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How to calculate percentage decrease from the original value

How to calculate percentage decrease from the original value

A drop from 80 to 60 is 25%, but a 25% rise from 60 only gets you to 75. Measure the drop from the right starting value, compare two numbers when neither came first, and work out what stacked discounts really take off.

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The starting value decides the answer

A percentage decrease is the drop divided by the value you started from. From 80 to 60 the drop is 20, and 20 is 25% of 80. Divide by the new value instead and you get 33.3%, which is a different question.

The same rule is why a drop and an equal rise do not cancel. Cut 80 by 25% and you have 60. Raise 60 by 25% and you have 75, because 25% of 60 is only 15. Getting back to 80 after a 25% drop takes a 33.3% rise. This catches people out with prices, salaries, and investment returns, where a loss needs a bigger gain to recover.

Direction matters for change between two numbers as well. 50 to 65 is a 30% rise, and 65 to 50 is a 23.08% fall, even though the gap is 15 both ways. When neither number is the starting point, such as two shops' prices on the same day, percentage difference is the fairer measure. Discounts add their own trap: an extra 10% off a sale price is taken from the already reduced price, so 20% and then 10% is 28% off, not 30%.

Measure the drop, compare the two values, then stack the discounts

For a single drop, use the Percentage Decrease Calculator. The Decrease from A to B tab takes the original value and the new value and returns the percentage decrease and the difference, with every step shown. The formula is (A − B) ÷ |A| × 100. The Decrease a value by P% tab works the other way: 250 decreased by 40% is 150. An original value of 0 has no answer and the calculator says so. If the new value is higher than the original, the result comes out negative. Reducing a value by more than 100% gives a negative result with a note.

When a value may have gone up or down, or when you need to compare two numbers, use the Percentage Change Calculator. Enter the original value A and the new value B, and Swap A and B reverses them. It shows the signed change first, (B − A) ÷ |A| × 100, then the difference and the percentage difference, |A − B| divided by the average of A and B, times 100. For 50 to 65 that is +30% change and a 26.09% difference. An original value of 0 has no percentage change, and the percentage difference is undefined when the two values add up to 0.

For a price with one or two discounts, use the Discount Calculator. Enter the original price, then the first discount as a percentage or a fixed amount. Add another discount for a stacked deal, and fill in sales tax if it applies. It returns the final price, the saving, the effective total discount, and the tax. 200 with 20% off and then another 10% off is 144.00, an effective discount of 28%. With 8% tax added, the final price is 155.52. Tax is always added after the discounts. A fixed discount larger than the price, or a percentage over 100, is an error.

Work out a drop, a change, and a stacked discount

  1. Write down which value came first. That is the number you divide by.
  2. Enter the original and new values in the Percentage Decrease Calculator to get the drop in percent and the amount.
  3. If the value could have gone either way, or neither value is the starting point, enter both in the Percentage Change Calculator and read the change or the percentage difference.
  4. For a price with more than one discount, enter each discount in the Discount Calculator in the order the shop applies them, and read the effective total.
  5. To undo a drop, do not add the same percentage back. A 25% drop needs a 33.3% rise to return to the start.

What these calculators will not decide for you

  • An original value of 0 has no percentage decrease or percentage change. Percentage difference is undefined when both values add up to 0.
  • The decrease calculator shows a negative result when the new value is higher. Read it as a rise.
  • The discount calculator always adds tax after the discounts. Places that tax the original price need a different calculation.
  • The currency symbol is for display only. No currency conversion is done.

Frequently asked questions

How do I calculate a percentage decrease?

Subtract the new value from the old value, divide by the old value, and multiply by 100. From 80 to 60 is a 25% decrease.

Why doesn't a 25% drop followed by a 25% rise get me back to the start?

The rise is worked out on the smaller number. 80 drops to 60, and 25% of 60 is only 15, so you end at 75.

What is the difference between percentage change and percentage difference?

Change is measured from the original value. Difference is measured from the average of both values, so it is the same either way round.

Is 20% off plus 10% off the same as 30% off?

No. The second discount is taken from the already reduced price, so 20% and then 10% is 28% off in total.

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