Percent Change Calculator

What this calculator does

You are watching a number over time, and it moved. Traffic, a price, a reading in a report, last quarter against this one. Did it go up or down, and by how much? That is a percent change, and it is the one to reach for when the value could swing either way.

Type the old figure and the new one, and the tool gives you the change and tells you whether it is a rise or a fall.

Using the calculator

1. Type the from value, the earlier or original figure.
2. Type the to value, the later or new figure.
3. Press Calculate.

The result is the size of the change as a percentage, labelled "increase" if the value went up or "decrease" if it went down. The from value cannot be zero, since the change is measured against it.

The formula | (change ÷ original) × 100

The percent change is:

((new value − old value) ÷ old value) × 100

Subtract the old from the new, divide by the old, and turn it into a percentage. If the new value is bigger the result is positive, an increase; if it is smaller the result is negative, a decrease. Either way it is measured against the old value, the one you are comparing back to.

Worked examples | both directions

Once up, once down.

• From 15 to 40: the change is 40 − 15 = 25, and 25 ÷ 15 = 1.6667, so about a 166.67% increase.
• From 40 to 15: the change is 15 − 40 = −25, and −25 ÷ 40 = −0.625, so a 62.5% decrease.

The same two numbers give very different percentages depending on which is the starting point, because the change is always measured against where you began.

Percent versus percentage points

This catches people out constantly, especially with rates. Suppose an interest rate moves from 4% to 6%. That is a rise of 2 percentage points, the plain difference between the two. But as a percent change it is ((6 − 4) ÷ 4) × 100 = 50%, because 2 is half of the starting 4. Both are correct, but they say different things, which is why news about interest rates, taxes and poll numbers usually talks in percentage points, to avoid the confusion. A percentage point is the gap between two percentages; a percent change is that gap measured against the starting percentage.

Change, increase, and decrease

This is the neutral, direction-agnostic tool. An increase and a decrease are the same calculation pointed one way or the other, and this one reports whichever happens. If you know the value only ever rises, the percent increase calculator is framed for that; if it only ever falls, the percent decrease calculator fits. For the full range of percentage questions, see the percentage calculator.

Questions people ask

What is the percent change from 15 to 40?

About a 166.67% increase. The change of 25, divided by the starting 15, times 100.

What is the percent change formula?

((new − old) ÷ old) × 100. A positive answer is an increase, a negative one a decrease.

Does it work for both increases and decreases?

Yes. It reports the size of the change and labels it an increase or a decrease depending on which way the value moved.

What is the difference between percent and percentage points?

A percentage point is the plain difference between two percentages. A percent change measures that difference against the starting percentage, so 4% to 6% is 2 percentage points but a 50% change.

Why do 15 to 40 and 40 to 15 give different percentages?

Because each is measured against its own starting value. The change is the same size, but the base it is compared with differs.

References

A note on the idea behind it. A percent change expresses the difference between an old and a new value as a fraction of the old, then as a percentage, positive for a rise and negative for a fall. It is distinct from a percentage point, which is the plain arithmetic difference between two percentages. For further reading, see Relative change and difference.

1. Percent change, the difference between a new and old value divided by the old value, expressed as a percentage.
2. Percentage point, the absolute difference between two percentages, distinct from the relative percent change between them.