Percentage Calculator
Use the percentage calculator to solve the three common percentage relationships: find a percentage of a value, find the percentage rate, or recover the original base value.
Answer
Result
30
15% of 200 is 30.
Check the work
Every line comes from the same calculation as the answer.
result = base × rate ÷ 100
| result | base × rate ÷ 100 | |
|---|---|---|
| 200 × 15 ÷ 100 | 30 |
How it works
Percentage problems describe a relationship out of one hundred. The same relationship can be solved in different directions depending on which value is unknown.
The three questions below are the same equation solved for a different unknown, so one calculator handles all three: choose what you want to find and enter the two values you know. The answer is calculated in your browser, and the formula, your substituted values and each step are shown from the same equation that produced it.
Formula
result = base × rate / 100
Multiply the base value by the percentage rate and divide by 100. The same equation can be rearranged to solve for the base or the percentage rate when those values are unknown.
Worked examples
- Try these numbers
What is 15% of 200?
- Start with result = base × rate / 100.
- Substitute the values: 200 × 15 / 100.
- 200 × 15 = 3,000, then 3,000 / 100 = 30.
15% of 200 is 30.
- Try these numbers
30 is what percent of 200?
- Rearrange the formula to rate = result × 100 / base.
- Substitute the values: 30 × 100 / 200.
- 3,000 / 200 = 15.
30 is 15% of 200.
- Try these numbers
30 is 15% of what original value?
- Rearrange the formula to base = result × 100 / rate.
- Substitute the values: 30 × 100 / 15.
- 3,000 / 15 = 200.
If 30 is 15% of the original value, the original value is 200.
Inputs and results
- Base value
- The whole or original amount that the percentage is applied to.
- Percentage rate
- The percentage written as a number such as 15 for 15%.
- Percentage result
- The portion of the base represented by the selected percentage rate.
When to use it
- Calculate the portion represented by a known percentage rate when the whole or base value is known.
- Find the percentage rate represented by one value relative to a non-zero base value.
- Reverse-solve the original base value when the percentage result and a non-zero rate are known.
Common mistakes
- Entering 0.15 when you mean 15%. In this calculator, enter 15 or 15% for a fifteen-percent rate.
- Swapping the base and percentage result when asking what percentage one value is of another.
- Trying to reverse-solve through a zero denominator, such as finding a rate from a zero base or a base from a zero rate.
What it does not do
- It does not apply tax, discount, tip, markup, interest, or other domain-specific business rules; those tasks need their own inputs and assumptions.
- It does not calculate percentage change between two time points or distinguish a percentage-point difference from a percent change.
- It does not decide whether a negative base, negative result, or negative rate is meaningful for the user's real-world context.
Method and assumptions
The calculator uses the arithmetic identity result = base × rate / 100 and deterministic rearrangements of that identity for reverse solving.
Inputs and outputs must be finite numbers. The engine rejects mathematically undefined reverse solves, such as trying to recover a base from a zero percentage rate or a percentage rate from a zero base.
No statistical model, live dataset, regulatory rule, or external assumption is required for this elementary arithmetic relationship.
Assumptions
- A rate entered as 15 means 15%, not 0.15.
- The calculation is exact; only the displayed figure may be shortened, and the result says so when it is.
Edge cases
- A zero percentage rate produces a result of zero for any finite base.
- Negative bases or rates are mathematically valid and can represent decreases or signed quantities, depending on the user context.
- Reverse-solving the base when the rate is zero is undefined because division by zero would be required.
- Reverse-solving the rate when the base is zero is undefined because division by zero would be required.
Sources and corrections
This calculator uses an elementary formula, so it needs no outside data source. The method, the rounding rules and how a reported error is corrected are set out in the site standards.
Result looks wrong?
Send the inputs you used and the answer you expected. Every report is checked against the formula and its tests, and confirmed errors are corrected in public.