Percentage Calculator
Percentages, discounts, and changes. Get the numbers right, without the guesswork.
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How to use this tool
- Choose a calculation type.
- Enter two numbers; decimals and zero are supported.
- Read the result and formula immediately.
Understand the percentage, not just the answer
A percentage describes a quantity relative to one hundred. The important first step is choosing the right base. Finding 20% of a price is a different operation from finding how much a price changed. DuoTools separates these cases and shows the arithmetic so you can check which quantity is being compared.
Find a percentage of a number
To find X% of Y, divide X by 100 and multiply by Y. For example, 12.5% of 80 is 0.125 × 80 = 10. A zero percentage gives zero, and zero as the number also gives zero. This calculation can use values above 100%; 150% of 80 is 120.
For a tip, tax estimate, allocation, or classroom exercise, enter the rate as the first value and the base amount as the second. The result has the same unit as the base: 20% of 150 euros is 30 euros, not 30%.
Compare an original and a new value
Percentage increase uses (new − original) ÷ |original| × 100. A change from 100 to 125 is 25%. Percentage decrease reverses the difference: (original − new) ÷ |original| × 100, so a move from 100 to 75 is a 25% decrease. A negative result means the actual direction is opposite to the mode you selected.
The original value cannot be zero because division by zero does not define a relative percentage change. For negative originals, this tool uses their absolute magnitude as the denominator. That convention is explicit in the formula; in financial reporting or another specialized context, check the comparison convention your work requires.
Calculate a discount and the amount you pay
Discount amount = original price × discount rate ÷ 100. Final price = original price − discount amount. A 20% reduction on 150 saves 30 and leaves 120. This tool accepts a nonnegative original price and a discount between 0% and 100%. It does not add tax, shipping, currency conversion, or other charges.
Successive discounts do not normally add together. Taking 20% off 100 leaves 80; taking another 10% off 80 leaves 72. That is a total reduction of 28%, not 30%. Each step uses the amount remaining at that stage.
Worked examples to try
| Question | Calculation | Answer |
|---|---|---|
| What is 12.5% of 80? | 12.5 ÷ 100 × 80 | 10 |
| Increase from 80 to 100 | (100 − 80) ÷ 80 × 100 | 25% |
| Decrease from 100 to 80 | (100 − 80) ÷ 100 × 100 | 20% |
| 20% discount on 150 | 150 − (150 × 0.20) | 120 final price |
A few things you might wonder
Why is a change from zero unavailable?
A relative change divides by the original value. When the original is zero, there is no finite percentage result. Report the absolute difference or use a context-specific alternative instead.
Why do increases and decreases use different bases?
The original amount is the base. Going from 80 to 100 is a 25% increase; returning from 100 to 80 is a 20% decrease. The difference is 20 in both cases, but the starting amounts differ.
Does the calculator round money correctly?
Results display up to eight decimal places and use JavaScript floating point. Currency-specific rounding, tax rules, and accounting precision are not implemented. Apply the rounding required for your use case.
Can I calculate a negative percentage?
The percentage-of-number and change calculations accept negative values. Discounts are restricted to 0–100% and nonnegative prices. A signed change is shown rather than silently converted to a positive number.
Check your inputs before using the result
Identify the original base, choose the matching mode, and check the displayed formula. Use unrounded values for intermediate steps when possible. These are general arithmetic results, not tax, investment, or accounting advice.