How to Calculate a Percentage

1.What a percentage is

A percent is a ratio written as parts per hundred. “15% of 80” means fifteen hundredths of 80. “12 is what percent of 80” asks for that same ratio in the other direction. Percent change asks how far a value moved relative to where it started, not relative to where it ended. The three setups share the part–whole idea; they do not answer the same question.

2.The formulas

What is P% of X? Multiply X by P/100. X is what percent of Y? Divide the part by the whole, then scale by 100 — Y must be nonzero. Percent change from A to B is (B − A) / A × 100; A must be nonzero, and the sign tells you increase versus decrease. A 15% rise followed by a 15% fall does not return to the start, because the second move uses a new base.

\[ \begin{aligned}\tfrac{P}{100}\times X &\quad\text{(P\% of X)} \\\tfrac{X}{Y}\times 100 &\quad\text{(X is what \% of Y)} \\\tfrac{B-A}{A}\times 100 &\quad\text{(percent change)}\end{aligned} \]

3.Worked example

The Percentage Calculator defaults to 15% of 80: (15/100)×80 = 12. The reverse check is the same pair: 12 is (12/80)×100 = 15% of 80. Percent change from 80 to 92 is (92 − 80)/80 × 100 = 15% increase. The calculator’s percent-change fields themselves default to 100 → 125 (a 25% increase); the 80 → 92 line is the write-up that keeps a 15% thread across all three setups.

\[ 0.15\times 80=12;\quad \frac{12}{80}\times 100=15\% \]

4.Part–whole playground

Switch among the three modes, then move the sliders. The bar shows part against whole (or start against end for change), and the caption substitutes the live numbers into the active identity plus the part–whole–percent triad. This is a teaching widget — no favorites, no full calculator chrome. Open the Percentage Calculator when you want all three boxes on one page.

5.Open the full calculator

The Percentage Calculator uses the same three identities, the same 15% of 80 example, and How it works plus FAQ on one page. Use it when you need to type values rather than slide them.