The Free Online Percentage Calculator is a tool that saves time and eliminates the need to remember all the equations to calculate percentages.
What is \(p=\)% of \(y=\)?
\[x = p\cdot y\]
What percentage is \(x=\) of \(y=\)?
\[p = \frac{x}{y}\]
What percentage increase/decrease is it from \(s=\) to \(t=\)?
\[p = \frac{t - s}{s} = \frac{t}{s} - 1\]
How much is \(x=\)\(p=\)%?
\[y = x\cdot (1 \pm p)\]
What percentage change does adding or subtracting an amount \(d=\) to \(s=\) represent?
\[p = \frac{(s + d) - s}{s} = \frac{d}{s}\]
\(x=\) is how much of \(p=\)%?
\[y = \frac{x}{p}\]
Financial Percent Calculators
After how many years will inflation at rate \(r=\)% lead to \(p=\)% of the original value?
\[\begin{array}{rl} (1-r)^n &= p\\ n\cdot\log(1-r) &= \log(p)\\ n&= \log_{1-r}(p) \end{array}\]
With inflation at \(r=\)% per year, what is the value loss after \(n=\) years?
\[p=1 - \left(1 - r\right)^n\]
After how many years will a value get to \(p=\)% (200% = doubling) at interest rate \(r=\)%?
\[\begin{array}{rl} (1+r)^k &= p\\ k\cdot\log(1+r) &= \log(p)\\ k&= \log_{1+r}(p) \end{array}\]
What selling price should I set to have \(n=\)$ remaining after a commission of \(p=\)%?
\[\begin{array}{rl} x - x p &= n\\ x(1 - p) &= n\\ x &= \frac{n}{1 - p} \end{array}\]
After we bought a stock for \(x=\)$, the stock price dropped from \(s=\)$ to \(t=\)$. How many more shares could we have bought now?
\[\begin{array}{rrl} & L&=x\left(\frac{t}{s}-1\right)\\ \Rightarrow & n&=-\frac{L}{t}\\ & &= \frac{x}{t} - \frac{x}{s} \end{array}\]
How much does a stock share need to rise to get back to the original price after a \(p=\)% drop?
\[ x \overset{-p}{\rightarrow} x' \overset{+p'}{\rightarrow} x \] Therefore \[ \begin{array}{rl} p &= \frac{x' - x}{x}\\ p' &= \frac{x - x'}{x'}\\ \end{array} \] Therefore \[\begin{array}{rl} p' &= \frac{x - x'}{x'}\\ &= \frac{x - (xp+x)}{xp+x}\\ &= -\frac{p}{p + 1}\\ &= \frac{1}{p + 1} - 1\\ \end{array}\]
What is a Percentage?
Comparing fractions with different denominators can be tricky. For example, which is larger: \( \frac{7}{15} \) or \( \frac{5}{12} \)? To compare, we could find a common denominator, but an easier approach is to normalize both fractions to a denominator of 100, converting them into percentages.
By multiplying \( \frac{7}{15} \) by \( \frac{100}{1} \), we get \( \frac{46.67}{100} = 46.67\% \). Similarly, \( \frac{5}{12} \times \frac{100}{1} = \frac{41.67}{100} = 41.67\% \). This shows \( \frac{7}{15} \) is larger.
This method of using a denominator of 100 simplifies comparisons and gives rise to the concept of percentages, represented with the symbol %. For instance, \( \frac{35}{50} = 70\% \), and \( 1.5 = 150\% \).
Example of Percentage Change
The change in the value of an amount can be expressed as a percentage increase or decrease relative to its original value. For example, if someone earning $500 per month receives a 5% raise, this means an additional $5 for every $100 of their salary. Thus, $100 becomes $105, and the total salary becomes:
\[ \text{New Salary} = \frac{105}{100} \times 500 = 525 \, \text{dollars}. \]
On the other hand, if their salary decreases by 5%, $100 is reduced to $95, resulting in:
\[ \text{New Salary} = \frac{95}{100} \times 500 = 475 \, \text{dollars}. \]
In general:
- For an increase of \( b\% \), the new amount is: \[ \text{New Amount} = \frac{100 + b}{100} \times a. \]
- For a decrease of \( b\% \), the new amount is: \[ \text{New Amount} = \frac{100 - b}{100} \times a. \]