Percentage change calculator

How to use the percentage change calculator

1. Type the old value in From and the new value in To.
2. The answer shows as you type: an increase or a decrease in percent, with the difference and the working.
3. Press the arrows between the boxes to swap the numbers and see the change the other way round.

The second box answers the opposite question: what a number becomes when it goes up or down by a percentage. It starts with 80 increased by 25%, which is 100.

The formula

Percentage change = (new − old) ÷ old × 100

A positive answer is an increase, a negative one a decrease. Some changes worked out with the calculator:

What changed	From	To	Change
Coffee price	2.50	2.80	+12%
Monthly pay	2,400	2,520	+5%
Town population	48,000	45,600	−5%
Test score	64	80	+25%

The town lost 2,400 people, and 2,400 ÷ 48,000 × 100 is 5%: a decrease of 5%.

Why up and down aren’t the same

A change is always a share of the starting value, so the same gap gives a different percentage in each direction. From 80 to 100 is an increase of 25%, but from 100 back to 80 is a decrease of 20%.

That’s also why a rise and a fall of the same percentage don’t cancel out. A share worth 100 that gains 50% is worth 150; if it then loses 50%, it’s worth 75. Once something has halved, it has to double, an increase of 100%, to get back to where it was.

Percent change or percentage points?

When the numbers are themselves percentages, two answers are possible. A loan’s interest rate going from 4% to 5% has risen by 1 percentage point, the gap between the two. As a percentage change, it has risen by 25%, because 1 is a quarter of 4.

Both are correct. Type 4% and 5% in the calculator, with the % signs, and it gives both: the change of 25%, and a difference of 1 percentage point.

Starting from 0, or below 0

From 0, there’s no percentage change: going from 0 to 12 sales isn’t any percentage of nothing. The calculator gives the difference instead.

From a negative number, the calculator divides by the old value’s size, without its minus sign, so going up is always an increase. A business that loses 50,000 one year and 20,000 the next has gone from −50,000 to −20,000: (−20,000 − (−50,000)) ÷ 50,000 × 100, an increase of 60%. Dividing by −50,000 as it is would call it a decrease of 60%, which reads the wrong way. Some textbooks and reports use other rules, so when you share a change from a negative value, say how you worked it out.

Percentage difference: no before or after

When two values don’t come one after the other, like the same phone at 80 in one shop and 100 in another, you can compare them with the percentage difference. Divide the gap by the average of the two numbers: 20 ÷ 90 × 100 is 22.2%. Unlike a percentage change, it’s the same either way round.

For other questions, like 15% of a bill or what percent 18 is of 24, use the percentage calculator.