, then falls by half to 75. The second percentage is applied to a larger base, so it removes more. To reverse a 50% rise you need a 33.3% fall.

## Reverse percentages

This is the one that costs money. If a discounted price is 56 after 30% off, the original is not 56 + 30%. It is 56 / 0.7 = 80.

The general rule: to add a percentage, multiply by (1 + rate). To remove one, divide by (1 + rate). Every tax, discount and markup calculation is one of those two.

Markup and margin are the same trap wearing different hats. A product costing 60 and selling at 100 carries a 66.7% markup on cost and a 40% margin on price. Quoting one when a stakeholder means the other is how pricing meetings go wrong.

## Percent versus percentage points

A conversion rate moving from 2% to 3% has risen by one percentage point and by 50 percent. Both statements are true and they describe the same change.

Which one you use is not a stylistic choice. "Conversion improved 50%" and "conversion improved 1 point" land completely differently in a board deck, and the second is usually the honest framing when the starting number is small.

## Compounding

Sequential percentage changes multiply rather than add. Three consecutive 10% increases are not 30% - they are 1.1³ = 1.331, so 33.1%.

This matters for anything measured monthly. 5% monthly growth is 79.6% annually, not 60%. Monthly churn of 5% leaves 54% of a cohort after a year, not 40%.

## Quick checks

- Percentage change should always be divided by the value you started from.
- To reverse a percentage, divide - never subtract.
- Sequential changes multiply, they do not sum.
- If the base changed between two figures, the percentages are not comparable.

Run the numbers through the [percentage calculator](/tools/percentage-calculator) if you want to check any of these against a worked example.