The basic formula for percentage change
Percentage change tells you how much something has gone up or down as a portion of what it was before. The formula is: divide the difference by the original amount, then multiply by 100.
In numbers: ((New Amount − Original Amount) ÷ Original Amount) × 100 = Percentage Change
If your rent was $1,000 and it is now $1,100, the difference is $100. Divide $100 by the original $1,000 to get 0.10. Multiply by 100 to get 10%. Your rent increased by 10%.
A negative result means the amount went down. If your utility bill dropped from $150 to $120, the difference is −$30. Divide by $150 to get −0.20. Multiply by 100 to get −20%. Your bill decreased by 20%.
Key Takeaways
- Percentage change = ((New − Original) ÷ Original) × 100; a positive result is an increase and a negative result is a decrease.
- Always divide by the original amount, not the new amount, or your percentage will be wrong.
- Percentage change is useful for comparing rent increases, property tax changes, or utility costs across different time periods or different properties.
- You can work backwards: if you know the percentage change and the original amount, you can find the new amount by multiplying the original by (1 + the percentage as a decimal).
Why percentage change matters for housing costs
A $50 rent increase sounds different depending on whether you pay $500 or $2,000 per month. Percentage change puts both on the same scale so you can compare them fairly. A $50 increase on $500 rent is 10%; the same $50 on $2,000 rent is only 2.5%.
Landlords often cite percentage increases when raising rent. Property tax assessments, insurance premiums, and utility rates all change by percentage. Understanding the math lets you check whether the number you are being quoted is accurate and whether it matches what you expected based on local trends.
Step-by-step walkthrough with a rent increase example
Suppose your rent was $1,200 last year and your landlord is raising it to $1,320 this year. Here is how to find the percentage change:
- Write down the original amount: $1,200
- Write down the new amount: $1,320
- Subtract: $1,320 − $1,200 = $120
- Divide the difference by the original: $120 ÷ $1,200 = 0.10
- Multiply by 100: 0.10 × 100 = 10%
Your rent increased by 10%. Many states have limits on how much rent can increase in a single year or require landlords to give notice before a raise takes effect. Knowing the percentage helps you determine whether the increase falls within your state or local rent control rules.
Working backwards: finding the new amount when you know the percentage
Sometimes you know the percentage change and need to find what the new amount will be. Use this formula: New Amount = Original Amount × (1 + Percentage as a decimal).
If your property tax is $2,000 and it is increasing by 3%, convert 3% to a decimal (0.03) and add 1: 1 + 0.03 = 1.03. Then multiply: $2,000 × 1.03 = $2,060. Your new tax bill will be $2,060.
For a decrease, subtract the percentage from 1. If your homeowners insurance is $1,200 and the rate drops by 5%, use 1 − 0.05 = 0.95. Then: $1,200 × 0.95 = $1,140. Your new premium will be $1,140.
Common mistakes to avoid
The most frequent error is dividing by the new amount instead of the original. If you divide $120 by $1,320 instead of $1,200, you get 0.091, or about 9.1%—which is wrong. Always divide by the starting point.
Another mistake is forgetting to multiply by 100. If you stop after dividing and get 0.10, that is the decimal form. You must multiply by 100 to convert it to a percentage (10%). Without that step, your answer looks like a decimal, not a percentage.
A third error is mixing up increases and decreases. A negative result (a minus sign) means the amount went down. Do not drop the negative sign or your answer will point in the wrong direction.
Comparing percentage changes across different properties or time periods
Percentage change lets you compare apples to apples even when the dollar amounts are different. If one apartment's rent went from $800 to $880 and another went from $1,600 to $1,760, both increased by 10%—even though the second one went up $160 and the first only $80.
You can also track your own housing costs over multiple years. If your rent was $1,000 in year one, $1,100 in year two, and $1,210 in year three, you can calculate the year-to-year change (10% each time) and see whether the rate of increase is staying steady or accelerating.
Using a calculator or spreadsheet
You can do percentage change math on any basic calculator by following the steps in order: subtract, divide, multiply by 100. Many people use a spreadsheet (Excel, Google Sheets, or similar) to track housing costs over time.
In Google Sheets or Excel, the formula looks like this: =(New−Original)/Original*100. If your original rent is in cell A1 and your new rent is in cell B1, you would type =(B1−A1)/A1*100 and press Enter. The spreadsheet will calculate the percentage change instantly and you can copy the formula down to compare multiple months or years at once.
Frequently Asked Questions
What if the original amount was zero or negative?
Percentage change does not work when the original amount is zero, because you cannot divide by zero. If you are comparing a cost that did not exist before to one that does now, percentage change is not the right tool—just state the new amount instead.
Can percentage change be more than 100%?
Yes. If something doubled, that is a 100% increase. If it tripled, that is a 200% increase. If your utility bill went from $50 to $200, the change is ($200 − $50) ÷ $50 × 100 = 300%. The amount increased by 300%.
How do I know if a percentage increase is reasonable for rent?
That depends on your state and local rent control laws. Some states cap annual increases at a set percentage (often 3% to 5%), while others have no limit. Check your state housing authority or local tenant rights organization to see what the legal maximum is in your area.
Should I use percentage change or dollar amount when comparing housing costs?
Use both. The dollar amount tells you how much more you will actually pay each month. The percentage tells you whether the increase is large relative to what you were already paying. Together, they give you the full picture.