The Basic Formula for Percentage Change

To calculate a percentage change, subtract the old value from the new value, then divide that difference by the old value, and multiply by 100. The formula is: ((New Value − Old Value) ÷ Old Value) × 100 = Percentage Change.

The result tells you how much something has grown or shrunk as a percentage of where it started. A positive number means an increase; a negative number means a decrease. This works for any two numbers you want to compare — rent prices, income, utility bills, population, or anything else measured over time.

The key is that you always divide by the old value, not the new one. That anchors the change to where you started, which is what makes the percentage meaningful.

Key Takeaways

  • Percentage change uses the formula ((New − Old) ÷ Old) × 100, and the result is always relative to the starting value.
  • A positive result means an increase; a negative result means a decrease.
  • The old value must never be zero, because you cannot divide by zero.
  • Percentage change and percentage point change are different — a change from 5% to 10% is a 5 percentage point increase but a 100% increase in the actual value.

Working Through a Real Example

Say your rent was $1,200 last year and is now $1,350. Subtract: $1,350 − $1,200 = $150. Divide by the old value: $150 ÷ $1,200 = 0.125. Multiply by 100: 0.125 × 100 = 12.5%. Your rent increased by 12.5%.

If your income was $40,000 and dropped to $36,000, the math is: ($36,000 − $40,000) ÷ $40,000 = −$4,000 ÷ $40,000 = −0.1 = −10%. Your income decreased by 10%. The negative sign tells you it went down, not up.

The size of the change depends entirely on the starting point. A $150 increase on $1,200 is 12.5%, but a $150 increase on $3,000 is only 5%. The same dollar amount produces different percentages because the old value is different.

When the Old Value Is Very Small or Zero

If the old value is zero, the formula breaks down because you cannot divide by zero. For example, if you had no income last year and earn $30,000 this year, there is no meaningful percentage change — you cannot say it increased by infinity percent, even though mathematically that is what the formula suggests.

In situations like this, describe the change in plain terms instead: "Income went from $0 to $30,000" or "A new program was added where none existed before." Percentage change only works when you have a real starting point to measure from.

When the old value is very small but not zero — say $10 — a $150 increase produces a 1,500% change. This is mathematically correct but can look shocking. It is still accurate; just remember that huge percentage changes often happen when the starting number is tiny.

Percentage Change Versus Percentage Points

These two terms sound similar but mean different things, and mixing them up causes real confusion. Percentage change is what the formula above calculates — the relative shift from one value to another. Percentage points is the simple difference between two percentages.

If unemployment was 5% last year and is 8% this year, that is a 3 percentage point increase. But the percentage change in the unemployment rate itself is ((8 − 5) ÷ 5) × 100 = 60%. The rate increased by 60%, even though it only went up 3 percentage points. Both statements are true; they just measure different things.

In housing and income contexts, you will see both used. A program might say "rent increased 12 percentage points" (from 28% to 40% of income) or "rent increased 43% in dollar terms" (from $1,000 to $1,430). Read carefully to know which one is being reported.

Using Percentage Change to Compare Different Situations

Percentage change lets you compare growth or decline across situations that start at different scales. If one person's rent went from $800 to $920 and another's went from $1,600 to $1,840, the dollar increases look different ($120 versus $240), but the percentage changes are identical: both are 15% increases. Percentage change strips away the scale and shows you the actual rate of change.

This matters when you are looking at how fast something is growing. A utility bill that increases 8% year over year is growing faster than one that increases 5%, regardless of whether the first bill started at $100 or $500. The percentage tells you the rate; the dollars tell you the size.

Common Mistakes to Avoid

The most common error is dividing by the new value instead of the old one. If you do that with the rent example, you get $150 ÷ $1,350 = 11.1%, which is close but wrong. Always divide by where you started, not where you ended up.

Another mistake is forgetting to multiply by 100. The formula gives you a decimal (0.125), and multiplying by 100 converts it to a percentage (12.5%). Without that step, you will report the change as 0.125 instead of 12.5%, which is off by a factor of 100.

A third mistake is using percentage change when the old value is zero or when you are comparing percentages to percentages (rather than raw numbers). In those cases, percentage points or plain language is clearer and more honest.

Frequently Asked Questions

Can percentage change be more than 100%?

Yes. If something doubles, that is a 100% increase. If it triples, that is a 200% increase. If you had $100 and now have $500, the percentage change is ((500 − 100) ÷ 100) × 100 = 400%. Large percentage changes happen when the new value is much larger than the old one.

What does a negative percentage change mean?

A negative result means the value went down, not up. If your expenses were $2,000 and dropped to $1,500, the percentage change is ((1,500 − 2,000) ÷ 2,000) × 100 = −25%. Your expenses decreased by 25%. The negative sign is part of the answer; do not drop it.

How do I calculate percentage change over multiple years?

Use the first year as the old value and the most recent year as the new value. If rent was $1,000 in 2020 and $1,350 in 2024, the change is ((1,350 − 1,000) ÷ 1,000) × 100 = 35% over four years. To find the average annual change, you would need a different formula (compound annual growth rate), but the basic percentage change always compares two points in time.

Why does the order matter in the formula?

The order matters because you are measuring change relative to the starting point. If you reverse it and subtract new from old, you get the opposite sign, which reverses the meaning. Always put the new value first in the subtraction, then divide by the old value. This anchors the percentage to where you began.