The Basic Formula for Percentage Increase

Percentage increase tells you how much something has grown as a portion 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 an equation, it looks like this:

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

The result is always a percentage. If you get 25, that means a 25% increase. If you get 0.5, that means a 0.5% increase. The decimal point matters.

Key Takeaways

  • Subtract the original value from the new value, then divide by the original value and multiply by 100 to find percentage increase.
  • A percentage increase of 50% means the new value is 1.5 times the original; a 100% increase means it doubled.
  • Percentage increase always uses the original value as the denominator, not the new value—this is the most common mistake.
  • Negative results mean the value decreased, not increased; this is called percentage decrease.

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 = 0.3

Step 3: Multiply by 100: 0.3 × 100 = 30

Your electric bill increased by 30%. This means the new bill is 130% of the old one—or 1.3 times as much.

Why the Original Value Matters

The original value always goes in the denominator (the bottom of the division). This is where most people slip up. You are measuring growth relative to where you started, not relative to where you ended.

If you used the new value instead, you would get a smaller percentage. In the electric bill example, dividing 36 by 156 gives 0.23, or 23%—which is wrong. The correct answer is 30% because the bill grew from a base of $120, not from a base of $156.

Think of it this way: a $36 increase on a $120 bill is a bigger deal than a $36 increase on a $1,000 bill. The percentage increase reflects that difference.

Percentage Increase vs. Percentage Decrease

If the new value is smaller than the original, you get a negative number. This is percentage decrease, not increase. The formula stays the same.

For example, if your bill dropped from $156 to $120:

((120 − 156) ÷ 156) × 100 = (−36 ÷ 156) × 100 = −23.08%

The negative sign tells you the value went down. You would say the bill decreased by about 23%, not increased. Do not drop the negative sign—it carries meaning.

Converting Percentage Increase to a Multiplier

Once you know the percentage increase, you can find the new value directly by using a multiplier. If something increases by 25%, the multiplier is 1.25. If it increases by 50%, the multiplier is 1.5. If it increases by 100%, the multiplier is 2 (it doubled).

The pattern: Multiplier = 1 + (Percentage Increase ÷ 100)

So if your original bill was $120 and it increased by 30%, the multiplier is 1 + (30 ÷ 100) = 1.3. Multiply: 120 × 1.3 = 156. This matches the new bill we calculated earlier. Using a multiplier is faster if you already know the percentage and need to find the new value.

Common Mistakes to Avoid

The most frequent error is dividing by the new value instead of the original. Another is forgetting to multiply by 100 at the end—if you stop after dividing, you have a decimal (0.3) instead of a percentage (30%).

A third mistake is treating percentage increase as additive across time. If something increases 10% one year and 10% the next, the total is not 20%. The second 10% is calculated on the new, larger base. After two 10% increases, the value is 1.1 × 1.1 = 1.21 times the original, or a 21% total increase.

Finally, do not drop the negative sign on a decrease. A −30% change is not the same as a +30% change, and the sign tells you which direction the value moved.

Frequently Asked Questions

What if the original value is zero?

You cannot calculate percentage increase when the original value is zero, because you would be dividing by zero. If something went from $0 to $100, you have infinite growth in percentage terms. In this case, describe the change in absolute dollars instead, or note that percentage increase does not explore.

How do I calculate percentage increase over multiple years?

Multiply the multipliers together, do not add the percentages. If a value grows 10% in year one and 15% in year two, multiply 1.1 × 1.15 = 1.265, which is a 26.5% total increase over both years. This accounts for the fact that year two's growth is applied to a larger base.

Is percentage increase the same as percent change?

Percent change is the broader term—it includes both increases and decreases. Percentage increase specifically means the value went up. The formula is identical; the only difference is whether the result is positive (increase) or negative (decrease).

Can percentage increase be more than 100%?

Yes. If something doubles, that is a 100% increase. If it triples, that is a 200% increase. If it goes from $10 to $50, the increase is ((50 − 10) ÷ 10) × 100 = 400%. There is no upper limit on percentage increase.