Percentages

At a glance 10 formulas

1. 1Percentage change$\text{change}\ \% = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$
2. 2Fraction to percent

   $\tfrac{1}{2}$

   50%

   $\tfrac{1}{3}$

   $33\tfrac{1}{3}$%

   $\tfrac{1}{4}$

   25%

   $\tfrac{1}{5}$

   20%

   $\tfrac{1}{6}$

   $16\tfrac{2}{3}$%

   $\tfrac{1}{7}$

   $14\tfrac{2}{7}$%

   $\tfrac{1}{8}$

   12.5%

   $\tfrac{3}{8}$

   37.5%

   $\tfrac{1}{9}$

   $11\tfrac{1}{9}$%

   $\tfrac{1}{11}$

   $9\tfrac{1}{11}$%

   $\tfrac{1}{12}$

   $8\tfrac{1}{3}$%

   $\tfrac{1}{16}$

   6.25%

3. 3Multiplier$x\%\ \text{up} \Rightarrow \times\left(1 + \dfrac{x}{100}\right)$$x\%\ \text{down} \Rightarrow \times\left(1 - \dfrac{x}{100}\right)$
4. 4More than, less than$x\%\ \text{more} \Rightarrow \text{less by } \dfrac{x}{100 + x} \times 100\%$$x\%\ \text{less} \Rightarrow \text{more by } \dfrac{x}{100 - x} \times 100\%$
5. 5Successive change$\text{net}\ \% = a + b + \dfrac{ab}{100}$$\text{equal rise and fall: } -\dfrac{a^2}{100}\,\%$
6. 6Three or more changes$\text{final} = \text{start} \times m_1 \times m_2 \times m_3$
7. 7Price, use and spend$m_{\text{use}} = \dfrac{m_{\text{spend}}}{m_{\text{price}}}$$\text{same spend: price up } x\% \Rightarrow \text{use down } \dfrac{x}{100 + x} \times 100\%$
8. 8Margin in points$\text{total} = \dfrac{\text{lead}}{\text{gap in points}} \times 100$
9. 9The part that stays$\text{new total} = \dfrac{\text{unchanged part}}{\text{its new share}}$
10. 10Pass both$\text{pass both} = 100 - (x + y - z)\,\%$