Percentage to Decimal Converter
Convert percentages to decimals and back, with the fraction form alongside.
What this tool does
A percentage to decimal converter divides the percentage by 100: 75% becomes 0.75 and 5% becomes 0.05. The reverse multiplies by 100. The conversion exists because 'percent' literally means 'per hundred' - the symbol is a unit that has to be removed before the number can be used in arithmetic. Chained percentages then multiply: 5% of 3% is 0.05 × 0.03 = 0.0015, which is 0.15%, not 8%.
Converts percentage to decimal and back, with the fraction form shown alongside.
Handles chained percentages correctly: 5% of 3% is 0.0015, not 0.2.
Explains why dividing by 100 is the whole conversion, so it can be done without a tool.
Shows the fraction form reduced to lowest terms for the common cases.
How to use it
- Enter a percentage to convert to decimal, or a decimal to convert to percentage.
- The other field updates automatically.
- Read the fraction form alongside for the common values.
- Use the chained calculator for a percentage of a percentage.
Why use this calculator
Converting a percentage to a decimal is the step that makes any percentage arithmetic possible - tax, discount, interest and probability all need the percent sign removed before the number works. Most people know the move is 'divide by 100', and just as many lose confidence at 0.075% or 3.25%, where the decimal places pile up. The chained case is where the real errors live: adding percentages that should multiply, which inflates answers by whole orders of magnitude.
Why we built it
We built the percentage to decimal converter to show the fraction alongside both forms, because the three representations - percent, decimal and fraction - are the same quantity and seeing all three settles the arithmetic. The percentage calculator works out a percentage of a number, the decimal to fraction calculator runs the other direction with repeating decimals, and the fraction calculator handles the fraction arithmetic itself.
For percentages that carry money, the discount calculator applies them to a price and the markup calculator works the margin side - both of which depend on this same conversion.
Who this tool is for
- Anyone doing tax, discount or interest arithmetic by hand
- Students moving between percentages, decimals and fractions
- Spreadsheet users entering rates as decimals
- Anyone double-checking a percentage calculation
When to use it
- Entering an interest or tax rate into a spreadsheet.
- Checking a discount that looks larger than expected.
- Converting a percentage probability for statistics.
- Moving between fraction, decimal and percent forms.
How it is calculated
Decimal = percentage ÷ 100. Percentage = decimal × 100. The fraction form is the percentage over 100, reduced: 75% is 75/100 = 3/4. For chained percentages, multiply the decimals: 5% of 3% is 0.05 × 0.03 = 0.0015. To apply a percentage to a number, multiply by the decimal: 15% of 80 is 0.15 × 80 = 12.
Worked example: 7.5% as a decimal is 0.075, as a fraction 7.5/100 = 15/200 = 3/40. Applied to 200, that is 0.075 × 200 = 15. Chained with 20%, 0.20 × 0.075 = 0.015, which is 1.5% - far smaller than the 27.5% that adding would suggest.
Percent changes add only when they describe separate effects on the same base. Two successive 10% rises give 1.10 × 1.10 = 1.21, a 21% total rise, not 20%. This is why sequential discounts and compound growth always multiply.
Common conversions
| Percentage | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 5% | 0.05 | 1/20 |
| 7.5% | 0.075 | 3/40 |
| 12.5% | 0.125 | 1/8 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 33.3% | 0.333 | 1/3 (approx) |
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Percentage | 7.5% |
| Second percentage (chain) | 20% |
With those inputs, the calculator returns:
- Decimal: 0.075
- Fraction: 3/40
- Chained with 20%: 0.20 × 0.075 = 0.015 (1.5%)
- 7.5% of 200: 15
Chained percentages, done right
| Calculation | Wrong (added) | Correct (multiplied) |
|---|---|---|
| Two 10% rises | 20% | 21% |
| 10% then 20% | 30% | 32% |
| 5% of 3% | 8% | 0.15% |
| 25% off then 50% off | 75% | 62.5% off total |
Successive changes multiply because each applies to the already-changed result. Two half-price discounts in a row take three quarters off the original price, not the whole thing.
What you enter, and what you get back
| Item | Details |
|---|---|
| Percentage or decimal | Either direction, converted live. |
| Second percentage | Optional, for the chained calculation. |
| Result | Decimal, fraction, chained result and the applied value. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Result ten times out | Decimal point in the wrong place. | Divide by 100, not 10 - two decimal places for whole percentages. |
| Chained percentages too big | Percentages added instead of multiplied. | Multiply the decimals; see the table above. |
| Repeating decimal in fraction form | Thirds and sevenths never terminate. | Keep the fraction form for exactness. |
| Spreadsheet shows 0.075 not 7.5% | Cell not formatted as percentage. | Format the cell, or multiply the rate by 100. |
Assumptions and limitations
- Converts a single percentage between forms; it does not assess the context of the calculation.
- Fraction form is exact for terminating decimals and approximate for repeating ones.
- Chained percentages assume each applies to the previous result, which is the usual convention.
- For money applications, rounding at each step can change the total slightly.
Frequently asked questions
How do I convert a percentage to a decimal?
Divide by 100, which removes the percent sign. 75% becomes 0.75, 5% becomes 0.05, and 7.5% becomes 0.075. Each whole percentage point is two decimal places, so 0.5% is 0.005.
How do I convert a decimal to a percentage?
Multiply by 100. 0.075 becomes 7.5% and 0.5 becomes 50%. In a spreadsheet, formatting the cell as a percentage does this automatically - the underlying value stays the decimal.
How do I convert a percentage to a fraction?
Write the percentage over 100 and reduce. 75% is 75/100 = 3/4, 12.5% is 12.5/100 = 1/8. For percentages with decimals, multiply top and bottom by 10 first: 7.5/100 becomes 75/1000 = 3/40.
Why do you divide by 100?
Because 'percent' means 'per hundred' - 75% is a ratio of 75 to 100, and dividing converts that ratio into the plain decimal 0.75 that arithmetic can use. The division is the entire conversion; there is nothing more to it.
How do I convert 7.5% to a decimal?
7.5% is 0.075. Move the decimal point two places left: 7.5 → 0.75 → 0.075. As a fraction it is 7.5/100 = 3/40. Applied to 200, it gives 0.075 × 200 = 15.
How do I convert a percentage to a ratio?
Divide by 100 and simplify both sides, or read the fraction directly. 40% is 40:100, which reduces to 2:5. 5% is 5:100 or 1:20. The ratio and the fraction carry the same information; the ratio simply emphasises the comparison.