The basic formula for percent change
Percent change measures how much a number has grown or shrunk compared to where it started. The formula is: (New Number − Old Number) ÷ Old Number × 100 = Percent Change.
The result tells you the direction and size of the change. A positive number means growth. A negative number means the value went down. For example, if rent was $1,000 and is now $1,200, the percent change is ($1,200 − $1,000) ÷ $1,000 × 100 = 20%. Rent increased by 20%.
The old number is always the starting point, even if it is smaller. This matters because reversing the numbers gives you a completely different answer. If you use the new number as the base instead, you get the wrong percent.
Key Takeaways
- Percent change uses the formula (New − Old) ÷ Old × 100, where the old number is always your starting point.
- A positive result means the number went up; a negative result means it went down.
- The order matters — using the new number as the base gives you a different (wrong) answer.
- You can use this same method for any two numbers: prices, rent amounts, income, property values, or population counts.
Step-by-step walkthrough with a real example
Say your property tax was $2,500 last year and $2,750 this year. Here is how to find the percent change:
- Subtract the old number from the new number: $2,750 − $2,500 = $250
- Divide that result by the old number: $250 ÷ $2,500 = 0.10
- Multiply by 100 to convert to a percent: 0.10 × 100 = 10%
Your property tax increased by 10%. The same steps work whether the change is up or down. If the new number is smaller than the old one, step 1 gives you a negative number, and your final answer is negative — which correctly shows a decrease.
When the old number is zero or negative
The formula breaks down if your old number is zero, because you cannot divide by zero. In that case, percent change does not have a meaningful answer using this method. If something went from $0 to $100, you cannot say it increased by a percent — it went from nothing to something, which is infinite growth in mathematical terms.
If your old number is negative (which can happen with profit/loss or temperature), the formula still works mathematically, but the result can be confusing to interpret. For example, if a business went from −$500 (a loss) to +$500 (a profit), the percent change is (+$500 − (−$500)) ÷ (−$500) × 100 = −200%. The negative sign does not mean the business got worse — it reflects the unusual starting point. In these cases, it is often clearer to describe the change in plain terms rather than as a percent.
Common uses in housing and real estate
Percent change appears throughout housing decisions. Property values often rise or fall by a percent each year. If a house was worth $300,000 five years ago and $360,000 today, that is a 20% increase. Rent increases are usually stated as a percent — a landlord might raise rent by 5% or 10% annually. If your rent is $1,200 and increases by 5%, the new rent is $1,260.
You might also use percent change to track your own finances: how much your income has grown, how much you are spending on housing compared to last year, or how property tax or insurance premiums have changed. The same formula works for all of these.
Percent change versus percent difference
Percent change has a direction — it assumes one number came first and one came second. Percent difference treats both numbers equally and asks how far apart they are, without assuming which is "old" or "new."
For most housing questions, you want percent change, because you care about the direction: Did rent go up or down? Did the property value increase or decrease? But if you are comparing two unrelated numbers (like the price of a house in two different cities), percent difference might be more useful. The formulas are slightly different, so make sure you know which one answers your question.
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 spreadsheet like Excel or Google Sheets, you can type the formula directly. In Excel, if your old number is in cell A1 and your new number is in cell B1, you would type: =(B1-A1)/A1*100
Spreadsheets are useful if you have many numbers to compare. You can set up the formula once and copy it down for dozens of rows. This saves time and reduces the chance of arithmetic mistakes, especially if you are tracking changes over several years or across multiple properties.
Frequently Asked Questions
What if the percent change is negative?
A negative percent change means the number went down. If rent dropped from $1,500 to $1,350, the percent change is (−$150) ÷ $1,500 × 100 = −10%. The rent decreased by 10%. The negative sign is part of the answer and tells you the direction of change.
Can I use percent change for very large numbers?
Yes. The formula works the same way whether the numbers are in the hundreds or the millions. A property value that went from $500,000 to $600,000 is a 20% increase, just like $5,000 to $6,000. The percent tells you the relative size of the change, not the absolute dollar amount.
Why does the order matter?
The old number is the baseline you are measuring against. If you reverse them, you are measuring against a different baseline, which gives a different answer. Going from $100 to $200 is a 100% increase, but going from $200 to $100 is a 50% decrease. The change is the same ($100), but the percent is different because the starting point is different.
What if I want to know the new number after a percent change?
Use this formula instead: New Number = Old Number × (1 + Percent Change ÷ 100). If rent is $1,200 and increases by 5%, the new rent is $1,200 × (1 + 5 ÷ 100) = $1,200 × 1.05 = $1,260. This is the reverse of finding percent change.