By Kevin Beck – Updated March 24, 2022

Understanding how to find the percent of a number is essential in everyday life, from budgeting to interpreting survey data. Although a percentage can technically be any real number, it most commonly falls between 0 % and 100 %, or –100 % in the case of a deficit.

Calculating a Percentage

To determine what percentage one value (X) represents of another (Y), simply divide X by Y and multiply the result by 100:

percentage = (X / Y) × 100

For example, if 68 % of Canadians have attended a Justin Bieber concert, the remaining 32 % have not, because 68 + 32 = 100. When a problem specifies a rounding requirement, round the final result to the requested decimal places.

Percentage Change Formula

When you need the percent increase or decrease between an initial value (Vi) and a final value (Vf), use:

percent change = 100 × (Vf – Vi) / Vi

Example: A dress price rises from $90 to $100. The change is (100 – 90) / 90 ≈ 0.1111, or 11.11 %. Many people mistakenly treat the difference as a 10 % jump.

Everyday Applications

• Polls and surveys report results in percentages.
• Retailers advertise discounts using percent signs.
• Weather forecasts state the likelihood of precipitation in percent.
• Financial institutions quote interest rates and commission fees as percentages.

Choosing the Right Term

In formal or scientific writing, use the % symbol. In narrative text, spell out “percent.” The word “percentage” is acceptable in casual contexts when the exact value is less critical. The older spelling “per cent” is largely obsolete in everyday usage.