Percentage of a Percentage Calculator

How it works

To find a percentage of another percentage, convert the first percentage to its decimal form by dividing by 100, then multiply by the second percentage. The result is expressed as a percentage.

The formula

Why this works: Taking a percentage of a number requires converting that percentage to a decimal first. When the "number" is itself a percentage, the same rule applies. Dividing the first percentage by 100 converts it to a decimal, then multiplying by the second gives the proportion of that second percentage. The result is always smaller than both inputs when both are under 100%.

Worked examples

When to use this

This calculation appears whenever a rate applies not to a full total but to a subset of it, or when you need to understand what a proportion of a rate actually equals across a whole group.

• Partially vatable invoices. A freelancer's invoice is £2,000, but only 70% of the work is subject to VAT at 20%. The VAT is 20% of 70% = 14% of the total, which is £280. Trying to apply 20% to the full £2,000 would overcharge by £120.
• Overlapping survey groups. A HR survey finds 60% of staff work remotely, and of those, 45% report lower stress. This means 27% of all staff work remotely and report lower stress, which is a more useful figure for a wellbeing strategy than the 45% in isolation.
• Cashback and rewards on eligible spending only. A credit card offers 2% cashback on grocery spending, and groceries account for 35% of the cardholder's monthly spend of £1,500. The effective cashback rate on total spend is 2% of 35% = 0.7%, worth £10.50 per month.
• Commission on a subset of sales. An agent earns 8% commission on overseas sales, which make up 25% of the company's total turnover of £800,000. The commission is 8% of 25% = 2% of turnover = £16,000 per year.
• GCSE and A-Level conditional probability. A statistics question asks: if 40% of students study history and 65% of history students also study geography, what percentage of all students study both? The answer is 40% of 65% = 26%, which requires this exact calculation.

Understanding the result

When both inputs are under 100%, the result is always smaller than either input. This is mathematically guaranteed: you are taking a fraction of a fraction. 20% of 50% = 10%, which is smaller than both 20 and 50. If your result appears larger than either input, check you have not accidentally added or swapped them.

The result is already expressed as a percentage. It does not need to be multiplied or divided further to be used in reports, comparisons, or further calculations. 12% of a total is 12%, regardless of how it was derived.

The calculation is commutative: 20% of 50% gives the same result as 50% of 20%. Both equal 10%. This means the order in which you enter the two percentages does not affect the answer, though the framing (which is the "of" and which is the "rate") matters for interpreting what the result represents in context.

Related concepts

• ➡ calculate what any percentage of a fixed total actually comes to
• ➡ discount calculator works out the total saving when two percentage reductions apply in sequence
• ➡ measure the arithmetic difference between two percentage values directly

How to do this in Excel

In Microsoft Excel or Google Sheets, put the first percentage in cell A1 and the second percentage in cell B1, then enter this formula in C1:

This converts A1 to its decimal form and multiplies by B1 to give the result as a percentage. For example, with A1 = 20 and B1 = 50, the formula returns 10. If your percentage values are stored in cells already formatted as Percentage (showing "20%" rather than "20"), use =A1*B1*100 instead to avoid double-dividing.

How to do this without a calculator

Convert the first percentage to a decimal by moving the decimal point two places left, then multiply by the second percentage. For 20% of 50%: 20 / 100 = 0.2, then 0.2 x 50 = 10%. For simple percentages like 10%, 25%, or 50% as the first value, the mental arithmetic is quick.

For 10% of any percentage, simply divide that percentage by 10. For 50% of any percentage, halve it. For 25%, halve it and halve again. These shortcuts cover many real-life scenarios without any calculation at all.

A useful cross-check: if you reverse the inputs, the answer should be the same. 30% of 70% = 21%, and 70% of 30% = 21%. If the two approaches give different answers, one of the multiplications is wrong.

Common mistakes

Related calculators