The Percentage Formula: Every Version Explained

Almost every percentage question you will ever meet is a variation of one idea: a part compared with a whole, expressed out of 100. Once you can see which part of a problem is the "part", which is the "whole", and which direction the change runs, the formula practically writes itself. This guide collects every version of the percentage formula in one place, explains when each one applies, and links each to a calculator that shows the working step by step.

1. The Core Formula: Part, Whole, Percentage

Three quantities, one relationship. Know any two and you can find the third.

The first row is what the What Percentage Calculator does. The second is the Percentage Calculator. The third is the Reverse Percentage Calculator. Same formula, three doors into it.

2. Percentage Increase Formula

Percentage Increase = ((New − Original) ÷ Original) × 100

Use it whenever one value clearly comes before the other. A salary of $52,000 rising to $58,000 is ((58,000 − 52,000) ÷ 52,000) × 100 = 11.54%. The denominator is always the earlier value; that is the single most common source of error.

To apply an increase rather than measure one, multiply: New = Original × (1 + rate). A 12% rise on 450 gives 450 × 1.12 = 504. Check any of these against the Percentage Increase Calculator, or follow the worked three-step method in how to calculate percentage increase.

3. Percentage Decrease Formula

Percentage Decrease = ((Original − New) ÷ Original) × 100

A price falling from $1,200 to $899 is ((1,200 − 899) ÷ 1,200) × 100 = 25.08%. To apply a decrease, multiply by (1 − rate): a 15% cut on 240 leaves 240 × 0.85 = 204.

The critical property to remember is asymmetry. A 50% fall followed by a 50% rise does not restore the original — 100 → 50 → 75. Verify with the Percentage Decrease Calculator.

4. Reverse Percentage Formula

Original = Final ÷ (1 ± rate)

Use a plus when something was added and a minus when something was taken away. A jacket costs $64 after 20% off, so the pre-sale price was $64 ÷ 0.80 = $80. A bill of $120 including 20% VAT was $120 ÷ 1.20 = $100 before tax. Subtracting 20% from the final figure gives the wrong answer in both cases — this is the classic reverse-percentage trap. The Reverse Percentage Calculator handles both directions.

5. Percentage Difference Formula

Percentage Difference = (|A − B| ÷ ((A + B) ÷ 2)) × 100

Use this when neither value is the starting point — two competing quotes, two sensor readings, two shop prices. Because it divides by the average of the two values, the answer is the same whichever order you enter them, and it is always positive. Comparing 40 and 60 gives (20 ÷ 50) × 100 = 40%, whereas percentage change from 40 to 60 is 50%. Both are correct; they answer different questions. The Percentage Difference Calculator keeps them apart.

6. Discount Formula

Saving = Price × (rate ÷ 100) and Sale Price = Price × (1 − rate ÷ 100)

30% off $150 saves $45 and leaves $105. Stacked discounts multiply rather than add: 20% off followed by an extra 10% off is 0.80 × 0.90 = 0.72, a 28% total reduction. Run the numbers in the Discount Calculator.

7. Markup and Margin Formulas

Markup% = ((Price − Cost) ÷ Cost) × 100 — based on what you paid.

Margin% = ((Price − Cost) ÷ Price) × 100 — based on what you charge.

These two are constantly confused, and the gap is expensive: a 100% markup is only a 50% margin. Use the Markup Calculator to price from cost, and read Margin vs Markup for the full comparison.

8. VAT and Sales Tax Formulas

Adding: Gross = Net × (1 + rate). Removing: Net = Gross ÷ (1 + rate).

At a 20% rate, $100 net becomes $120 gross, and $120 gross unwinds to $100 net. The VAT Calculator does both directions and shows the tax component separately, which is what you need for bookkeeping.

9. Percentage Points — Not a Formula, but Essential

When the quantities themselves are percentages, the language changes. An interest rate moving from 4% to 6% has risen by 2 percentage points, and by 50% in relative terms. Central banks and statistical agencies use percentage points precisely to avoid this ambiguity, and headlines that ignore the distinction can overstate a change several times over. Read more in What Is a Percentage?

Mental Shortcuts Worth Memorising

• 10% — move the decimal one place left. 10% of 84 is 8.4.
• 5% — half of 10%. 5% of 84 is 4.2.
• 15% — 10% plus 5%. Useful at restaurants; see the Tip Calculator.
• 1% — move the decimal two places left, then scale up for any rate.
• Reversibility — x% of y always equals y% of x. 18% of 50 is the same as 50% of 18, which is 9.

Choosing the Right Formula

Sources and method: the formulas above follow standard arithmetic conventions for relative change and difference, and the percent versus percentage-point distinction matches the reporting practice of statistical agencies such as the U.S. Bureau of Labor Statistics. Written and reviewed by the Snap Percent Calc editorial team; every worked example was verified against the site's own calculators.