How to Calculate Percentage Increase (With Examples)

To calculate a percentage increase, subtract the old value from the new value, divide by the old value, and multiply by 100. Going from 80 to 100 is an increase of 25 percent. The same method works for prices, salaries, sales and savings. The rest of this guide shows the formula, worked examples and the mistakes to avoid.

The percentage increase formula

Use this formula:

Percentage increase = (New value − Old value) ÷ Old value × 100

The old value is the base. The result is the change as a share of the base, not as a share of the new value. That detail causes most errors.

If the result is negative, the value went down. A negative result is a percentage decrease, and the same formula works for it.

Step by step: a salary example

Suppose your monthly salary goes from 2,500 to 2,800. Follow these steps:

1. Find the difference: 2,800 − 2,500 = 300.
2. Divide the difference by the old value: 300 ÷ 2,500 = 0.12.
3. Multiply by 100: 0.12 × 100 = 12.

The salary increase is 12 percent. You can check it in reverse: 2,500 × 1.12 = 2,800.

More examples

The table below uses the same formula for four changes.

The change is +20, +15, +30 and +20 in the four rows, but the percentage depends on the base. A 20 point change on a base of 40 is much bigger than the same change on a base of 200.

Why the base matters

A percentage up and the same percentage down do not cancel out. Take 100 and apply two changes:

• 100 goes up 20 percent to 120.
• 120 goes down 20 percent to 96.

You end at 96, not 100. The second change is taken from a larger base, so it removes 24, not 20. To return to 100 after a 20 percent drop from 100, you need a 25 percent rise from 80.

Percentage decrease

The formula is the same, with a negative result. Suppose a jacket drops from 120 to 96:

• Difference: 96 − 120 = −24.
• Divide by the old value: −24 ÷ 120 = −0.2.
• Multiply by 100: −20.

The price fell by 20 percent.

Find the original value from a percentage

Sometimes you know the new value and the percentage, and you need the old value. Divide the new value by 1 plus the percentage, written as a decimal:

Old value = New value ÷ (1 + percentage)

Suppose a price is 115 after a 15 percent rise. The original price is 115 ÷ 1.15 = 100. Do not subtract 15 percent from 115, because that gives 97.75, which is wrong.

Common mistakes

• Using the new value as the base. For 80 to 100, the increase is 20 ÷ 80 = 25 percent. Dividing by 100 gives 20 percent, which is wrong.
• Adding two percentages. A 20 percent rise followed by a 20 percent fall does not return to the start, as the example above shows.
• Forgetting the multiplication by 100. The result 0.25 is a quarter, which is 25 percent only after you multiply by 100.
• Rounding too early. Keep the full decimal until the last step, then round.

How Percent & Finance Calc Pro helps

Percent & Finance Calc Pro is a percentage calculator app for iPhone. The percentage change calculators are part of the free version. You enter the old and new values, and the app shows the percentage and the formula with lettered inputs. The value before a change calculator answers the reverse question, such as the price before a 20 percent rise.

The app also keeps your most used calculations at the top, and you can star any calculation to pin it. Pro adds more calculations, such as effective annual rate and real return after inflation. See the app page for the full list.

For a related guide, read how to calculate discount, VAT and profit margin. It uses the same method for prices and margins.

If you want to check a change in your own numbers, try Percent & Finance Calc Pro. You can find more calculators on the apps page.

Frequently asked questions

Is percentage increase the same as percentage points?

No. A percentage increase compares a change with the old value. A percentage point is the simple difference between two percentages. If a rate goes from 4 percent to 5 percent, it rises by one percentage point, but the increase is 25 percent (1 ÷ 4).

Why do I get a different answer when I divide by the new value?

Dividing by the new value gives a different base, so the result is wrong for a change. The base must be the original value. Use the old value every time you calculate a percentage increase.

Can I use this formula for interest or growth over several years?

For one change, yes. For growth over several years, use a compound growth rate instead. Compound growth applies the rate to the value after each period, so the total is not a simple sum of the yearly percentages.

How do I calculate a percentage increase in a spreadsheet?

Use the formula (new − old) ÷ old, then format the cell as a percentage. The spreadsheet does the multiplication by 100 for you when you use the percent format.