Percentage increase vs. discount: how to calculate both correctly

Calculate percentage increases and discounts with clear examples. Learn why a 20% discount and a 20% increase do not cancel each other out.

Start with the amount the percentage applies to

A percentage describes a part of a starting amount. A 20% discount means subtracting 20 out of every 100 parts of the original price. A 20% increase means adding that proportion to the starting amount. The arithmetic is simple once you identify the correct starting number.

The most common mistake is using the same percentage after the starting amount has changed. That is why a discount followed by an equal percentage increase does not bring you back to the original price.

How to calculate a discount

To find a discounted price, multiply the original price by one minus the discount rate expressed as a decimal. For a 20% discount, the decimal rate is 0.20 and the remaining proportion is 0.80.

• Original price: $100.00
• Discount amount: $100.00 × 0.20 = $20.00
• New price: $100.00 − $20.00 = $80.00
• Direct calculation: $100.00 × 0.80 = $80.00

Both approaches give the same answer. Showing the discount amount separately can help when you want to explain how much was saved. The direct calculation is useful when you only need the final price.

How to calculate an increase

For a percentage increase, multiply the starting amount by one plus the decimal rate. Increasing $80 by 20% means multiplying $80 by 1.20.

• Starting amount: $80.00
• Increase amount: $80.00 × 0.20 = $16.00
• New amount: $80.00 + $16.00 = $96.00

Notice that the increase adds $16, while the earlier discount removed $20. The rate is the same, but its base is different. To get from $80 back to $100, you need an increase of $20 divided by $80: 0.25, or 25%.

How to find the percentage change between two amounts

Subtract the old amount from the new amount, divide the difference by the old amount, and multiply by 100. For example, a price moving from $50 to $65 increases by ($65 − $50) ÷ $50 × 100 = 30%.

Always label the old and new amounts. Reversing them changes the question. Moving from $65 down to $50 is a decrease of approximately 23.08%, because $65 is now the starting amount.

Two discounts happen one after another

A 10% discount followed by another 10% discount is not a 20% discount. Starting at $100, the first discount gives $90. The second takes 10% of $90, which is $9, leaving $81. The combined discount is 19% of the original price.

Make percentage calculations easy to check

Keep the starting amount, percentage, change amount, and result on separate labeled lines. Use extra decimal places during intermediate calculations and round the final amount appropriately for your example.

Calculator Duo is an upcoming iOS calculation-sheet app designed around visible steps and editable calculations. While it is in development, these examples provide a useful structure for checking percentage math in any calculator.