Price cuts, falling sales, and business losses all come down to one skill: taking a percentage off a number, or measuring how big a drop was. This guide shows how to decrease a number by a percentage, how to find the percentage decrease between two values, and how to find loss percentage.

How to decrease a number by a percentage

Multiply the number by what is left after the decrease:

New value = Original × (1 − Percentage ÷ 100)

To decrease 80 by 15 percent: 80 × (1 − 0.15) = 80 × 0.85 = 68. You can also take the percentage off in two steps: 15 percent of 80 is 12, and 80 − 12 = 68.

Finding the percentage decrease between two numbers

When you know the old and new values and want the size of the drop:

Percentage decrease = (Old − New) ÷ Old × 100

If a price falls from 250 to 200, the decrease is (250 − 200) ÷ 250 × 100 = 20 percent. Always divide by the original value, not the new one.

The percentage change calculator works out the percentage increase or decrease between any two values.

How to find loss percentage

A loss happens when the selling price (SP) is below the cost price (CP). To find loss percentage:

Loss = CP − SP     Loss % = Loss ÷ CP × 100

Loss percentage example

You buy a phone for 1,200 and sell it for 1,050. The loss is 150, so the loss percentage is 150 ÷ 1,200 × 100 = 12.5 percent.

Selling price from a loss percentage

To find what you sold for after a known loss: SP = CP × (1 − Loss % ÷ 100). A 12.5 percent loss on 1,200 gives 1,200 × 0.875 = 1,050. Profit percentage works the same way with a plus sign: Profit % = (SP − CP) ÷ CP × 100.

Reversing a percentage decrease

To find the original value after a decrease, divide instead of multiply:

Original = New value ÷ (1 − Percentage ÷ 100)

If 68 is the price after a 15 percent cut, the original was 68 ÷ 0.85 = 80. Adding 15 percent back to 68 would give 78.20, which is wrong, because the 15 percent was taken from 80, not 68.

Successive decreases

Two decreases in a row multiply; they do not add. A 20 percent drop followed by a 10 percent drop leaves 0.8 × 0.9 = 0.72 of the original, a total decrease of 28 percent, not 30.

Percentage decrease reference

Decrease	Multiply by	100 becomes
5%	0.95	95
10%	0.90	90
15%	0.85	85
25%	0.75	75
40%	0.60	60

Common mistakes

• Dividing by the new value. Percentage decrease and loss percentage always use the original or cost price.
• Adding successive cuts. Multiply the remaining fractions instead.
• Reversing by adding the percentage back. Divide by (1 − p) to undo a decrease.

Discounts are the most common percentage decrease of all; see how to calculate discount percentage.

For exam results, read how to calculate percentage of marks.

To skip the arithmetic, use a free online calculator and check each step.