Percentage Calculator

There are only three fields, but what X and Y mean depends on the question you pick.

1. Open the Calculate menu and choose the question: What is X% of Y?, X is what percent of Y?, Percentage change from X to Y, Increase Y by X%, or Decrease Y by X%.
2. Type a number in X. It is the percentage in the first, fourth and fifth questions, the part in the second and the old value in the third.
3. Type a number in Y. It is the whole in the first and second questions, the new value in the third and the starting value in the fourth and fifth.
4. Read the large answer and the formula beneath it, which has your numbers filled in so you can check the working or repeat it by hand.

The page opens on 20% of 150, which gives 30. The percentage change question also shows the difference between the two values and the multiplier, so going from 50 to 65 reports 30% and 1.3×.

Typical uses include checking a test score (38 out of 50 is 76%), finding a share of a bill, working out how much a price has risen since last year, or testing a claim such as a 15% saving. Pick the question first and the two numbers follow naturally. If the answer looks implausible, the usual cause is X and Y entered the wrong way round, which matters for every question except the first.

All five questions are rearrangements of one relationship between a part, a whole and a percentage.

• X% of Y is X / 100 × Y. For 15% of 80 the answer is 12.
• X as a percent of Y is X / Y × 100. A score of 45 out of 60 is 75%. Y cannot be zero, and the answer can pass 100: 75 is 150% of 50.
• Percentage change is (Y - X) / |X| × 100. From 50 to 65 is +30%. From 65 back to 50 is -23.08%, not -30%, because the base is now 65. The tool divides by the absolute value of X and refuses a starting value of zero.
• Increase Y by X% is Y × (1 + X / 100) and Decrease Y by X% is Y × (1 - X / 100). Raising 200 by 12% gives 224, and lowering it by 12% gives 176.

Percentages are shown to two decimal places and plain values to up to four. Working backwards is not a separate option, but you can do it by hand: if a price of 120 includes a 20% rise, the original was 120 divided by 1.2, which is 100. You can then confirm it by choosing Increase Y by X% with Y as 100 and X as 20.

The arithmetic is simple, but the interpretation causes most errors.

• Percentage points are not percent. A rate rising from 10% to 12% is 2 percentage points but a 20% increase.
• Reversing a change is not symmetrical. A 25% fall takes 100 to 75, and a 25% rise then gives 93.75. To undo a 25% cut you need a 33.33% rise.
• Successive percentages multiply. Two 10% rises make 21%, not 20%. The discount calculator handles stacked offers for this reason.
• Name the base. Change is always measured against the starting value. Starting from a negative number is ambiguous: going from -50 to -25 shows +50% here because the tool uses the absolute starting value, but your field may define it differently.
• Round last. Rounding midway compounds small errors.

For tax on a price, the VAT and sales tax calculator adds or removes it in one step. To turn a fraction into a percentage, work it out in the fraction calculator, and for a set of numbers use the average calculator. For longer expressions with brackets, the scientific calculator accepts a postfix percent sign, though it simply divides by 100.