The Basic Formula for Percentage Increase

Percentage increase tells you how much something has grown as a percentage of what it started at. The formula is straightforward: subtract the original amount from the new amount, divide that difference by the original amount, then multiply by 100.

Written as a formula, it looks like this:

Percentage Increase = ((New Amount − Original Amount) ÷ Original Amount) × 100

The result is always a number followed by a percent sign. A 50% increase means something grew to 1.5 times its original size. A 100% increase means it doubled. A 200% increase means it tripled.

Key Takeaways

  • Percentage increase uses the formula: ((New Amount − Original Amount) ÷ Original Amount) × 100.
  • You always divide by the original amount, not the new amount — this is the most common mistake.
  • A negative result means the amount decreased, not increased; this is called percentage decrease.
  • The formula works for any measurement: prices, salaries, populations, test scores, or household expenses.

Working Through a Real Example

Say your electric bill was $120 last month and $156 this month. To find the percentage increase:

Step 1: Subtract the original from the new: 156 − 120 = 36

Step 2: Divide by the original: 36 ÷ 120 = 0.30

Step 3: Multiply by 100: 0.30 × 100 = 30%

Your electric bill increased by 30%. This means the new bill is 130% of the old bill (100% original plus 30% increase).

Why You Divide by the Original Amount

The original amount is your baseline — the thing you're measuring change against. If you divided by the new amount instead, you would get a different (and wrong) answer. Using the electric bill example, dividing 36 by 156 gives you 23%, which is incorrect.

Think of it this way: a $36 increase on a $120 bill is a bigger deal than a $36 increase on a $500 bill. The original amount tells you how significant the change really is. That's why it goes in the denominator.

Handling Decreases and Negative Results

If the new amount is smaller than the original, the formula still works — you just get a negative number. A negative result means percentage decrease, not increase.

For example, if your water bill dropped from $80 to $60:

((60 − 80) ÷ 80) × 100 = (−20 ÷ 80) × 100 = −25%

Your bill decreased by 25%. Some people report this as "a 25% decrease" and others as "−25% change" — both are correct. The negative sign tells you the direction of the change.

Using a Calculator or Spreadsheet

You can do this math on any calculator by following the steps in order: subtract, divide, multiply by 100. On a computer spreadsheet like Excel or Google Sheets, you can enter the formula directly into a cell.

In Excel or Google Sheets, if the original amount is in cell A1 and the new amount is in cell B1, type: =((B1-A1)/A1)*100

The spreadsheet will calculate the percentage increase when ready. This is useful if you have many numbers to compare — for instance, tracking price changes across multiple utility bills or salary increases over several years.

Common Mistakes to Avoid

The most frequent error is dividing by the new amount instead of the original. This flips your answer and makes small increases look smaller and large increases look larger than they really are.

Another mistake is forgetting to multiply by 100 at the end. If you stop after dividing, you get a decimal (like 0.30) instead of a percentage (30%). Both represent the same thing, but percentages are easier to read and compare.

A third error is mixing up the order of subtraction. Always subtract the original from the new, not the other way around. If you reverse it, you get a negative result even when the amount increased.

When You Might Use This in Real Life

Percentage increase comes up whenever you want to understand how much something has changed relative to where it started. Homeowners use it to track utility bill changes month to month. Renters use it to understand rent hikes. You might use it to see how much your property taxes went up, how much your insurance premiums increased, or how much your home's value has grown.

It's also useful for comparing changes across different things. A $50 increase on a $100 bill (50% increase) is bigger than a $50 increase on a $500 bill (10% increase), even though the dollar amount is the same. Percentage increase makes that comparison clear.

Frequently Asked Questions

What's the difference between percentage increase and percentage change?

Percentage change is the broader term — it includes both increases and decreases. Percentage increase specifically means the amount went up. If you get a negative result using the formula, that's a percentage decrease, which is a type of percentage change.

Can percentage increase be more than 100%?

Yes. If something triples, that's a 200% increase. If it quadruples, that's a 300% increase. There's no upper limit. A 100% increase means something doubled; anything above that means it more than doubled.

Do I need to round my answer?

That depends on your purpose. For household bills or straightforward comparisons, rounding to the nearest whole number (like 30% instead of 29.7%) is usually fine. For financial or technical work, you might keep one or two decimal places. The formula itself doesn't require rounding — it's up to you.

What if the original amount was zero?

You can't divide by zero, so the formula breaks down. If something grew from zero to any amount, you can't express that as a percentage increase using this method. In that case, you would just describe the change in absolute terms instead.