How to Calculate Percentage Change

Percentage change tells you how much a value has gone up or down as a percentage of where it started. It is the change divided by the original value, times 100. A positive answer is a percentage increase and a negative one a percentage decrease: a board game going from £50 to £65 is a 30% increase.

Percentage change = change ÷ original value × 100, where the change is the new value minus the original value. A board game’s price goes from £50 to £65: the change is 15, so 15 ÷ 50 × 100 = 30, a 30% increase. Always divide by the original value, never the new one; that is the GCSE exam tip.

Subtract the original value from the new value, divide by the original value and multiply by 100. From £50 to £65 the change is 15, and 15 ÷ 50 × 100 = 30, so a 30% increase. From 250 to 300 the change is 50, and 50 ÷ 250 × 100 = 20%. If you want to increase a number by a percentage instead, see the Percentage Increase and Decrease lesson.

The same formula; the change comes out negative. A clock’s price drops from £80 to £60: the change is 60 − 80 = −20, and −20 ÷ 80 × 100 = −25, so a 25% decrease. A table bought for £1,200 and sold for £960 has a change of −240, and −240 ÷ 1,200 × 100 = −20%, a 20% decrease.

Always the original value, the one you started with. The sign of the answer then tells you which way it went: positive is an increase, negative a decrease. Ignore details the formula does not use: a table bought for £1,200 and sold for £960 after three years is a 20% decrease, and the three years do not come into it.

Pick the original value and the new value from the table first, then apply the formula. A cinema had 1,500 visitors in week 2 and 1,425 in week 4. The change is 1,425 − 1,500 = −75, and −75 ÷ 1,500 × 100 = −5, so visitors fell by 5% from week 2 to week 4. The weeks in between do not matter.