What is the percentage increase?
Increase a number by a percent, or enter two numbers to see the percentage increase between them.
- New value
- 92
80 increased by 15% is 92.
- Increase or decrease
- Increase
- Amount of increase
- 12
- In words
- increased by 15%
New value: 92. 80 increased by 15% is 92.
How to calculate
Increases a number by a percentage, or finds the percentage increase from one number to another, or the original number.
Example with the default inputs (Original value 80, Percentage increase 15%): 80 increased by 15% is 92.
Formula: B = A + |A| × p ÷ 100, so p = (B − A) ÷ |A| × 100, where A is the original value and B the new value.
- The increase is measured against the size of the original value, |A|; for a positive A, B = A × (1 + p ÷ 100).
- A negative percentage increase is a decrease.
- There is no percentage increase from 0: the original value must not be 0.
- Finding the original value from the new value and the increase can give two answers, one positive and one negative: both are shown.
Worked examples
Each example is checked against the calculator on every build.
- Original value 80, Percentage increase 15% gives New value 92, Amount of increase 12, Increase or decrease Increase, In words increased by 15%.Source: hand calculation in content.mdx: 15% of 80 is 12, and 80 + 12 = 92
- Original value 50, New value 65 gives Percentage increase 30%, Amount of increase 15.Source: hand calculation in content.mdx: (65 − 50) ÷ 50 × 100 = 30%
- New value 92, Percentage increase 15% gives Original value 80.Source: hand calculation in content.mdx: 92 ÷ 1.15 = 80
- Original value 200, New value 150 gives Percentage increase -25%, Amount of decrease 50, Increase or decrease Decrease, In words decreased by 25%.Source: hand calculation in content.mdx: (150 − 200) ÷ 200 × 100 = −25%, a decrease
- Original value 0.5, Percentage increase 300% gives New value 2.Source: hand calculation in content.mdx: 0.5 × (1 + 3) = 2
How it works
For an original value A, a new value B, and a percentage increase p:
B = A + |A| × p ÷ 100, so p = (B − A) ÷ |A| × 100
|A| is the size of A without its sign. For a positive A (the usual case) this is B = A × (1 + p ÷ 100).
Fill in any two of the three and the calculator finds the third:
- New value: B = A + |A| × p ÷ 100.
- Percentage increase: p = (B − A) ÷ |A| × 100. A negative answer is a decrease.
- Original value: if A is positive, A = B ÷ (1 + p ÷ 100); if A is negative, A = B ÷ (1 − p ÷ 100). Each answer counts only if it has the sign it assumed, so there can be no answer, one, or two (one positive and one negative). The calculator shows every one.
It also shows whether the change is an increase, a decrease, or no change, and the amount: the amount of increase B − A when B is at least A, or the amount of decrease A − B when B is smaller (80 to 72: amount of decrease 8).
The answer reads "A increased by p% is B" for p of 0 or more, and "A decreased by |p|% is B" for a negative p: 80 with p = −10% gives "80 decreased by 10% is 72." The same words show as the "In words" row.
Assumptions
- The original value must not be 0: there is no percentage increase from 0.
- The increase is measured against |A|, so an increase is always a positive percentage, even from a negative start.
- Percentages are in percent points: type 15 for 15%.
- An original value of 0 gives no answer, and the page says: "The original value cannot be 0: a percentage increase is measured against it."
Worked examples by hand
80 increased by 15%. 15% of 80 is 80 × 15 ÷ 100 = 12, so the new value is 80 + 12 = 92 (the same as 80 × 1.15).
From 50 to 65. (65 − 50) ÷ 50 × 100 = 15 ÷ 50 × 100 = 30%, an amount of 15.
What number increased by 15% gives 92? A = 92 ÷ 1.15 = 80. The negative case, 92 ÷ (1 − 0.15) = 108.24, is not negative, so it does not count.
From 200 to 150. (150 − 200) ÷ 200 × 100 = −25%, a decrease of 50 (amount of decrease 50).
0.5 increased by 300%. 0.5 × (1 + 3) = 2.
Other questions people ask
How do I increase a number by a percentage?
Multiply the number by 1 plus the percentage as a decimal. To increase 80 by 15%, work out 80 × 1.15 = 92. You can also find 15% of 80 (12) and add it on: 80 + 12 = 92.
How do I calculate the percentage increase between two numbers?
Subtract the original number from the new one, divide by the original, and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.
How do I find the original number before a percentage increase?
Divide the new number by 1 plus the increase as a decimal. If a price is 92 after a 15% increase, the original was 92 ÷ 1.15 = 80. Taking 15% off 92 would give 78.20, which is wrong, because the 15% was worked out on 80, not on 92.
What does a negative percentage increase mean?
A decrease. From 200 to 150 is an increase of −25%, which is the same as a 25% decrease. For decreases on their own terms, the percentage change calculator reports the direction too.
Can a percentage increase be more than 100%?
Yes. An increase of 100% doubles a number, 200% triples it, and 300% makes it four times as big: 0.5 increased by 300% is 0.5 × 4 = 2.
Is a 10% increase followed by a 10% increase the same as a 20% increase?
No, it is a 21% increase, because the second 10% is worked out on the bigger number. 100 becomes 110, and 110 becomes 121. Repeated increases multiply: 1.1 × 1.1 = 1.21.