Percent Decrease Calculator

What this calculator does

A jacket dropped from 120 to 90. Your load time fell from 4 seconds to 2.5. The new number is smaller, and you want the size of that fall as a percentage. That is a percent decrease, measured against the value you began with.

Type the starting value and the final value, and the tool works out the decrease.

Using the calculator

1. Type the initial value, the original amount.
2. Type the final value, the reduced amount.
3. Press Calculate.

You will get the percentage along with the word "decrease". The starting value cannot be zero, since there would be nothing to measure against. And if you enter a final value that is actually larger, the tool will tell you it is an increase instead.

The formula | (drop ÷ original) × 100

The percent decrease is:

((initial value − final value) ÷ initial value) × 100

Work out the drop, the initial minus the final, then ask what fraction of the original that drop is, and turn it into a percentage. As with an increase, you divide by the starting value. The decrease is measured against where you began, not against the smaller number you ended on.

A worked example | 200 to 120

Say a price fell from 200 to 120.

1. The drop: 200 − 120 = 80.
2. As a fraction of the original: 80 ÷ 200 = 0.4.
3. As a percentage: 0.4 × 100 = 40%.

So it is a 40% decrease. The 80 is compared against the starting 200, which is why the same 80 drop would be a different percentage if the price had started somewhere else.

Two discounts do not add up

A useful one for shopping. If an item is 30% off and then a further 15% comes off at the till, that is not 45% off. The second discount comes off the already-reduced price, not the original, so the decreases multiply rather than add. Take 30% off 100 and you have 70; take 15% off that 70 and you have 59.50, which is a 40.5% discount overall, not 45%. Stacked reductions always come out a little less than their sum.

Decrease, increase, and change

A decrease, an increase and a general change are really one calculation: the gap between two values, measured against the starting one. This tool is framed for things going down. When a value rises, the percent increase calculator fits better, and when you want the change whichever way it goes, the percent change calculator covers both. For the broader set of percentage questions, see the percentage calculator.

Questions people ask

What is the percent decrease from 200 to 120?

40%. The drop of 80, divided by the original 200, times 100.

What is the percent decrease formula?

((initial − final) ÷ initial) × 100. The drop divided by the starting value, as a percentage.

Do I divide by the original or the final value?

The original. A percent decrease is measured against where you started.

Is 30% off then 15% off the same as 45% off?

No, it is 40.5% off. The second discount applies to the already-reduced price, so the discounts multiply rather than add.

What if my final value is higher than my initial value?

Then it is an increase, and the tool will say so. For that case the percent increase calculator is the better fit.

References

A note on the idea behind it. A percent decrease expresses the drop between two values as a fraction of the starting value, then as a percentage. Because each reduction is measured against its own base, successive discounts combine by multiplying, leaving a total slightly smaller than their sum. For further reading, see Relative change and difference.

1. Percent decrease, the drop between two values divided by the starting value, expressed as a percentage.