Percentage Calculator
Three percentage operations in one tool: find X% of a number, work out what percent A is of B, and calculate the percentage change between two values.
How it works
Percent of a number: number × percent ÷ 100. So 18% of £850 is 850 × 18 ÷ 100 = £153.
What percent A is of B: A ÷ B × 100. £45 out of £180 is 45 ÷ 180 × 100 = 25%. The answer can exceed 100% — £250 out of £200 is 125%, meaning A is a quarter bigger than B — which is perfectly valid and often exactly what you want when comparing this year against last.
Percentage change: (new − old) ÷ old × 100. A price rising from £2,000 to £2,500 is a 25% increase; the same formula gives a negative result for decreases. Always divide by the ORIGINAL value — dividing by the new one is the classic mistake.
Percentage changes are not symmetric, and this trips people up constantly: a 25% fall needs a 33.3% rise to get back to where you started. Drop £100 to £75, and recovering the lost £25 from a £75 base is 25 ÷ 75 × 100 = 33.3%. The smaller the base you are climbing from, the bigger the percentage needed — which is why a 50% loss requires a 100% gain to break even.
For the same reason, applying a rise and then an equal fall does not return you to the start: increase by 20% then decrease by 20% and you end at ×1.20 × 0.80 = 0.96 — four per cent below where you began. Sequential percentages always multiply, never add, whether they are discounts, rises or investment returns.
Distinguish percentages from percentage POINTS: if a rate moves from 10% to 12%, it has risen by 2 percentage points but by 20% in relative terms (2 ÷ 10 × 100). Headlines routinely blur the two, and the difference is enormous — the three modes of this calculator let you compute either version explicitly rather than guessing which one a headline means.
FAQ
How do I work out a percentage of a number?
Multiply the number by the percentage and divide by 100: 18% of 850 is 850 × 18 ÷ 100 = 153. Mental shortcut: find 10% by dividing by ten, 1% by dividing by a hundred, then scale up — the fastest way to sanity-check discounts and tips.
How do I calculate percentage increase or decrease?
Subtract the old value from the new, divide by the old value, multiply by 100: (new − old) ÷ old × 100. Rent going from £1,200 to £1,320 is a 10% increase. The base is always the original figure; using the new figure understates rises and overstates falls.
How do stacked discounts combine?
They multiply rather than add: 20% off then a further 10% off leaves you paying 0.80 × 0.90 = 72% — a 28% total discount, not 30%. The same logic applies to consecutive price rises, which is why two 10% increases add up to 21%, not 20%.
What is the difference between a percentage and a percentage point?
A percentage point is the simple arithmetic gap between two rates; a percentage change is that gap relative to the starting rate. An interest rate moving from 10% to 12% is up 2 percentage points, but up 20% in relative terms (2 ÷ 10 × 100). When a headline says something "rose 20%", check which of the two it means — they describe very different events.
If my investment falls 25%, what gain gets me back to even?
A 33.3% gain, not 25%. Falling from £100 to £75 loses £25, but recovering £25 from a £75 base requires 25 ÷ 75 × 100 = 33.3%. Losses and gains are measured from different bases, so they are never symmetric — and the deeper the loss, the harsher the arithmetic: a 50% fall needs a 100% rise to break even.
Can a percentage be more than 100?
Yes — it simply means the first number is larger than the one you are comparing it to. £250 as a percentage of £200 is 125%; sales that double are a 100% increase; treble is 200%. The "what percent A is of B" mode handles these without complaint, and values over 100% are standard in growth figures, price comparisons and statistics.
Why doesn't a 20% rise followed by a 20% fall cancel out?
Because the fall is applied to a bigger base than the rise was. Start at 100, rise 20% to 120, then fall 20% of 120 — that is 24, landing you at 96, four per cent below the start. Sequential percentage changes always multiply (×1.20 × 0.80 = 0.96), so equal-and-opposite moves never quite cancel unless both are zero.