Percentage decrease calculator

Percent decrease is the drop divided by the original value, times 100. From 1,250 to 950 the drop is 300, and 300 / 1,250 = 0.24, so the decrease is 24%. As a signed change it is -24%; "a 24% decrease" and "a change of -24%" mean the same thing.

The original is always the larger of the two numbers in a decrease, and that is why a fall and the rise that reverses it never match. Going back up from 950 to 1,250 is the same 300, but divided by 950 it is a 31.58% increase. The gap widens fast as the fall gets deeper: undoing a 10% fall takes an 11.11% rise, a 25% fall takes 33.33%, a 50% fall takes 100%, and a 90% fall takes 900%. Anyone who has watched an investment halve and then "recover 50%" has met this.

A decrease cannot be more than 100% for anything that cannot go below zero. A 100% decrease takes a price to nothing, so "200% cheaper" or "reduced by 150%" describes something impossible. If a calculation produces a decrease over 100%, it has almost certainly divided by the new number instead of the old one: 1,250 down to 250 is an 80% decrease, but 1,000 / 250 gives 400%.

Taking a percentage off a number is a single multiplication by 1 minus the rate. 1,250 less 24% is 1,250 x 0.76 = 950, and a 30%-off sale on an 80 item is 80 x 0.7 = 56.

Discounts that stack do not add. 20% off, then a further 10% off the reduced price, is 0.8 x 0.9 = 0.72 of the original, a 28% decrease rather than 30%. On 1,250 that is 900, not 875. The order does not matter, but the second discount always applies to a smaller number than the first did.

Working backwards from a reduced figure is the other place people slip. If 950 is the price after 24% off, the original is 950 / 0.76 = 1,250. Adding 24% back on gives 950 x 1.24 = 1,178, which is wrong because the 24% is then taken from the smaller number: 950 is 76% of 1,250.

When the two numbers are already percentages, such as a pass rate falling from 80% to 60%, say which measure you mean. That is a fall of 20 percentage points and a 25% decrease, and both are true.