Percentage and discount calculator with steps
Work out percentages and sale prices, with each step shown so you can check the maths.
Accepted input
Plain numbers, including decimals and negatives where they make sense. No currency is assumed, so use any currency or unit. Results are rounded to two decimal places for display only.
How to use this tool
- Pick the calculator that matches your question and fill in its boxes.
- The answer and the working appear underneath immediately.
- For prices, enter the original price, the discount percentage and, if needed, a tax percentage.
Formulas
| Calculator | Formula |
|---|---|
| Percentage of a number | (percent ÷ 100) × number |
| Increase or decrease | ((new − old) ÷ |old|) × 100 |
| Percentage difference | (|A − B| ÷ average of A and B) × 100 |
| Discount | discount = price × rate ÷ 100; final = price − discount; tax is added on the discounted amount |
Worked examples
20% of 150 is (20 ÷ 100) × 150 = 30.
80 to 100 is a 25% increase; 100 to 80 is a 20% decrease. The same gap gives different percentages because the starting value differs.
80 and 100 differ by 22.22% (20 ÷ 90 × 100) when you compare them as peers rather than before and after.
Price 80, 25% off, 10% tax: discount 20, discounted price 60, tax 6, final price 66.
Edge cases
A change from zero has no percentage, because the formula divides by zero, so the tool says it is undefined. The same applies when two values average to zero. A discount above 100% or below 0% is rejected. Tax rules, rounding and whether tax applies before or after a discount differ by shop and country, so the final price on a receipt may differ slightly.
Notice
This is a general-purpose calculator. It is not financial, tax or legal advice.
One worked example for each calculator
- Percentage of a number. 15% of 240 is (15 ÷ 100) × 240 = 36.
- Increase or decrease. From 50 to 65 is ((65 − 50) ÷ 50) × 100 = 30% increase. From 200 to 150 is ((150 − 200) ÷ 200) × 100 = −25%, which the tool shows as −25% followed by the word “decrease”.
- Percentage difference. For 40 and 60, the difference is 20 and the average is 50, so the percentage difference is 20 ÷ 50 × 100 = 40%.
- Discount and final price. A price of 1,200 with 15% off and 5% tax: discount = 180, discounted price = 1,020, tax = 51, final price = 1,071.
Which calculator to use
| Question | Use |
|---|---|
| “What is 12% of this amount?” | Percentage of a number |
| “How much did it go up or down?” | Increase or decrease, with an old and a new value |
| “How different are these two figures?” with no before or after | Percentage difference |
| “What will I pay after the sale?” | Discount and final price |
Notes on the maths
- Increase or decrease uses the old value as the base, and uses its absolute value so the sign of the change reads correctly. Changes between negative numbers can be hard to interpret in everyday terms, so check that the answer makes sense for your situation.
- Percentage difference divides by the average of the two numbers, so it is the same whichever one you enter first. It is not the same as percentage change.
- Results are rounded to two decimal places for display. Internally, calculations keep full precision.
- Tax is optional and is added to the discounted price. Leave it blank for none.
Input rules and edge cases
- Boxes must contain numbers. Empty boxes show a prompt, not an error.
- A change from zero is reported as undefined, because the formula divides by zero.
- Two values that average to zero, such as 5 and −5, give an undefined percentage difference.
- A discount must be between 0 and 100 and the price must not be negative.
Troubleshooting
| What you see | Likely reason | What to try |
|---|---|---|
| “Enter both numbers” | One box is empty or not a number | Fill in both boxes |
| Result differs from the receipt | The shop rounds or taxes differently | Treat the receipt as final |
| Percentage looks wrong | Old and new values swapped | Check which number is the starting value |
This calculator is for general use and is not financial, tax or legal advice. For step-by-step explanations of discounts, see how to calculate discounts and final prices.
Frequently asked questions
Is tax added before or after the discount?
Here tax is added after the discount. Some places calculate it differently.
Why is a 25% increase not reversed by a 25% decrease?
Because the second percentage applies to a larger number.
Can I use any currency?
Yes. The tool just works with numbers.