How do you calculate percent change?

Subtract the old value from the new value, divide by the old value, then multiply by 100. From 50 to 65: 15 ÷ 50 × 100 = 30% increase.

How do you work out a percent decrease?

Use the same formula. The answer comes out negative, which means a decrease. From 200 to 150: −50 ÷ 200 × 100 = −25%, a 25% decrease.

Is percent change the same as percent difference?

No. Percent change compares with the starting value. Percent difference compares two values with their average, and is used when neither one is the starting point.

Can percent change be more than 100%?

Yes, for an increase. Going from 20 to 50 is a 150% increase. A decrease can't be more than 100%, because that would take a positive amount below zero.

What if the old value is 0?

Percent change isn't defined, because you'd be dividing by zero. Describe the change as an amount instead.

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Percent change calculator, with the steps shown

Type an old value and a new value to get the percent increase or decrease, with each step written out. Two more tabs add or take off a percent, and find a percent of a number.

Starting value (old)New value

25% increase

From 80 to 100: a change of +20

Steps

Find the change: new − old = 100 − 80 = 20.
Divide the change by the starting value: 20 ÷ 80 = 0.25.
Multiply by 100 to make it a percent: 0.25 × 100 = 25%.
The answer is positive, so it is an increase: 25% increase.

The percent change formula

Percent change = (new value − old value) ÷ old value × 100. A positive answer is a percent increase and a negative answer is a percent decrease. The key is to always divide by the old value, the one you started from.

For example, a plant grows from 80 cm to 100 cm. The change is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25. Multiply by 100: a 25% increase.

Why the starting value matters

Going from 80 to 100 is a 25% increase, but going back from 100 to 80 is only a 20% decrease, because the change of 20 is compared with 100 this time. That's why a 25% rise followed by a 20% fall brings you back to where you started, and why "50% up then 50% down" leaves you lower than you began.

Increase or decrease by a percent

To increase 80 by 15%, find 15% of 80 (12) and add it on: 92. To decrease, take it away: 68. The quick way is a multiplier: 80 × 1.15 = 92 and 80 × 0.85 = 68. Shops use the decrease for sales, and the increase for tax and price rises.

Percent change and percentage points

When the numbers are already percents, be careful. A test score rising from 40% to 50% is a rise of 10 percentage points, but a percent change of 25%, because 10 ÷ 40 = 0.25. News reports mix these up all the time.

Questions people ask

How do you calculate percent change?: Subtract the old value from the new value, divide by the old value, then multiply by 100. From 50 to 65: 15 ÷ 50 × 100 = 30% increase.
How do you work out a percent decrease?: Use the same formula. The answer comes out negative, which means a decrease. From 200 to 150: −50 ÷ 200 × 100 = −25%, a 25% decrease.
Is percent change the same as percent difference?: No. Percent change compares with the starting value. Percent difference compares two values with their average, and is used when neither one is the starting point.
Can percent change be more than 100%?: Yes, for an increase. Going from 20 to 50 is a 150% increase. A decrease can't be more than 100%, because that would take a positive amount below zero.
What if the old value is 0?: Percent change isn't defined, because you'd be dividing by zero. Describe the change as an amount instead.

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