The basic formula for percent change
Percent change tells you how much something has grown or shrunk as a percentage of where it started. The formula is: divide the difference between your new number and your old number by the old number, then multiply by 100.
Written out: ((New Number − Old Number) ÷ Old Number) × 100 = Percent Change
The result is positive if the number went up and negative if it went down. For example, if your property tax was $3,000 last year and $3,300 this year, the change is $300. Divide $300 by $3,000 to get 0.10, then multiply by 100 to get 10% — your tax increased by 10%.
Key Takeaways
- Percent change uses the old number as the base, not the new number or the average of both.
- A positive result means growth; a negative result means decline.
- The formula works for any two numbers: home values, utility bills, mortgage rates, or property dimensions.
- Percent change is different from percentage points — a rate that moves from 3% to 5% has risen 2 percentage points, not 2%.
Why the old number matters as your starting point
The old number is your baseline because it represents the original state before the change happened. If you used the new number instead, you would get a different answer that does not reflect how much the original amount actually shifted.
Think of it this way: if your home's assessed value was $200,000 and is now $250,000, the change is $50,000. Dividing by the old number ($200,000) gives you 25% growth. If you divided by the new number ($250,000) instead, you would get 20% — which is mathematically correct for that division but does not answer the question "how much did my starting value grow?"
Working through a home maintenance cost example
Say your homeowner's insurance premium was $1,200 per year two years ago and is now $1,380. Here is the step-by-step calculation:
- Find the difference: $1,380 − $1,200 = $180
- Divide by the old amount: $180 ÷ $1,200 = 0.15
- Multiply by 100: 0.15 × 100 = 15%
Your insurance cost rose 15%. This matters because it tells you whether the increase is in line with inflation (usually 2–3% per year) or whether your insurer is raising rates faster than the economy overall.
Handling negative percent change (when numbers go down)
The formula works the same way when something decreases. If your home inspection revealed $5,000 in needed repairs but you negotiated the seller down to $3,500, the change is $3,500 − $5,000 = −$1,500.
Divide by the original: −$1,500 ÷ $5,000 = −0.30, then multiply by 100 to get −30%. The negative sign tells you the number went down. You can also say "the repair estimate decreased by 30%" or "you saved 30% off the original estimate."
Percent change versus percentage points
These two are often confused. Percentage points are the simple difference between two percentages. Percent change is how much one percentage has grown or shrunk relative to itself.
Example: if mortgage interest rates moved from 6% to 7.5%, that is a 1.5 percentage point increase. But the percent change in the rate itself is ((7.5 − 6) ÷ 6) × 100 = 25%. The rate grew by 25% of what it was before. Both numbers are correct — they just answer different questions. When discussing rates or percentages, be clear which one you mean.
When you have more than two data points
If you are tracking something over multiple years or months, calculate percent change between each pair of consecutive numbers. For a home value that was $150,000 in 2020, $165,000 in 2021, and $180,000 in 2022, you would calculate the change from 2020 to 2021 separately from the change from 2021 to 2022.
From 2020 to 2021: ((165,000 − 150,000) ÷ 150,000) × 100 = 10%. From 2021 to 2022: ((180,000 − 165,000) ÷ 165,000) × 100 = 9.1%. This shows you the growth rate each year, which is more useful than lumping all three years together.
Common places homeowners use this calculation
You might calculate percent change when comparing utility bills from one season to the next, tracking property tax increases year over year, measuring how much your home's value has appreciated, or seeing how much a contractor's estimate changed after a second walkthrough.
It is also useful for understanding whether a price increase is typical. If your water bill went from $40 to $50, that is a 25% jump — worth investigating whether something is leaking. If your property tax went from $3,000 to $3,060, that is 2%, which is closer to normal annual growth.
Frequently Asked Questions
What if my old number was zero?
You cannot divide by zero, so the formula breaks down. In this case, you can only describe the change in absolute terms: "the cost went from $0 to $500" rather than a percent. Some people say the change is "infinite" or "undefined," but for practical purposes, just state the dollar amount.
Should I round my answer?
For most homeowner purposes, rounding to one or two decimal places is fine. A 15.3% increase and a 15.27% increase mean roughly the same thing. If you are comparing multiple years or using the number for a formal document, keep more decimal places until the final answer.
Can percent change be more than 100%?
Yes. If something doubled, that is a 100% increase. If it tripled, that is a 200% increase. If your home renovation budget went from $10,000 to $35,000, the change is ((35,000 − 10,000) ÷ 10,000) × 100 = 250%. Large percent changes are common in construction and repair estimates.
How is percent change different from a percentage of something?
Percent change compares two different numbers to show growth or decline. A percentage of something is a part of a whole. If your home is worth $300,000 and you put down 20%, that is $60,000 — a percentage of the total. Percent change would compare your down payment to a previous down payment you made.