Percentage Calculator

The six calculations, and which one you need

"What is X% of Y" is the everyday case: a 15% tip on a £64 bill, 20% VAT on a net price, 8% commission on a sale. Divide the percentage by 100 and multiply.

"X is what percent of Y" turns two absolute numbers into a proportion: 34 out of 40 as a score, 1,200 of a 5,000 target. Divide, then multiply by 100.

"Percentage change from X to Y" measures movement over time — a price rise, a traffic increase, a weight loss. Subtract the old value from the new, divide by the old, and multiply by 100. Which value is the baseline matters enormously and is the source of most percentage errors.

Adding and subtracting a percentage handle markups and discounts directly. "X is Y% of what number" is the reverse case: you know the part and the proportion and want the whole — useful for backing out an original price from a sale price.

Percentage points are not percentages

If an interest rate moves from 4% to 6%, that is a rise of two percentage points and an increase of fifty percent. Both statements are true and they describe the same event with wildly different emotional weight, which is precisely why the distinction gets abused in reporting.

The rule is simple: use percentage points when comparing two percentages, and percent when describing relative change. A poll moving from 40% to 44% has gained four points, or ten percent of its previous share.

When you read a percentage change in a headline, the useful question is always "percent of what?" A statistic that a treatment "halves your risk" means very little without knowing whether the risk went from 80% to 40% or from 0.002% to 0.001%.

Why percentage changes do not cancel out

A 50% fall followed by a 50% rise does not return you to where you started. £100 falls to £50, then rises by 50% of £50 — which is £25 — leaving £75. The percentages are calculated on different bases.

To reverse a drop of X%, you need a rise of X / (100 − X) × 100. Recovering from a 50% loss requires a 100% gain. Recovering from an 80% loss requires 400%.

The same asymmetry applies to discounts and markups. A 20% markup followed by a 20% discount leaves you 4% below the original price. Retailers who mark up and then discount are not being generous; they are exploiting the fact that the two percentages have different bases.

Stacking discounts and taxes

Successive discounts multiply rather than add. Thirty percent off, then a further twenty percent off, is not fifty percent off — it is 0.7 × 0.8 = 0.56, so 44% off. This is a common and profitable source of confusion in retail.

Order does not matter when everything is multiplicative: applying tax then a discount gives the same result as the discount then the tax. It does matter when a fixed amount is involved — a £10 voucher applied before or after a percentage discount produces different totals, and the voucher is worth more applied afterwards.

The reverse-percentage calculation is the one to reach for when you want to know the original price from a sale price. If something is £48 after 20% off, it was £48 ÷ 0.8 = £60, not £48 + 20%.