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Percentage change calculator

The percent increase or decrease between two numbers, worked out exactly.

Percentage change from one number to another

25% 25% increase

How we got this

  1. Subtract the old value from the new one: 100 − 80 = 20
  2. Divide by the old value: 20 ÷ 80 = 0.25
  3. Multiply by 100: 0.25 × 100 = 25%, a 25% increase
Increase or decrease a number by a percentage

Result 100

How we got this

  1. Add the percentage to 100%: 100% + 25% = 125%, or 1.25
  2. Multiply: 80 × 1.25 = 100
Before an increase or decrease: the original amount

Original 80

How we got this

  1. A 20% decrease means the new amount is 80% of the original: 100% − 20% = 80%
  2. Original = 64 ÷ 0.8 = 80
Percentage difference between two numbers

Difference ≈ 22.222222%

How we got this

  1. The difference, ignoring sign: |80 − 100| = 20
  2. The average of the two: (80 + 100) ÷ 2 = 90
  3. Divide and multiply by 100: 20 ÷ 90 × 100 = ≈ 22.222222%

Worked out on your device. Nothing is sent anywhere.

Percentage change, step by step

Percentage change answers "by how much did it grow or shrink, compared with where it started?" The formula is (new − old) ÷ |old| × 100. A price that goes from $80 to $100 rose $20, which is 25% of the original $80. Going back down from $100 to $80 is a fall of 20%, because the $20 is now measured against $100.

Adding or taking off a percentage

To increase a number by P%, multiply it by (1 + P/100); to decrease it, multiply by (1 − P/100). A $80 item with 25% added costs $80 × 1.25 = $100. A 20% discount on $100 is $100 × 0.8 = $80. To find a price before a percentage was added, divide instead: $100 ÷ 1.25 = $80.

The original amount, before a change

When you know the amount after a percentage change and want the amount before it, divide by the same factor: original = new ÷ (1 ± P/100). Pay of $2,300 after a 15% raise was $2,300 ÷ 1.15 = $2,000; a $64 price after 20% off was $64 ÷ 0.8 = $80. Taking the percentage off the new amount doesn’t work, because the percentage was of the original. A decrease of 100% or more can’t be undone: it leaves nothing, whatever you started with.

When to use percentage difference

When neither number is the starting point (two shops' prices, two measurements of the same thing), percentage difference compares them fairly: the gap divided by their average. It gives the same answer whichever way round you enter them.

Questions

How do I calculate a percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100. From 80 to 100: (100 − 80) ÷ 80 × 100 = 25%. If the answer is negative, it is a decrease.

Why isn’t a 50% rise followed by a 50% fall back to where I started?

Because each percentage is of a different number. 100 up 50% is 150; 150 down 50% is 75. To undo a 50% rise you need a 33.3% fall, and to undo a 50% fall you need a 100% rise.

How do I find the original price before a discount?

Divide the sale price by what is left after the discount. After 20% off you pay 80% of the original, so a $64 sale price was $64 ÷ 0.8 = $80. Adding 20% back on gives the wrong answer ($76.80), because the 20% was taken from the bigger, original price. After an increase, divide by 1 plus the percentage: pay of $2,300 after a 15% raise was $2,300 ÷ 1.15 = $2,000.

What’s the difference between percentage change and percentage difference?

Percentage change has a direction: it measures from an old value to a new one, so 80 → 100 is +25% but 100 → 80 is −20%. Percentage difference compares two values neither of which comes first, dividing by their average: 80 and 100 differ by 22.2% either way round.

What are percentage points?

The plain difference between two percentages. A rate rising from 4% to 5% has gone up 1 percentage point, which is a 25% increase in the rate itself. News reports often mix the two up.

Can I work out the change from a negative number?

Yes. The change is divided by the size of the starting value (ignoring its minus sign), so a loss shrinking from −50 to −25 counts as a 50% improvement. A change from 0 has no percentage: any change from nothing is infinitely large.

Is what I type saved or sent anywhere?

No. Every calculation happens in your browser. Your numbers appear in the page address only so you can bookmark or share the result.

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