How to calculate a percentage of a value
Use this formula: value × rate ÷ 100. To find 20% of 150, calculate 150 × 20 ÷ 100 = 30. Check which value the percentage is based on before you start.
How to calculate a discount
First calculate the discount, then subtract it from the original price. An item priced at 80 with a 25% discount has a reduction of 20 and a final price of 60. Direct formula: original price × (1 − rate ÷ 100).
How to calculate an increase
Add the percentage amount to the original value. If 120 increases by 10%, the increase is 12 and the new value is 132. Direct formula: original value × (1 + rate ÷ 100).
What percentage is one number of another?
Divide the part by the total and multiply by 100. If 18 out of 60 tasks are completed, the result is 18 ÷ 60 × 100 = 30%. The total must not be zero.
Why do equal increases and discounts not cancel out?
The starting values change. A value of 100 that increases by 20% becomes 120. A later 20% discount on 120 produces 96. The same percentage was applied to different values.
Percentages and percentage points
A rate that goes from 10% to 15% rises by 5 percentage points. The relative increase in the rate is 50%, because (15 − 10) ÷ 10 × 100 = 50. Choose the right expression to avoid confusion.
Check your result
Check the starting value, keep decimal places during the calculation and round only at the end. For monetary amounts, also check the rounding rule used for the charge.
Try the percentage calculator to check an example step by step.
Match the calculation to the question
These are three different questions: “What is 15% of 200?”, “What percentage of 200 is 30?” and “What was the total if 30 represents 15%?”. For the first, the amount is 200 × 15 ÷ 100 = 30. For the second, the rate is 30 ÷ 200 × 100 = 15%. For the third, the total is 30 ÷ 0.15 = 200. Identify the missing quantity before choosing an operation.
Successive discounts do not simply add up
Example: an item costs 200 and receives a 20% discount. That takes off 40, leaving 160. A further 10% discount on the reduced price takes off 16, producing a final price of 144.
The total reduction is 56, or 28% of 200. Adding 20% and 10% would give 30%, but incorrectly assumes both reductions use the original base. Check whether the second offer applies to the reduced price and whether the offers can be combined.
Compare the final amount, including charges
Consider a purchase of 120 with a 15% discount and delivery costing 18. The item becomes 102; delivery takes the total back to 120. A different offer with no discount but free delivery could cost the same. Use confirmed conditions rather than assuming the advertised percentage determines the best purchase.
If an amount rises from 80 to 100, the increase is 25%: divide the difference of 20 by the starting amount, 80. Moving from 100 back to 80 is a 20% decrease. Reversing direction changes the base. A rate moving from 10% to 15% rises by five percentage points; its proportional increase is 50%.
Common percentage questions
Does a 20% increase undo a 20% discount?
No. Reducing 100 to 80 removes 20%. Adding 20% to 80 adds 16 and gives 96. Returning from 80 to 100 requires a 25% increase.
When should I round?
Keep precision through intermediate steps and round the final display. For an actual purchase, check the seller’s rules for instalments and rounding.
Check each step with the percentage calculator, noting the base before comparing your result.
