The Basic Formula for Percentage Change

To find the percentage change between two numbers, subtract the original number from the new number, divide that result by the original number, then multiply by 100. The formula is: ((New Number − Original Number) ÷ Original Number) × 100 = Percentage Change.

The order matters. The original number is always the starting point — the number you're measuring change from. The new number is where you ended up. If you reverse them, you'll get the wrong answer with the wrong sign.

A positive result means an increase. A negative result means a decrease. For example, if a home inspection cost $300 last year and $360 this year, the change is ((360 − 300) ÷ 300) × 100 = 20%. If it dropped from $360 to $300, the change is ((300 − 360) ÷ 360) × 100 = −16.7%.

Key Takeaways

  • Subtract the original number from the new number, divide by the original, and multiply by 100 to get percentage change.
  • A positive percentage means the number went up; a negative percentage means it went down.
  • The original number is always the denominator — it's your baseline for comparison.
  • Percentage change is useful for tracking home values, repair costs, property tax increases, and utility bills over time.

Working Through a Real Example

Say your property tax bill was $2,400 one year and $2,520 the next. Here's how to calculate the change step by step.

Step 1: Subtract the original from the new: $2,520 − $2,400 = $120.

Step 2: Divide by the original: $120 ÷ $2,400 = 0.05.

Step 3: Multiply by 100: 0.05 × 100 = 5%.

Your property tax increased by 5%. This same method works for any two numbers — home prices, insurance premiums, square footage, or interest rates.

When the Original Number Is Zero or Negative

If your original number is zero, you cannot divide by zero, so percentage change cannot be calculated. This happens rarely in homeownership contexts, but it's worth knowing. For example, if you had no mortgage one year and took out a $300,000 mortgage the next, there is no meaningful percentage change to calculate because you started from zero.

If the original number is negative (which might occur in accounting contexts, like a negative balance or a loss), the formula still works mathematically, but the result can be confusing to interpret. In most home-related situations, you'll be working with positive numbers on both sides.

Percentage Change vs. Percentage Point Change

These are not the same thing, and mixing them up leads to confusion. Percentage change is what we've been calculating — the relative shift from one number to another. Percentage point change is the simple difference between two percentages.

For example, if your mortgage interest rate was 3% and rose to 4%, that's a 1 percentage point increase. But the percentage change in the rate itself is ((4 − 3) ÷ 3) × 100 = 33.3%. When you see headlines about rates or statistics, check whether they're talking about points or percentage change — they mean very different things.

Using Percentage Change to Track Home Costs

Homeowners use percentage change to understand whether costs are rising faster than expected. If your homeowners insurance premium jumped from $1,200 to $1,380, that's ((1,380 − 1,200) ÷ 1,200) × 100 = 15%. Knowing the percentage helps you decide whether to shop for a new policy or accept the increase as normal market movement.

You can also use it to compare your home's value over time. If your home was worth $350,000 when you bought it and $420,000 five years later, the percentage change is ((420,000 − 350,000) ÷ 350,000) × 100 = 20%. This tells you how much your equity has grown relative to your purchase price, which is more meaningful than the dollar amount alone.

Common Mistakes to Avoid

The most frequent error is using the new number as the denominator instead of the original. If you calculate ((New − Original) ÷ New) × 100, you'll get a different answer. Using the wrong denominator is especially easy to do when the numbers are close together or when you're working quickly.

Another mistake is forgetting to multiply by 100 at the end. If you stop after dividing, you'll have a decimal (like 0.15) instead of a percentage (15%). The decimal is technically correct mathematically, but it's not what most people mean when they ask for a percentage.

A third pitfall is applying percentage change to percentages themselves. If your mortgage rate was 4% and is now 5%, you cannot say it increased by 25% — that confuses percentage point change with percentage change. Stick to the formula and be clear about what you're measuring.

Frequently Asked Questions

Can percentage change be more than 100%?

Yes. If something doubled, that's a 100% increase. If it tripled, that's a 200% increase. If your home repair estimate went from $500 to $2,000, the percentage change is ((2,000 − 500) ÷ 500) × 100 = 300%. There's no upper limit.

What if the new number is smaller than the original?

You'll get a negative percentage, which correctly shows a decrease. If your utility bill dropped from $180 to $135, the change is ((135 − 180) ÷ 180) × 100 = −25%. The negative sign tells you the number went down, not up.

How do I calculate percentage change on a calculator or spreadsheet?

On a basic calculator, enter: (New − Original) ÷ Original × 100. In a spreadsheet like Excel or Google Sheets, use the formula =(B2-A2)/A2*100, where A2 is the original number and B2 is the new number. The spreadsheet will calculate it instantly and you can copy the formula down for multiple rows.

Is percentage change the same as percent increase or percent decrease?

Yes. Percentage change is the umbrella term. Percent increase and percent decrease are just the positive and negative versions of the same calculation. The formula and method are identical — the sign of the result tells you which direction the change went.