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Calculators

Percentage Increase & Decrease Calculator

Start from a value and a percentage to get the new figure — or go the other way and recover the original from a value that has already changed. Reversing is where most mistakes happen, because taking the same percentage back off does not undo an increase.

What do you want to do?

Enter a value and a percentage to see the result.

An increase and a decrease do not cancel out

Adding 50% then taking 50% off does not return you to the start — it leaves you 25% below it, because the second percentage is applied to a larger number.

How to use this tool

  1. Choose whether you are increasing a value, decreasing it, or working backwards to the original.
  2. Enter the value. In reverse mode this is the figure you already have, after the change.
  3. Enter the percentage. In reverse mode use a negative number if the value went down.
  4. The new figure appears underneath, along with the multiplier that was applied.

Formula and method

Applying a change

new = old × (1 + p ÷ 100)

A 15% increase multiplies by 1.15; a 15% decrease multiplies by 0.85. Working with the multiplier rather than adding and subtracting is what makes chained changes easy to reason about.

Reversing a change

old = new ÷ (1 + p ÷ 100)

Dividing by the multiplier undoes it. This is why you cannot recover the original from a 100% decrease — the multiplier is zero, and nothing divided by zero is defined.

Worked examples

Increase 250 by 15%

  1. Multiplier: 1 + 0.15 = 1.15
  2. 250 × 1.15 = 287.5

250 increased by 15% is 287.5.

A price is 92 after a 20% discount — what was it before?

  1. Multiplier: 1 − 0.20 = 0.80
  2. 92 ÷ 0.80 = 115

The original price was 115.

Up 50%, then down 50%

  1. 100 × 1.5 = 150
  2. 150 × 0.5 = 75

You end at 75, not 100 — 25% below where you started.

Notes and limitations

  • An increase and a decrease of the same percentage do not cancel out, because the second is applied to a different base. Up 50% then down 50% leaves you 25% down.
  • To reverse a change, divide by the multiplier — do not subtract the same percentage. Taking 20% off 115 gives 92, but adding 20% to 92 gives 110.4, not 115.
  • A 100% decrease cannot be reversed. Everything is gone, and any original value would produce the same result.
  • Percentage points and percent are different. A rate moving from 4% to 6% rose two percentage points, which is a 50% increase.

Frequently asked questions

How do I increase a number by a percentage?

Multiply by 1 plus the percentage as a decimal. To add 15%, multiply by 1.15. To add 7.5%, multiply by 1.075.

How do I find the original price before a discount?

Divide the price you paid by 1 minus the discount as a decimal. After 20% off, divide by 0.8. Do not add 20% back on — that gives a different, wrong answer.

Why doesn't adding then subtracting the same percentage return the original?

Because the second percentage is applied to a changed number. Adding 50% to 100 gives 150, and 50% of 150 is 75 — larger than the 50 you added. The two operations are not inverses.

How do I apply two percentage changes in a row?

Multiply the multipliers together. A 10% rise followed by a 5% fall is 1.10 × 0.95 = 1.045, a net increase of 4.5%.

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