Percentage Change Formula Explained

A price went from $40 to $50. Is that a 20 percent jump or a 25 percent jump? The answer is 25 percent, and the reason comes down to one small rule: you divide the change by the original value, not the new one. The percentage change formula is ((new – old) / old) x 100. Get the denominator right and every answer falls into place.

The Percentage Change Formula

Percentage change measures how much a value grew or shrank compared to where it started. You use it whenever you have two numbers, an old one and a new one, and want the size of the shift as a percent.

The formula has three simple steps:

1. Find the change: new value minus old value.
2. Divide that change by the old (original) value.
3. Multiply by 100 to turn the decimal into a percent.

Written out, that is ((new – old) / old) x 100. The sign of your answer tells the story. A positive number means the value went up. A negative number means it went down. Keep the minus sign; it is not a mistake, it is information.

Why You Divide by the Original

The most common mistake is dividing by the wrong number. Percentage change always measures growth relative to the starting point, so the old value belongs on the bottom.

Think about what “percent change” is really asking: out of where you began, how big was the move? The change is a slice, and the original value is the whole pie it came from. If you divide by the new value instead, you are measuring against the wrong whole and your answer will be off.

This is why $40 to $50 is not the same size move as $50 to $40. Going up, the base is 40, so 10/40 gives 25 percent. Going down, the base is 50, so 10/50 gives 20 percent. Same 10-dollar gap, different starting points, different percents. The base decides everything.

If you instead want to apply a known percent to a value and find the result, that is a different task. Our guide on percentage increase and decrease covers that, and how to calculate a percentage covers basic “X% of Y”.

What Counts as Old and What Counts as New

The formula only works if you assign the two values correctly. The old value is where you started, and the new value is where you ended up. Mixing them up flips the sign of your answer.

In a comparison over time, the old value is the earlier reading and the new value is the later one. A stock at $80 in January and $92 in March uses 80 as the old value and 92 as the new value. The earlier date points you to the base.

When time is not involved, the old value is your reference or baseline, the thing you measure against. Compare a budget of $500 to actual spending of $560, and the budget is the base. Set the base first, and the rest of the formula falls into line.

A Worked Example (Increase)

Say a jacket was $40 last month and is $50 today. How big is the increase in percent? Plug the numbers into the formula and work one step at a time.

1. Change: new – old = 50 – 40 = 10.
2. Divide by the old value: 10 / 40 = 0.25.
3. Multiply by 100: 0.25 x 100 = 25.

The result is +25 percent, a 25 percent increase. The answer is positive, which confirms the price went up. Notice we divided by 40, the original price, not by 50.

You can sanity-check any increase quickly. A 25 percent rise means the change should be one quarter of the base. One quarter of 40 is 10, which matches the 10-dollar jump exactly. If the change and the base do not fit together like that, recheck your setup before trusting the number.

Percentage Decrease Works the Same Way

You do not need a different formula for a drop. The same ((new – old) / old) x 100 handles decreases too. The math simply produces a negative number, and that minus sign is what tells you the value fell.

Reverse the earlier example. The jacket was $50 and is now $40. Work the steps again.

1. Change: new – old = 40 – 50 = -10.
2. Divide by the old value: -10 / 50 = -0.2.
3. Multiply by 100: -0.2 x 100 = -20.

The result is -20 percent, a 20 percent decrease. The negative sign is doing real work here; it flags a drop. This is also why the increase and the decrease are not equal. Up from 40 was +25 percent, but down from 50 is only -20 percent, because each time you divide by that trip’s own starting value. To confirm results like these fast, drop the two numbers into our Percentage Calculator.

Percentage Points vs Percent

Here is a distinction that trips up even careful readers. When the values you compare are themselves percentages, “percentage points” and “percent” mean two different things.

• Percentage points: the plain gap between two percents. Going from 10% to 15% is a rise of 5 percentage points, because 15 minus 10 is 5.
• Percent (relative change): that same move, run through the percentage change formula. ((15 – 10) / 10) x 100 = 50%. So it is a 50 percent increase relative to the starting 10%.

Both statements describe the same shift, but they are not interchangeable. A headline that says a rate “rose 50 percent” and one that says it “rose 5 percentage points” can point to the exact same change from 10% to 15%. When you read or write about changing percentages, name which one you mean.

Common Mistakes to Avoid

Most percentage change errors come from a few repeat offenders. Watch for these and your answers will stay reliable.

• Dividing by the new value. The base is always the old value; using the new one throws the answer off.
• Dropping the minus sign. A negative result is not a typo. It marks a decrease, so keep it.
• Forgetting to multiply by 100. Skip this step and you report 0.25 instead of 25 percent.
• Confusing points with percent. A rise from 10% to 15% is 5 points but a 50 percent relative change.
• Swapping old and new. The earlier value is old; the later value is new.

When in doubt, write down your old and new values first, then plug them in. A slow, labeled setup beats a fast, scrambled one every time.

Frequently Asked Questions About Percentage Change

Sources

This article is for general education only, not professional or financial advice. Always double-check the math for your own numbers before you rely on it. Reviewed for accuracy by Prof. Dr. Khalil Mudassar, PhD. Last updated September 11, 2026.