How to Calculate a Percentage Increase

A percentage increase shows how much a value grew, relative to where it started. It works for a price, a salary, a follower count, or a test score. One formula covers them all.

The short answer: subtract the old value from the new one, divide by the old value, then multiply by 100. The result is the percent increase. Below is the formula and a few real examples.

Why learn it? Because percentages let you compare changes of different sizes on a fair footing. A $5 rise means little until you know what it rose from. The percent puts every change on the same scale, so you can weigh a raise against a rent hike against a price cut.

The percent change formula

Percent change always compares the change to the starting value, not to the new one. That starting value is the key. Here is the formula:

Increase % = ( new − old ) / old × 100

Each part is simple:

• old is the value you started with.
• new is the value you ended with.
• The result is a percent. A positive number is an increase, a negative one is a decrease.

Everyday examples

Say your salary rises from $40,000 to $44,000. Plug the numbers in.

1. Subtract: 44,000 − 40,000 = 4,000.
2. Divide by the old salary: 4,000 / 40,000 = 0.1.
3. Multiply by 100: 0.1 × 100 = 10.

That is a 10% raise. Now a price example: a coffee goes from $25 to $30 for a monthly subscription.

1. Subtract: 30 − 25 = 5.
2. Divide: 5 / 25 = 0.2.
3. Multiply by 100: 20.

The price rose 20%. Same formula, different numbers.

One more, with rent. It climbs from $1,200 to $1,320. Subtract to get 120, divide by 1,200 to get 0.1, then multiply by 100. That is a 10% rise. Notice the pattern: the bigger the starting value, the smaller a fixed dollar change looks in percent terms. A $120 jump is 10% on $1,200 rent but 48% on a $250 bill.

How to calculate a decrease

A decrease uses the exact same formula. The difference comes out negative, which tells you the value fell. Say that $30 subscription drops back to $24.

1. Subtract: 24 − 30 = −6.
2. Divide by the old price: −6 / 30 = −0.2.
3. Multiply by 100: −20.

The price fell 20%. Note a quirk: a 20% rise followed by a 20% fall does not return you to the start. The rise and the fall are measured against different starting values, so $25 up 20% is $30, but $30 down 20% is $24, not $25.

Percent versus percentage points

This is the mistake that trips people up. A percentage point is a flat gap between two percentages. A percent change is relative.

Say a savings rate moves from 2% to 3%. That is a rise of 1 percentage point. But as a percent increase it is much bigger: ( 3 − 2 ) / 2 × 100 = 50%. Both statements are true. They just measure different things, so name which one you mean.

A faster shortcut

Once the formula clicks, there is a quicker route. Divide the new value by the old one, then read the result. A ratio above 1 is an increase, a ratio below 1 is a decrease.

1. Divide: 44,000 / 40,000 = 1.1.
2. Subtract 1: 1.1 − 1 = 0.1.
3. Multiply by 100: 10% increase.

This is the same math in one fewer step. It also makes the reverse easy: a ratio of 1.1 means the new value is 110% of the old one. Use whichever version you find clearer.

Common mistakes to avoid

• Dividing by the new value instead of the old one. Always divide by where you started.
• Forgetting to multiply by 100. A result of 0.1 is 10%, not 0.1%.
• Confusing percent change with percentage points. They are not the same.
• Assuming a rise and an equal fall cancel out. They do not, because the base changes.

Frequently asked questions

What if the old value is zero? The formula breaks, because you cannot divide by zero. A jump from 0 to any number has no defined percent increase.

Can the increase be over 100%? Yes. If a value more than doubles, the increase passes 100%. Going from 10 to 30 is a 200% increase.

How do I reverse it? To grow a value by a percent, multiply by one plus the decimal. To raise 40,000 by 10%, compute 40,000 × 1.1 = 44,000.

How do I find the original value? Work backward. If a price is $44 after a 10% rise, divide by 1.1 to get the start: 44 / 1.1 = $40. Dividing undoes the increase.

Does the order of two changes matter? For the final value, no. A 10% rise then a 20% rise gives the same result either way, because you multiply by 1.1 and 1.2 in any order. For the percent change at each step, though, the base differs.